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Condensed Matter Theory
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It is well known that non-zero negative exchange energy indicates that a singlet state of electrons is energetically more favorite than a triplet one. Sufficiently strong thermal fluctuations destroy any magnetic spin order, so singlet and triplet order becomes equiprobable in the crystal. Hence below a certain temperature (say T*) the energy gain of the singlet order may be larger than the destroying thermal energy, and then preferred singlet pairs become stable. Thus the pairing energy is the difference between two energies:
E1. Energy of the stable singlet;
E2. Energy of the state without spin ordering, where singlet/triplet are equiprobable.
Note: we consider conduction electrons, i.e. electronic wave packets are much larger than lattice constant. So the result is not related with antiferromagnetic order.
This simple logic shows the electron pairing can be derived only from the non-zero negative exchange energy. Feel free to comment or to correct the result.
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Thank you for the reference. The spin-mediated interaction between electrons takes place. However, for the superconductivity the spin interaction seems to be too weak, because the distance between electrons in a pair may be up to 100 nm, much larger than distances of spin-mediated forces.
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In this model, the number of density of available states for the charge carriers near Fermi level comes around 10^22. Will this much number come for bulk insulating ceramics. For the calculation of number of density of available states for the charge carriers near Fermi level, f0 (resonance frequency) is taken as 10^13Hz. Why? Could you please help me.
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I humbly suggest this video.. CBH fitting using Origin 2019 software is included
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In the BCS theory the pair density depends on temperature, meaning that pairs can be created/annihilated by temperature variations. On the other hand, in some experiments the supercurrent, once excited, runs for many months, indicating that any pair recombination doesn’t take place (pair recombination would dissipate the initial momentum of pairs). Can we solve the contradiction?
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Ultrasound attenuation is very sensitive & dependent on direction, you are right, please see for a response studied by me:
Best Regards.
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Superconducting electron pairs occur on the Fermi surface, where the electron kinetic energy is a few eV. The binding energy of paired electrons is usually a few 10-3 eV, so the electrons seemingly cannot remain paired. However, pairs are stable until thermal fluctuations destroy them. Is the situation paradoxical?
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To your first remark, the answer for the single pair case I discussed is: in principle yes, in practice no. The likelihood of a pair breaking by a collision with an electron of the Fermi sea is limited by the probability of finding a final state at energy (E_F - e), where e is the pair binding energy, for the electron. At temperature T, we know from the properties of the Fermi-Dirac distribution, that there will be empty states in an interval of width 2 kT below E_F, where k is the Boltzmann constant. If the temperature is too low, the probability of finding an empty state at (E_F - e) will be negligibly small. Only when kT gets of the order of e will the pair breaking process take place. Note that this is a very qualitative discussion. In the true BCS ground state, the correlation between millions of pairs leads to an energy gap, and the pair breaking becomes even more difficult.
To your second remark, the answer is given by a calculation of the spatial extension of a Cooper pair, which yields a value of the order of 10^4 Angstroms. So, instead of speaking of a bound state in the traditional sense we are here in the presence of long range correlations, involving the overlap of millions of pairs, as discussed above, which explains the sharpness of the superconducting transition.
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Most conventional theories of superconductivity (SC) use the second quantization notation (SQN) where all electrons are assumed indistinguishable, every electron can take every state in the momentum space. However, a sample shows that SQN is insensitive for supercurrent description.
For clarity we consider only 4 electrons (which may belong to arbitrary many-body system): a non-dissipative singlet pair (e1,e2) and two normal (dissipative) electrons e3, e4 . We investigate two cases, A and B:
A. The non-dissipative pair (e1,e2) is permanent. Then an initial non-zero momentum Px of the pair is also permanent. Obviously, this permanent Px is a supercurrent;
B. The non-dissipative pair (e1,e2) is not permanent, i.e. a recombination is possible: e1, e2 become normal, e3, e4 become non-dissipative and back. But at every time moment there are one non-dissipative pair and two normal electrons:
(e1,e2)singlet + e3 + e4 <=> e1 + e2 + (e3,e4)singlet
In case B the initial non-zero momentum of the pair (e1,e2) dissipates, because the electrons e1,e2 become periodically dissipative and there is no external force to give to the newly created pair (e3,e4) exactly the same momentum Px, which the pair (e1,e2) had. So the momentum Px of the system dissipates and the current vanishes. Thus non-permanent pairs cannot keep a supercurrent (otherwise the momentum conservation law is violated; the atom lattice took the momentum Px of the broken pair e1,e2, hence Px of the new pair (e3,e4) must be zero). Notable is the fact that both cases A and B are identical in SQN due to equal occupation numbers (in both cases there are exactly two normal and two SC electrons). However, the case A is superconducting and the case B is dissipative. The cause of the paradox is the indistinguishability of electrons.
Thus the SQN principle of indistinguishability of particles is insensitive to the supercurrent description, we should consider the normal and SC-electrons as distinguishable, i.e. non-exchangeable in the momentum space particles.
So far nobody could plausibly reconcile this paradox and conventional theories of SC.
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Yes, a qualitatively correct description is a precursor for an accurate approach. For the above considered problem a brief description is : in superconductors there are two electronic components (SC electrons, normal electrons), distinguishable in the momentum space. That is every electron belongs to its component as long as the SC state persists, any interchange between components is impossible. Mathematically this mean we should introduce two Fock spaces or two sets of quantum states, which don’t overlap (i.e. there are not common states).
One important consequence: all derivations of conventional theories should be revised within the two-space-approach.
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A newest Nature paper E. T. Mannila et al, "A superconductor free of quasiparticles for seconds" https://www.nature.com/articles/s41567-021-01433-7 shows that superconducting (SC) pairs persist at least for seconds. The measurement device detects single pair-breaking-events for a large pair population, so the average life time of each pair is much longer than a few seconds (probably, many hours). Thus, every pair hosts its electrons a long time. In most SC-experiments worldwide, the measurement time is much shorter than the life time of the long-hosting SC-states, therefore we can assert that the SC-electrons and normal electrons are non-exchangeable during the measurement, i.e. the SC-electrons do not hop into normal states (at least during the resistance measurement). If so, then the SC-electrons and normal electrons are distinguishable and the superconductor has two distinguishable electronic components: (i) SC-electrons; (ii) normal electrons.
Each of the distinguishable components has its own set of quantum states, its own one-particle-wavefunction, its own Fock space, although the components are overlapped in the real space.
Mainstream theories of superconductivity (BCS etc.) operate within one electronic component and don't take into account this distinguishable 2-component-nature. Should the theories be updated according to the newest finding ?
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A simple answer, electrons at the Fermi level are given by the equation pF = ℏ kF if they are around the Fermi surface then there is a linear approximation to that equation: δp = ℏ ( k - kF ), i.e., which is consistent for most normal metals and serves well for the Fermi-Dirac distribution, the Sommerfeld expansion, the Fermi liquid theory and the concept of quasiparticles.
In addition, electrons are fermions which means they can only occupy one state with one value for spin +/- 1/2, therefore a Fermi Dirac distribution in momentum space implicitly shows that electrons are separate in momentum space if they are treated using QM and for 3 approximations, the free, the quasi-free, and the tight-binding ones.
Best Regards.
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I read some paper about this subject [ Yen-Chun Peng Optical Material 39 2015; Luis A. Agapito PHYSICAL REVIEW X 5, 011006 (2015) ... ] then they show how to do and some values. 
The valence configurations of the atoms were 4s2 3d10 for Zn, 2s2 2p4 for O.
The energy cutoff : 380eV
The change in energy: d-5 eV/atom
maximum force: 0.03 eV/anstrong
maximum stress: 0.05 GPa
maximum displacement tolerances: 0.001 anstrong
The energy convergence criterion: d-6 eV
The Ud value for Zn-3d : 10 eV
The Up value for O-2p orbital: 7 eV
This is my scf file. If someone know where I was wrong please correct me!!!
Many thanks !!!
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forces may not work with DFT+U, and since you are using forc_conv_thr = 1.0d-4, it might be a problem.
except for that, you can try pbesol for obtaining better values.
regards
M Chaitanya Varma
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I am doing a PhD in AdS/CMT. In order to have a better understating of the physics of the systems the correspondence aims to describe, I am looking for accessible reviews or online seminars about the mostly commonly used experimental techniques for probing strongly coupled materials such as the cuprates in their strange metal phase.
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Please, have a look the following lecture: http://qpt.physics.harvard.edu/talks/upenn.pdf
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when a 2DEG is subjected to the magnetic field, the energy is split in the form of Landau levels. and the QHE is explained on that basis. however, in the case of quantized resistance is obtained without a magnetic field. then how Landau levels are formed in QSHE?
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Dear Shlu,
As shown in 4he attached figure , the charge current flows from left to right through a conductor Hall bar. If the charge current is non-polarized (with equal numbers of spin-up and spin-down electrons), the spin imbalance does not induce a charge imbalance or transverse voltage at the Hall cross. If electrons, which are polarized in the direction of magnetization M, are injected from a ferromagnetic electrode while a circuit drives a charge current (I) to the left, a spin imbalance is created. This produces a spin current (IS) without a charge current to the right of the electrode. Spin–orbit interactions again separate spin-up and spin-down electrons, but now the excess of one spin type leads to a transverse charge imbalance and creates a spin Hall voltage, VSH. As the distance, L, between the electrode and the Hall cross increases, the voltage signal decreases, allowing the decay length of spin currents (spin diffusion length lsf) to be measured. More details about SQHE will be presented in Chapter 9 of my Book, about spin transport in nanostructures.
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In non-local measurements, we apply current between two leads and measure voltage on different leads away from the current leads. to calculate resistance, do we need to divide the non-local voltage by current - as such current is not flowing through the voltage leads?
can you please suggest good literature on non-local measurements?
Thanks
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Dear Shalu Pathak, in addition to all the interesting answers,
To understand the role of nonlocality between the current ja(z) and the electrical field applied Eb(z´) to a normal metal, i.e.,
ja(z) = (integral from 0 to infinite) K(z,z')ab Eb(z´)
where the radius of the kernel K(z,z')ab ~ l (the mean free path) please review section 3 of the classical work:
Best Regards.
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I have several confusions about the Hall and quantum Hall effect:
1. does Hall/QHE depend on the length and width of the sample?
2. Why integer quantum Hall effect is called one electron phenomenon? there are many electrons occupying in single landau level then why a single electron?
3. Can SDH oscillation be seen in 3D materials?
4. suppose if there is one edge channel and the corresponding resistance is h/e^2 then why different values such as h/3e^2, h/4e^2, h/5e^2 are measured across contacts? how contact leads change the exact quantization value and how it can be calculated depending on a number of leads?
5. how can we differentiate that observed edge conductance does not have any bulk contribution?
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You distinguish a normal classical Hall efect from a Quantum Hall effect.
Normal size devices exhibit the first, contain considerable number of electrons.
The magetic field acting on the current pushes electrons to one side of the device
and is counteracted by the Hall voltage set up from charge accumulation. Proportionality between magnetic field and Hall voltage for steady current.
Quantum devices contain fewer electrons in narrow or small devices (Nanostructures) . The magnetic field provokes the equivalent of Landau levels that contain the states for electrons. These pass at regular intervals as the magnetic field increases. Thus there are regular jumps
in the electron conductance as magnetic induction increases.(In single electron conductance, or normal quantum hall effect
The fractional quantum Hall effect is believed to be the consequence of electron interactions and quasi particle formation. This is an extremly complicated phenomena, and not nearly as well understood as many would have you believe.
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What are the quantum materials? Quantum phenomenon takes place in every material at atomic level. then how to define quantum materials? is Iron (magnetic materials) quantum material as it shows magnetism which is the quantum phenomenon? if not then what are quantum materials?
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Quantum materials are I believe are those materials that exhibit wave behavior, or equivalently particle-wave duality.
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The Nilsson diagram is obtained by solving the Schrodinger equation. If the deformation parameters are continuous, I wonder the orbits should be continuous as well. If the Pauli exclusion principle is the reason, the nilsson quantum number are not always equal, such as 5/2[402] and 5/2[642], why?
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ear
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Dear and Distinguished Fellows from the solid-state physics RG community.
Does have anyone read after 20 years the preprint from Prof. Laughlin A Critique of two metals?
I read it when I was a PhD student. I think his opinion after 20 years deserves more attention. Please, feel free to follow down the link to the arXiv preprint if somebody has an interest and please leave your opinion:
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Dear RG community, this review thread is about the role of RKKY interaction in solid-state physics. I want to learn more about it. I would like to know for example, what physics effects RKKY describe well.
The RKKY exchange interaction (Ruderman - Kittel - Kasuya - Yosida) is defined as an indirect exchange interaction between magnetic ions, carried out through itinerant conduction electrons.
In rare-earth metals, whose magnetic electrons in the 4f shell are shielded by the 5s and 5p electrons, the direct exchange is rather weak and insignificant and indirect exchange via the conduction/itinerant electrons gives rise to magnetic order in these materials.
Some initial clarifications:
  1. For this thread, the are two types of electrons: itinerant or conduction electrons and localized electrons.
  2. Indirect exchange is the coupling between the localized magnetic moments of magnetic metals via the conduction electrons, while direct exchange occurs between moments, which are close enough to have sufficient overlap of their wavefunctions.
RKKY interaction takes place in metals and semiconductors, where itinerant electrons mediate the exchange interaction of ions with localized oppositely directed spins, partially filled d and f shells.
The physical mechanism is the following: Conduction/itinerant electrons interact with the effective magnetic field of the i-th site of the crystal lattice and acquire a kind of spin polarization. When passing through the next lattice site, relaxation of the magnetic moments of the electron and the site will cause mutual changes in both the spin polarization and the spin of the lattice site.
Hereby, RKKY can be described using the concept that conduction electrons move in an effective field created by a localized magnetic moment of one site.
[1] M.A. Ruderman and C. Kittel, Phys. Rev. 96, 99 (1954).
[2] T. Kasuya, Prog. Theor. Phys. 16, 45 (1956).
[3] K. Yosida, Phys. Rev. 106, 893 (1957).
[4] D. I. Golosov and M. I. Kaganov, J. Phys.: Condens. Matter 5, 1481-1492 (1993).
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The following paper is worth mentioning in this thread:
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Hello, I'm trying to understand the calculation of Green functions in dirty metals. Typically, in such calculations the contributions of Feynman diagrams with intersecting impurity lines are neglected. An explanation of this can be found in the textbook of Abrikosov, Gor'kov and Dzyanoshinsky, but I don't quite understand it. It is said in the book that when integrating over momenta, the region far from the Fermi surface simply renormalizes the chemical potential. This is clear for a diagram with two crosses, however, not obvious at all for more complicated diagrams. Is there a renormalization trick involved? Could you offer an explanation, or direct me to another source with a more detailed discussion of the matter?
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Dr. A. A. Bespalov in addition to all the interesting & concerning answers to this thread, you could check the original paper by Prof. S. Edwards on non-magnetic impurity scattering in normal metals.
The physics of the approximation was set up in his classical paper: S. F. Edwards (1961) The electronic structure of disordered systems, Philosophical Magazine, 6:65, 617-638.
It gives insights to understand what means an undressed/dressed Green function
and further applications as those in the AGD book.
Best Regards.
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I am a graduate student majoring in the condensed matter theory.
Nowaday I want to study the gauge theory on my own, but it is very hard to understand the idea.
So I am finding the open coursewares for gauge theory but I cannot find one.
Would you help me?
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i work on condense mater ,many work in my page
i hope to help you
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What could be the reason for a charge up in a device. I noticed that when I measure the temperature dependence of resistance, at the lowest temperature there is i very sharp increase in resistance. this increase depends upon waiting time at the lowest temperature. Why device charge up with time. if I restart measurements again, it starts from the initial value.
please someone experienced this?
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As a preliminary question:
1. which sort of material is your device made of? (metal, semiconductor, organic, other?),
2. what is the topology of the conducing layer (3D, 2D, 1D, powder-like, etc...)?
3. and what is the size of the active layer (cm or mm or µm or less)?
As a matter of fact, in a material with a low number of electrons, even a moderate number of electronic traps can capture electrons and greatly affect the conductivity. This is however unlikely in a metallic device.
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For the simulation purpose, I need force-field for Mn3O4. I searched and tried a lot but almost unable to get appropriate force-field parameters for it. Can anyone help me by suggesting or availing it ?
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You can try with Swissparam to generate required force-fields parameters.
Please follow the link:
Upload your structure in .mol2 format. You can use Avogadro or Jmol to prepare the structure in .mol2 format. Once prepared, run the .mol2 structure and wait for few minutes to get output file from Swiss param based software and then do the required changes for the force-field parameters.
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Generally, when we calculate the carrier density in 2DEG from SdH oscillations (Field dependence of sheet resistance) and QHE (field dependence of Hall resistance) it should match. In some cases it was found that carrier density calculated using both data differ. What is the reason behind this difference? What is the physics behind the calculation of carrier density from SdH oscillations and Hall resistance data?
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It is because SdH oscillation can only occur for those carriers with sufficiently high mobility, whereas in a Hall measurement all carriers are taken into account. So, in cases where transport happens through multi carriers with both high and low mobilities, you may notice such a difference in the value of carrier density obtained from these two measurements.
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The second quantization notation operates with occupation numbers. For electrons within a quantum system the occupation number of each state is 1 or 0. However, local states in crystals do not necessarily overlap in the real space, and, thus, in one crystal can exist manifold identical local states. Does it mean that the occupation number is also larger than 1 ? How we can use the second quantisation in this case ?
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Thank you, Prof. Stanislav Dolgopolov, yes in BCS superconductors, they both are the same, Tc and TBEC, somehow if I remember my course in superconductivity (we used D Gennes and LifPit IX Vol books) the resistivity is zero, so we do have 2e charged particles (a supercurrent), and somehow this is important. Superconductivity is a different phenomenon from BEC. Their ground states are totally different.
You see, these classical books did separate well the two phenomena (also Abrikosov book on metals). Something that I guess, became forgotten with High-Tc compounds. And I guess it has been due to the persistence to fit with one theory, the phase diagram of High Tc.
Thank you for the nice discussion.
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The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state. Entering the superconducting state, electric currents are set up near its surface and this cancels the applied magnetic field within the superconductor. So, it seems that electron movements become possible which were not before possible and this is demonstrated by the Meissner effect. Does this amount to emergent degrees of freedom relevant to the 2nd law of thermodynamics?
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The question is right, although is not usual, Prof H.G. Callaway.
Lest consider BCS superconductors:
  • The vortex motion is henceforth a new degree of freedom in BSC superconductors.
  • The number of charge particles N = 2 |ψ|2 also is.
  • The phase of the Cooper pair φ.
Why? because they are bound by commutation relations, the same way that r and p operators are bound in quantum mechanics.
Please see:
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Hello Everyone,
Recently I am doing some Phonon branchesbased studies. For some materials the gap between the optical and acoustic branch is small, for some it's large and for some there is no gap.
So how this gap affects the material property or what is its physical significance?
Thanks,
Abhinav Nag
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In addition to the very interesting answers provided before, Prof. Abhinav Nag, I would like to point out that in the optical phonon brach occur an interesting macroscopic relationship for some insulators (ionic crystals), the Lyddane–Sachs–Teller relation (LST) which determines the ratio of the natural frequency of longitudinal optic lattice phonons of an ionic crystal to the natural frequency of the transverse optical lattice vibrations for long wavelengths (or zero) wavevectors.
The ratio is that of the static permittivity to the permittivity for frequencies in the visible range
Wikipedia commons source:
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Science does not stand still. New opportunities for research keep appearing and, as a result, new findings and discoveries happen hand to hand with artifact discoveries. These discovery some time with considerable controversy in the literature, sometimes at unusually impoliteand unprofessional levels. Some time artifact discoveries also surprised the world of science.
1) Different groups presents different results on same material and trying to prove each other results as wrong. Is it not sicietificy sound if these groups exchange specimens before they claim the work of others is simply wrong?
2) In some cases materials have been considered to be with ground breaking discovery when the data can be interpreted more simply via other well-known mechanisms. Is it not import to look wider before claims a breakthrough discovery?
3) In some cases the experimental results are true, despite theory implying that this is not possible. Is it appropriate to reject a experimental output just because theory doesn't exits which can explain it?
4) Controversy and attention on a new anomalous phenomenon such as Room Temperature Superconductivity.
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You are right Dear Prof. Aga Shahee. Anyway, thank you so much.
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In standard text books about Superconductivity like "Buckel" one learns that two fermionic electrons (each spin s=1/2) couple and form a boson with total spin of S=0, which is a singlet state (the spins are anti-parallel).
Is there anything preventing them from forming a triplet state S=1 (the spins are parallel)?
Is it related to symmetry considerations?
What would be the consequences of a S=1 state?
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In addition to all interesting answers in this thread Prof. Magnus Schlösser .
I will add 2 classical references for triplet superconductivity, also called unconventional superconductivity:
  • L. Gorkov: Superconductivity in heavy fermion systems. Sov. Phys. Rev. A Phys 9, pp. 1-116, 1987.
  • M. Sigrist & K. Ueda: Phenomenological theory of unconventional superconductivity. Rev. Mod. Phys. 63, pp. 239, 1991.
Some heavy fermions crystals & A-phase of 3He isotope are triplet paired. Also the strontium ruthenate crystal as already was mentioned in a previous post.
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I am currently reading some papers in the field of high Tc superconductivity. Some concepts confuse me. Can you tell me the definitions of spin wave, spin density wave, spin excitation, spin fluctuation, spin gap, charge density wave and charge order? What are the differences and correlations between these concepts? And, what their relationships with high Tc superconductivity?
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Dear Prof. Qingyong Ren
In addition to all interesting answers in this thread & for a deeply understanding of the phenomenology & the theory of spin waves & magnons---using the equation of motion of the magnetic moment & from where the concepts you mentioned (spin wave, spin density wave, spin excitation, spin fluctuation & spin gap ) were borrowed, you can studied from these books:
[1] The Nature of Magnetism by M.I. Kaganov & V. M. Tsukernik, Science for everyone, Mir-Moscow, 1995.
[2] Eletrodynamics of continuous media, L. Landau & E. Lifshitz, ch V-#48 pp 167, eq 48.2, Pergamon 1984. They use the phi thermodynamic potential free energy.
[3] Statistical Physics Vol 2 by E. Lifshitz & E. Pitaevskii ch VII Magnetism, Pergamon 1980.
[4] Spin Waves by A. I. Akhiezer, V. G. Bar'yakhtar, and S. V. Peletminskii. North-Holland & Interscience (Wiley) 1968.
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Is the Sound Velocity Anomaly a fingerprint of charge order transition temperature or it is a finger print of a temperature where lattice degrees of freedom show divergence? (Which may be due to different reasons.)
I have come across few research articles, where sound velocity anomaly has been take as a fingerprint of charge order phase transition temperature. I believe sound velocity should changes across any phase transition and thus sound velocity anomaly is just an indication of occurrence of either structural or magnetic or electronic phase transition. Correct me if I'm wrong
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Dear Prof. Aga Shahee
Your question is interesting & quite relevant, henceforth I will try to answer partially your question in a couple of posts in your thread:
A sound velocity anomaly can be directly calculated by means of Ehrenfest relations for 2nd order phase transitions-PT. For instance a jump in sound velocity can be calculated at the superconducting transition temperature Tc. This is an anomaly that have been observed in some materials. See [1] for example to have a better idea, but I can refer to some specific literature if you wish.
This is part of the question, but what I cannot do now is to relate the jump to an structural phase transition which I guess is a 1st order PT [2] quoting & is associated with a dynamical instability by the soft mode. According to some authors [3] a physical explanation will be "...the soft mode happens when cooling a material from a temperature above Tc, a normal mode of vibration of the crystal decreases to 0 freq when the crystal becomes unstable & distorts to a new structure..."
Finally, respect to lattice degrees of freedom showing divergence, I guess this is what happens to 1D systems (according to Peierls & Landau [4]), isn´t it?
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By quasi-particle I mean in the sense of particles dressed with their interactions/correlations? If yes, any references would be helpful. 
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Dear Prof. Sandipan Dutta , in adittion to all interesting answers of this compelling thread, I will add a link to a book, where the concept of quasiparticles is masterfully explained by to of the creators of the quasiparticle approach:
Quasiparticles by Prof. M. I. Kaganov, and Academician I. M. Lifzhits.
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I wish to do DFT calculations and use the frozen phonon approach via Phonopy. Should I pay attention to the magnetic moments?
Sometimes, individual atoms in a crystal have different magnetic moments. Does this have any additional effect?
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Dear Hitanshu Sachania and Franklin Uriel Parás Hernández You might take a look at the following preprint. It adresses the question of this thread. Regards.
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For the transition from insulator to metal, there have different transition mechanisms.
How to distinguish Anderson transition (Anderson insulator was induced by the disorder-induced localization of electrons) from Mott transition (Mott insulator was induced by the Coulomb repulsion between electrons. This transition can be controlled by the mechanisms of  oxygen vacancy controlled electron filling), especially in 2 or 3-dimensions materials.
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Hello,
Anderson transition is a one body problem in which localization results from quantum interferences effects. The metal to insulator transition can occur at any fiilling (carrier density) , only the strength of the disorder controls the position of the mobility edge that separates extended from localized states.
The Anderson transition does not open a gap in the one particle spectrum.
However, the Mott transition is a many body feature, that occurs at specific band filling and controlled by the strength of the coulomb electron-electron interaction. At the metal to insulator transition, in contrast to Anderson transition a finite gap opens in the charge spectrum.
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Generally we say that the density of states (DOS) at Fermi level contribute to many phenomenon. However in the Dirac cone DOS is zero at Fermi level. What does it mean and what are its consequences? Why it is important in topological insulators to have Dirac point at the Fermi level. is it not good if Dirac point is in the gap of bulk band structure instead of Fermi level?
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this is due to the erroneous proof of fermi energy level by Dirac, with correct mathematics on the chemical potential fermi level is no more a straight line instead it is a oblique line connecting VB to CB. and this line is the line of transition, so any point chosen on this have meaning...later more on this.
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I have read Fukui's paper( attached below) and I want to use his method to calculate Chern number on honeycomb lattice. How can I discrete the Brilliouin Zone to fit it's square discretion ?
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I know that wave-packet is the super-imposed form of the waves. It is created when some waves have interference and a particle (say electron) can be represented by a wave-packet. I am bit confused actually a single wave is associate with a particle then why in case of wave-packet we associate more then one wave with a particle?
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The concept of wave packet has undergone many, more or less subtle, variations during the last 100 years. Sure, interference is important, but it is not all. The common motive is that when a system admits a continuous band of wave solutions (classical or quantum, it does not really matter), its dynamics can exhibit localized-interference features that behave differently from the individual waves. They appear as persistent "objects" with strikingly different properties than those of the waves that compose them (for example, their apparent collective - or "group" - velocities can be quite different). Examples are vortices, maelstroems and tsunamis in hydrodynamics and, why not, particles and "resonances" in subatomic physics. The concept is nice, interesting, and probably contains a lot of truth, though it need not be strictly applicable to all the situations where it was tried. In any case, any kind of wave equation (be it Schroedinger or other) leads to this kind of discussions.
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I know that when we plot band structure i.e E vs. k, the shape is parabolic. But when we plot band structure for E vs k, where k is different points (gamma, M, K or K') of Brillouin zone edge points, why it is not parabolic and have other interfering bands?
Please see the attached images (from Google).
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Usually, k = -pi/a -> pi/a refers to a one dimensional system and the parabolic dispersion is characteristic of free fermions E = p^2/2m , that is, no interaction is considered.
When you go to higher dimensions, say 2d, you should describe your energy as a surface instead of a curve as it will depend on kx and ky , E(kx,ky). To avoid ploting a complex surface in the case when you have interaction and the surface is not parabolic, you just calculate a path of some values in your domain passing by some high symmetry points, in which we can by this especial names, Gamma, X, M , etc.
Usually Gamma represents the center of your Brillouin Zone. For exemple, Gamma = (kx=0, ky=0) in 2d, and Gamma = (kx= 0, ky=0, kz=0) in 3D.
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Graphene Electronics Vs Silicon Electronics !!
Silicon has a band gap of 1.1 eV but graphene is zero band gap semi metal. Therefore graphene has a very less scope in achieving the goal. Further, Doped graphene layer can have certain band gap which can be used in electronic applications similar enough to those using Silicon.
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No.
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stacking one layer on another monolayer of graphene in a 'magic angle' changes the properties of the bilayer significantly. Which phenomenon will be responsible for the superconductivity. I already encountered lesser conductivity of ordinary bilayer as compared to that of a monolayer graphene.
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I must say, it is a good question. In general Graphite consists of graphene layers with ABAB..... stacking or Bernal stacking. If you go from top to bottom approach for example mechanical exfoliation of graphite, bernal stacked FLG (few layer Graphene) can be obtained. On the other hand, if you want to deposite a single layer on top of the other in order to get FLG again, then it is hard to get ABAB.. stacking rather it may yield twisted graphene layers with some angle. This process can lead to generate van hove singularities in the crystal lattice which then tend to show new and exciting phases of matter under consideration.
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Sometimes researchers getting new results out from the similar experiments done by other researchers. But, if they propose some new phenomena against the existing one, the scientific community is not easily accepting. So far I observed, people, trusting, following and try to prove the scientific phenomena (physics) proposed by well-known persons in scientific society. If those results not accepted by any high impact journal community, still, it get accepted by a low impact journal community which infer proposed phenomena were not studied properly.
Would you mind to tell what is real science then? What's exact factor decides the quality of scientific phenomena?
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The impact factor of a journal is not always related to the quality of the research published on it. IF is just a librarian's number to assess the number of citations of the journal against their number of papers. Good science and papers will always be found, even in low IF journals (probably up to some threshold level). IF is not a measure of the quality of the paper.
"Real science" as you name it, should always be reproducible, and possible to explain through the simplest explanation (Occam's razor).
Scientific community should never be "easily accepting", that is the main idea of peer review, letters and comments on paper. Scientific community should be all the opposite of easily accepting; and good science should pass the test of the peer review of scientific community.
If I submit a paper, I want it tested under the highest degree of scrutiny. If the paper and its explanations are correct, it must pass all the tests from the scientific community.
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Please help me to clarify doubts on it
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Is there any better technique relative to one reported by Kwon and co-workers, The interfacial segregation growth technique using Graphite powder coating on a poly-crystalline Ni layer (deposited on the glass substrate) yields High crystalline quality of single- layer graphene synthesized at low temperatures? Since in this case, the problem lies in the deposition of Ni on the glass and then it's removal after the growth.
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I know this fact actually, since transferring monolayer graphene on to a substrate is prone to degarde the quality of graphene imposing contamination or defects on it. So it was seen that when graphite powder is coated on Ni substate (has high carbon solubility) deposited on glass, graphene layer forms by interfacial segregation. Afterwards Ni is etched away, thus one gets graphene without any transferring. Hence this method is better than the conventioned CVD growth of Graphene on Ni/Cu.
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electron and hole effective mass
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The same question has been asked already and was answered very well by Filip Tuomisto. I'll simply copy and paste his answer so all credits to him. (A simple google research would have given you the answer very quickly without having to wait for an answer here btw)
"The concept of effective mass follows from physicists' love for simple relations such as Ohm's law (current density = conductivity x electric field intensity) or Newton's second law of motion (acceleration = force / mass). For a free electron, the mass in the latter is just the electron mass. But, if one wants to write a similar relation for a charge carrier in a crystal lattice, the situation changes. Going through the math (see any solid state physics textbook) allows you to write F = m x a, where the force is charge x electric field, but the mass is no longer the mass of the electron, but reflects the curvature of the conduction band bottom (for electrons) or valence band top (for holes), as it is inversely proportional to the second derivative of the energy as a function of k. This is the so-called effective mass. Again, physicists like simple things, so one often expresses the effective mass as a constant x electron mass, although this has very little (or nothing) to do with the actual physics of the situation. Hence: it is just a practical mathematical construction aimed at simplifying equations (in a similar manner as the reciprocal lattice, for example). The hole itself is also a mathematical construction helping us to avoid using negative values for mass in the simple equations (the effective mass for conduction occurring through the unoccupied electron states in the valence band would be negative, if we didn't invert the charge).
In the majority of cases, the top of the valence band is clearly "flatter" than the bottom of the conduction band. From this follows that the hole effective mass is often larger than the electron effective mass. The top of the valence band tends to be flatter due to the asymmetry of the situation: you are talking about the highest occupied states for electrons. The bottom of the conduction band is formed by the lowest unoccupied states."
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can someone please explain me in simple physics that why spin-orbit coupling is relativistic?
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A short summary: there is no derivation of spin-orbit coupling (or even the spin) in "classical" quantum mechanics by the principle of correspondence. You can of course conclude the phenomenon from experiments.
However, an "ab initio" derivation of the phenomenon is possible if you reduce the relativistic Dirac equation to the matter terms (neglecting anti-matter components). The resulting equation is often referred to as the "Pauli equation" (https://en.wikipedia.org/wiki/Pauli_equation#Relationship_with_the_Schr%C3%B6dinger_equation_and_the_Dirac_equation)and contains spin-orbit coupling (and other corrections like the "Darwin term").
So, since the origin of that term is the relativistic equation, it's called a rekativistic term.
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Von- Hove singularities are said to be non-smooth points corresponding to M-points in first B.Z. What do they actually signify?
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In two dimensions, a saddle point in the electronic band structure leads to divergence in the density of states, also known as a Van Hove-singularity (VHS). When the Fermi energy is close to the VHS, interactions, however weak, are magnified by the enhanced density of states (DOS), resulting in instabilities. In twisted graphene layers, both the position of fermi energy and that of the VHSs can be controlled by gating and rotation respectively, providing a powerful toolkit for manipulating electronic phases.
However, although the band structure of graphene contains a VHS, its large distance from the Dirac point makes it prohibitively difficult to reach by either gating or chemical doping. By introducing a rotation between stacked graphene layers, it is possible to induce VHSs that are within the range of fermi energy EF achievable by gate tuning.
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Degeneracy of electrons in graphene is 4. 2 for isospin and 2 for real spin. How do we get the degeneracy here?
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Dear Mukesh,
It is true that you are right that you have four degeneracies of the graphene system assuming the four symmetries of the lattice (not of the electrons)
- Translations in each Bravais sublattice A to A and B to B.
- Mirror reflection between A and B
- A rotation symmetry of sixty degrees ( C pi/3)
But that is independent of what I have been speaking about the isospin and spin or the electronic degeneration. This is only due to the lattice symmetries. Is this what you were thinking about?
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Generally band E-k band diagram of a material look like parabolic type. However this is not the case in the TIs. Why bands in TIs are like this (Fig. shown)? Is it due to spin-orbit splitting however generally this type of splitting is seen on the energy axis and not on the k-axis.
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Thank you
Behnam Farid
for your nice explanation and Bahadır Ozan Aktaş for the suggestions!
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Hello everyone,
I have written a small code that performs linear Spin Wave for simple antiferromagnetic Heisenberg Hamiltonian. It takes spin Hamiltonian as an input and performs Holstein-Primakoff, Fourier transformations as well as linearization.
Now, I would like to extend it for the further neighbors. Now, let's say, I have a site A and a cite B, and now I add A2 and B2 sites to my model system, so that I can add, let's say, J_2*\vec{S_A}*\vec{S_A2} Heisenberg term to my initial model. Do I have to add J_1*\vec{S_A2}*\vec{S_B2} aswell? And what about the boundary conditions then?.. Also, if I add a third neighbor, I am working with a decently sized cluster already...
Also, in my case, I expect system to stay bipartite, i.e. have two magnetic sublattices. But what if I don't know what the magnetic order would be?
Thank you!
Ekaterina
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Dear Ekaterina Pärschke,
First about your last question. In the linear spin-wave approximation you are supposed to know the magnetic order (the ground state or a meta-stable state). That is because this approach consider small precession of the spins around their equilibrium orientation. If you have a set of interactions, only nearest neighbors (n.n.), or second nearest neighbors, or even other complex interactions such as the Dzyaloshinskii-Moriya, and you don't know the magnetic order, it needs to be determined first, normally with a spin dynamics algorithm (I use the https://github.com/spirit-code/spirit developed in my institute in Forschungszentrum Jülich, Germany).
Now that you have your magnetic order, you can calculate the spin-wave spectrum with as many neighbors as you want.
On calculating the spin-wave spectrum, we normally perform a Fourier transformation of the hamiltonian (more precisely of the dynamical matrix). This Fourier transformation can be done exactly and efficiently if the interactions are of short range, such as in a nearest-neighbors-only model, where we only have to sum the contribution from the site on the left, the one of the right, and a local contribution if any (this in one dimension), it could look like: H(k) = sum_j J_0j exp (i R_j k) = J exp( -a k ) + J_0 + J exp( a k ). Considering the second nearest neighbors is not much of a problem, we would have: H(k) = J_2 exp( -2 a k ) + J_1 exp( - a k ) + J_0 + J_1 exp( a k ) + J_2 exp( 2 a k ). (sorry my lack of rigor here, I just want to give you a feeling.)
So, if you have a single atom in the unit cell, you are going to get a single spin-wave mode. For two atoms, you have the right to two modes, and so on. Please notice that this has nothing to do with the number of neighbors you considering for your interactions.
I have faced these problems you are working on myself. This paper of mine might help for I give a lot of detail on the appendices:
Let me know if I can further help.
Best regards,
Flaviano dos Santos
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I am calculating the size of the CdS quantum dot by using Brus equation from the TAUC Plot. so, in that brus equation contains reduced mass of electron and hole as shown in uploaded figure. where can I found these values?
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here
Citation: J. Chem. Phys. 80, 4403 (1984); doi: 10.1063/1.447218
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We all know one of the most widely studied phenomena in condensed-matter physics is Kondo effect.
Very briefly the milestones are as follows: This field began in 1933 when Wander Johannes de Haas and co-authors reported an unexpected rise in the resistivity of some gold samples at low temperature [1]. First, Phil Anderson formulated a microscopic model of how local moments form in metals with magnetic impurities. Anderson showed that Coulomb interactions are the reason the magnetic impurity behaves like a local moment [2]. Jun Kondo calculated the scattering rate of conduction electrons from local moments to second order and was able to reproduce the low temperature upturn and the depth of the resistivity minimum [3]. In Kondo's solution the calculated logarithmic divergence cannot physically persist to zero temperature. The zero-temperature limit remained unsolved. The calculated logarithmic divergence cannot physically persist to zero temperature. Renormalization group was required to solve this so-called Kondo problem [4]. It has been the subject of numerous reviews since the 1970s. Up to date, various approximate solutions have been introduced.
While Kondo's calculations were able to reproduce the resistivity upturn, There is a dramatic decrease in resistance in the superconductivity phase. What is the relationship between Kondo effect and superconductivity? Does anybody know about the latest work on this issue? Particulary, Is there anyone who is aware of a study about the solution of Kondo problem with DMFT (Dynamical Mean-Field Theory)?
[1] W.J. de Haas, J. de Boer, and G.J. van den Berg, Physica 1, 1115 (1933)
[2] P. W. Anderson, Phys. Rev. 124 41 (1961)
[3] J. Kondo, Prog. Theo. Phys. 32 37 (1964)
[4] K. Wilson, Rev. Mod. Phys. 47 773 (1975)
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Dear Bahadir,
The Kondo effect describes one state of a magnetic impurity and the electric conductivity. The physical model which explains this effect is pseudogap Anderson's model employed for heavy fermions too and quantum critical transition phases. Broadly speaking, the main feature is that below 10K the resistivity increase instead to decrease as in usual metals happens.
Curiously, the dynamics of the magnetic moments induced in d-wave superconductor ,as the cuprates are doped with non-magnetic impurities, can be described as a psedogap Kondo model.
A very good review where Kondo effect and d-superconductivity appears well related is
Rev. Mod. Phys. 79, 1015 (2007)
arXiv:cond-mat/0606317v3
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I know that spin-orbit interaction is between spin and electrons' motion in the orbit. why these two interact? why spin-orbit is always relativistic?
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Since the rotation speed of the electron v around the nucleus is relativistic, the nucleus creates a magnetic field of the form B = vXE / c2 where E is the electric field viewed by the electron, which is central E = | E / r | r and v = p / m. In addition, E derives from the potential V : E = (1 / e) dV / dr. Thus, by subtitution, we obtain the following expression for B :B = (1 /me r c2)(dV/dr) L, where L = rXp is the oribtal momentum. Finally, the electron having a magnetic moment due to its spin m=-guBS, it interacts with the magnetic field B,(Zeeman like-effect called spin-orbite interaction) as ESO=-m.B = -a L.S, where a=uB (1 /me r c2)(dV/dr) is the spin-orbite parameter which can be calculated in the quantum approach :
a~ (guB2Z4)/(n3 (L(L+1/2)(L+1)) , n=principal quantum number, L:magnetic quantum number, Z: atomic number)
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In Slave-Boson formalism we define
ci+=bifi+
then this yields,
<ci+cj>=<bifi+bjfj>~<fi+fj><bibj>
with a constrain
Σ(fifj++bibj)=1
where
<bibj>=δ.
- Does δ physically correspond to the number of density of “boson” or “vacancy” (namely “holes”)?
- In strong U limit does the above constrain physically mean “the total number of holes and electrons in a site allways equals to one”?
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Dear Behnam Farid, Thank you very much for your detailed explanations. Best regards.
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For the usual doping process, within the resonable bonds we can say that the value of oxygen excess  is not very well established, but the ambient highest Tc suggests optimal doping. Remember the GS of the generic phase diagram for the class of layered copper oxide SCs in ½ filled case: We are in the AF Mott insulator state first. We dope hole with small doses.
Which one of the following scenarios is physically true?
1. When the hole concentration started to increase gradually, this causes to create RVB pairs. In a certain value of doping the pair and hole concentration will balance between each other and we will have optimal doping value of intermediate regime.
2. The pairs already exist. When the holes are doped, this will destroys the pairs. In the corresponding doping value, again we will have an optima.
Afterwards, we will begin to loose holes and pairs balance, then a metallic Fermi liquid will occurs in overdoped regime.
Additionally; what is the actual charge carrier for High-Tc SCs? Doublons, holes or pairs?
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Dear Behnam Farid, Thank you very much for your recommendations. Bests.
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Reliable examples of second order phase transition have not been found. why? Second order phase transitions, L.Landau and his successors (by Yuri Mnyukh )
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Phase transitions often break symmetries (this is the case of the Ising model). In these cases, the high temperature (low coupling) phase has typically the symmetry of the Hamiltonian H, whereas the low temperature (high coupling) phase shows a lower symmetry (and an enhanced order). Physically, this is because not all the states of H are “accessible” anymore by fluctuations energy wins over entropy in other words. The phenomenon that the system chooses one state during the phase transition is called spontaneous symmetry breaking. For example the Hamiltonian of the Ising model has a spin-flip symmetry, while the ferromagnetic state is either spin-up or spin-down. This symmetry is spontaneously broken during the phase transition as the system selects one of the two possible states as the ground state. The thermodynamic behaviour in each of the phases can be characterized by an order parameter, let us call it m (for magnetisation in the Ising model), and restrict to a scalar order parameter for simplicity (this is fine when discussing most order-disorder phase transitions). The order parameter m changes in a non-analytical way at the phase transition point. The order parameter is usually constructed in that way that m = 0 in the disordered state and m = 1 in a perfectly ordered state.
At first order phase transitions, the order parameter jumps discontinously at the transition temperature, typically Tc, from 0 to a finite value. This involves a latent heat ∆Q = Tc∆S: while T remains constant at the critical value Tc during the transition, the entropy S changes. As the energy in terms of the latent heat cannot be instantaneously redistributed, a mix of phases occurs during the transition (e.g. liquid water and ice at the melting point).
At second order phase transitions, instead, the order parameter increases slowly and continuously from 0 to a finite value at Tc. There is a discontinuity in the specific heat at Tc, while the correlation length and the susceptibility diverge at Tc.
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When Dirac published his equation he has supposed to have find the spin because probably he found half integer values for the angular momentum. But according to the solutions of this equation, it is clear that the “ns” states correspond to just one spin state, contrary to that is generally supposed.
The two sub-shells of the “np” “nd” and “nf” shell correspond to an additional quantum state to that of the “ns” states, with a different number of states. This is exhibited for example with the Zeeman Effect. This is different from the classical notion of spin according to Uhlenbeck G.E. and Goudsmit S., where the spin hypothesis was proposed to explain the two subshells “np” “nd” and “nf”.
This is also established with the calculation of the magnetic moment of different compounds.
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Dear all: Many thanks for your interest in this question. Recently, (9 days ago) your comments lead me to study the limits of the quantum number m. I underline that the half quantum contribution, ½h to the angular momentum, has always the sign. It seems to me that this strongly indicate that the notion of rotation does explains the two subshells. Of course not all of you probably share my approach, it always like this in research and it is natural. The discussion allows to clarify our point of view.
I am now in my 82 year and it becomes often difficult for me to follow you. This to say that I am progressively becoming really retired.
Tanks again Yours Xavier
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Hi for everyone,
Why is there TM mode as the imaginary part of Graphene conductivity is positive?
Also, why is there TE mode when the imaginary part of Graphene conductivity is negative?
Thanks,
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Thanks for your reply Mr.Farmani
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The first work of Bohr has led to suppose that indeed the magnetic moment is the leading property in QM and the work of Sommerfeld also. But the half values Bohr magneton in the experimental measurement of magnetic moment appear as a difficulty. The hypothesis of Uhlenbeck and Goudsmit with the hypothesis of the spin seemed to give a good answer, but the g or Landé factor given by Dirac g=k/(k+1/2) giving good interpretations indicate that we miss one point. Then why use the action just in the wave equation?
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Dear Sofia: Thanks for your interesting comment. You say “NOT TRUE! The spin of the electron doesn't indicate a rotation around itself. Trials to explain the magnetic moment as coming from a charged sphere rotation around itself, failed.” I agree but for many people the spin is still an own rotation. So when I say "The notion of spin is closely connected with that of space." I mean the rotation it was first supposed to be a rotation.
So let me say like this “the notion of rotation is closely related to the notion of space!” Do you agree?
Now, how can be two objects without possible interactions than that of their existence? Do we must consider them without relative motion or not? If we consider a motion does this motion is only in a plan of rotation or do we have to consider a motion along the perpendicular direction of the plan of rotation? Kind regards Xavier
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Topological phase in condense matter, Wannier calculation, HSE.
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Ok thanks Helman, i will try this.
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It's known that the Density functional theory (DFT) is the most successful approach to compute the electronic structure of matter.
It's useful in the study of matter properties of as optical, electrical, chemical, mecanical, structural, therodynamic and so on...
But, I had never the occasion to applicate it, and I want to know how to applicate this calculation to caracterize thin films as CZTSSe for example.
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How to use DFT, first of all you should know basics of DFT, beside that ,you should have a software specially used for this pupose. for example VASP, Guassian, etc I have uploaded some lectures about the basics of the DFT, and there is also a lecture,  how to use VASP. There is a paper by E Chagaro etal , they have done DFT simulation for CZTS, CZTSe, CZTSSE etc , good luck   http://kummelgroup.ucsd.edu/pubs/papers_2016/CHagarov%20CZTS-Se%20DFT%20Phase%20stability%20JCP%202016.pdf
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Iam trying to find effective dielectric constant of two mixtures.i.e. mixing a gas to a nanomaterial. we can use either Maxwell Garnett theory or Bruggeman. In my case the volume fraction is greater than unity. i.e x = Gas / Material is greater than unity which effective medium approximation has to be used Maxwell Garnet or Bruggeman
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Hi Senthil,
It’s been a while since I’ve worked with these theories, hope this helps a little.
My work was about conductive (i.e. dielectric constant = infinity) particles inside an insulating polymer matrix. It might be a little different if the filler particles are not metallic.
There are 2 major shortcomings of Maxwell-Garnett and Asymmetric-Bruggeman. Both assume spherical filler particles. And they do not represent any frequency dependence.
Maxwell-Garnett Formula is based upon the assumption of spatially separated conductive particles. Therefore, it is only valid for the case of small volume fractions of inclusions. It does not have a particular percolation threshold. The material is assumed to be an insulator until all the host material is replaced by the conductive filler.
Asymmetric Bruggeman shows an extremum of the overall permittivity for a filler fraction of 0.33, no matter what the permittivity of the insulating host or the shape of the inclusions may be (it assumes spherical particles).
Depending on your system, you might want to look into percolation theory. I can recommend this literature:
Gantmakher, V.F., Electrons and disorder in solids. 2005, Oxford; New York: Clarendon Press ; Oxford University Press. x, 225 p.
Zallen, R., The physics of amorphous solids. 1983, New York: Wiley. xi, 304 p.
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Hi guys,
This is zhenhua wu, I am asking for some help about the KP hamiltonian of a 2D HgTe/CdTe well.
The BHZ hamiltonian is very successful in describing the TI edge states in a 2D HgTe/CdTe well. Recently people have proved the existence of the weyl semimetal phase in a 3D HgTe crystal with stress (Nat. Comm. 2016, 7,11136) and also in the 2D HgTe/CdTe well undergoing a phase transition from the aforementioned TI state by tuning the well thickness (Phys. Rev. Lett. 2017, 118, 156401).  A tight binding hamiltonian is given in the ref prl 118, 156401.  Is there a 4x4 BHZ kp hamiltonian for HgTe well weyl semimetal which has the same format as that describs the TI state but just with different parameters, like changing the value of M? I hope to get this hamiltonian and directly apply it in the transport simulation utilizing the scattering matrix formalism.  Thanks!
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Hi, zhenhua. On the basis of what I have understood from your above text, you want to look for a k \cdot p Hamiltonian describing weyl semimetal in  HgTe. In Nat. Comm. 2016, 7,11136 you mentioned, the bulk Hamiltonian without strain is H=H_{luttinger}+H_{bia}. Note that H_{bia} breaks the bulk inversion symmetry. Since generally we can get weyl semimetal from TI by breaking time-reversal symmetry or inversion symmmetry, thus I think by only tuning the parameter in H_{bia}, the weyl semimetal is available. 
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This is highly related to the critical phenomena in strongly correlated electron systems. Through this challenging question, I would like to invite those active researchers who have long been involved in the field of statistical physics and theoretical condensed matter physics so that we can at least find some clue to proceed ahead.    
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We have, O. Cépas and myself (Phys. Rev. B 76, 020401(R) have studied the effects of disorder in manganites (microscopic approach) , more precisely  we have focused on correlated disorder... and have compared our calculations to Monte Carlo calculations in the case of uncorrelated disorder,... the spirit of our approach is somehow different from  what was done before, we proceed within a two step approach : (1) we calculate the effect of the disorder on the Mn-Mn couplings (disorder effects fully included) and then we treat the disordered Heisenberg model beyond mean field to calculate the magnetic properties TC, spin stiffness,...
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Since X-ray’s frequency is too big to vibrate electrons, refractive index is nearly 1 to any materials which means its velocity doesn’t change at any environments. Scattering is interaction between bound electrons and light, I think this concludes X-ray can’t ‘feel’ bound electrons. But it does. why?
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You were taught correctly but you'll have to arrange your knowledge of what happens at what frequency.
1. X-ray is an electromagnetic field. The action of magnetic field component of that field is usually much weaker, so one usually speaks in terms of vibrating electric field. And the response of the system to the electric field is generally captured by dielectric function. I thought that would simplify understanding. 
2. Inelastic Compton scattering happens at frequencies still higher than those used for the  X-ray scattering. So in this frequency range it is not relevant.
3. There are unbound (free) electrons, loosely bound electrons (outer shells) and strongly bound inner shell electrons . Typical  resonant frequencies of outer shell electrons are at most in ultraviolet. In X-ray range their response to electric field is  just as free electrons' with the only difference that their density varies in space. Inner shell electrons have resonant  frequencies in X-ray range  Their contribution is different and, close to resonance, much stronger.  But the resonances are narrow and usually X-ray scattering does not use the frequencies of the characteristic lines.  Fast electrons used to  produce X-ray excite them of course.  So, what is left is weak scattering on free and loosely bound electrons which behave in this frequency region just like free. This weak scattering + interference allows X-ray diffraction. 
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How to calculate superconducting property or any related parameter of an organic molecule/superconductor using Gaussian 09?
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Thanks Dr. Murat for your suggestion.
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  why in bulk semiconductor we assume that effective mass equal to electron mass, but in small one we not assume that?
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I don't understand what you mean by small one. But in semiconductor physics, the effective mass, is the mass of the pseudo-particle called Bloch electron, and it does not have the same mass as the electron. One extreme example of this is graphene, where the electron have zero mass. In this answer in Quora I exaplin how it work  https://www.quora.com/How-is-it-that-electrons-act-like-massless-particles-in-graphene
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A postdoctoral research position is available in the Large's group in the Department of Physics and Astronomy at UTSA. The successful candidate will be responsible for conducting research in the area of theoretical and computational nanophotonics and plasmonics. He/She must have a strong background in computational Physics and have previous experience with electromagnetic simulation tools for the modeling of the optical response of metallic nanostructures such as FDTD, DDA, BEM, FEM/FEA, or Green Dyadic method. The candidate should also be familiar with Linux environment and be able to run basic commands in a terminal-like environment, and possess basic programming skills in C/C++, Fortran, Matlab, or any other scientific language. In addition to plasmonic materials, expertise in semiconductor, magnetic materials, two-dimensional materials, or other types of materials will be considered as a plus. The candidate will be working on several independent projects simultaneously and will be involved in both stand-along theory projects and collaborations with experimental groups. The candidate must be self-motivated, methodical, detail-oriented, and possess good oral and written skills.
The position is anticipated to start in Fall 2017 but the starting date can be discussed.
Please send a cover letter detailing your experience, a CV, and the contact information of three references to Dr. Large.
Contact: Dr. Nicolas Large, Nicolas.Large@utsa.edu
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FDTD, DDA, BEM, FEM/FEA, or Green Dyadic method. The candidate should also be familiar with Linux environment.
I miss just these Items 
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Dear friends, i need a brief explanation regarding the energy dependency of nuclear dissipation coefficient. SM analysis of evaporation residue cross section measurement shows both energy dependent dissipation coefficient and constant dissipation coefficient in two independent results. However pre-scission neutron multiplicity analysis also shows,  energy dependent dissipation coefficient for reproducing Npre values. 
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Dear Dr. Muhammed Shareef,
Dissipation coefficient should be a function of the relative energy since the kinetic energy of relative motion of nuclei is transformed into intrinsic energy of nucleons and excitation of collective motion.  The number of excited degrees of freedom and strength of their amplitudes determine dissipation coefficient for the relative motion. Therefore, theoretical models devoted to study the dissipation of the initial kinetic energy should take into account the possible mechanisms of dissipation as coupling between degrees of freedom describing physical process of heavy ion collisions. For example, in our first work in this field we had found that nucleon exchange  between interacting nuclei is one of main mechanisms [see attached papers].  We found a reason of non-equilibrium sharing excitation energy between interacting nuclei. Conclusion is that dissipation coefficient should be sensitive to the collision energy. 
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I have read already Dzyallonskii's paper as well Moriyas paper which is the two basic paper discussed and derived the reason of spin canting. However, I am finding it difficult to understand. I do not need any mathematical explanation for my understanding. I just want to know the phenomenological concept behind the spin canting in Hematite. Yes, it is well known that spin canting arises when an isotropic superexchange interaction combined with the Spin-Orbit coupling (SOC). But I fail to have a clear picture about this, means how the SOC gives rise to canting and why it just vanishes below the morin transition in hematite. 
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you may want to take a look at the first chapter in the book of Maekawa and Khaliullin (Springer series) to answer your question.  I believe they work it out nicely.
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I make thin films and I use glasses as substrate. A single grid's dimension in my evaporation system is 16mm x 6mm. I work in 10-6 Torr vacuum.
How can I cut my glasses with rectangular geometry?
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But you can do this easily by a glass cutter http://www.zh-kv.com/Kaivo_En/ProductView.asp?ID=29&SortID=128
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Many articles states about three interactions (Fe-Fe, Fe-R, and R-R) in orthoferrites either at or below Neel Temperature. Not many evidence were found regarding the predominant interactions at high temperatures and interaction with respect to rare earth concentrations. What will be the effect on the interactions at high rare earth concentrations and at high temperature?
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In orthoferrites dominant are Fe-Fe interactions. Even at high concentration rare earth moments can order at very low temperature (usually below 10K) and thus contribute to magnetic properties.
Best regards, Bartek
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We know that some of the Weyl semimetals show negative magnetoresistance in presence of parallel electric and magnetic fields, which is indicative of the chiral anomaly due to Weyl fermions. But there are other negative linear magnetoresistance (NMLR) phenomena like NLMR in magnetic materials, NLMR due to geometry or size effects of the samples (current-jetting effect), NMLR in quantum limit etc. How to differentiate these NLMR phenomena with the chiral anomaly induced NLMR phenomena ( Adler–Bell–Jackiw chiral anomaly) in a Weyl semimetal?
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Respected Behnam sir and Daniel Sir,
     Thank you very much for your valuable references. 
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This question is related to magnetism and application of density functional theory (DFT)
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OK. Let me see if I can figure it out something..
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Consider a two eigen wave functions A, B, where A is in the ground state in the lowest frequency mode, and B is in the first excitation state in the highest frequency mode in the Debye model. The expectation value <x> for the deviation from the equilibrium positions in the lattice of the sum A+B, <A+B|x|A+B> would vibrate at 50% higher frequency than the highest frequency allowed in the solid. Is there any principle or rule that eliminate such unallowable higher frequency lattice vibrations caused by the sum of two wave functions in different normal modes in the Debye model?  
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Thank you for your quick answer. Consider a case in which the temperature is immediately above 0K. There would be just a few phonons in the solid at such a low temperature. Suppose there is just a single phonon in the highest frequency mode. This would be equivalent to the case I wrote in my question, as there is no phonon in all the other modes than the highest frequency mode. In all the other modes, the quantum number is just 0, but in the highest frequency mode, the quantum number is 1. Since the total wavefunction of the system is the sum of eigen wavefunctions over all normal modes, we have to consider the behavior of the sum of two wavefunctions A+B in my question. Then the higher frequency vibration than the highest frequency allowed in the system is inevitable. How such higher frequency vibration is eliminated in the real solid?
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We know that Allen-Dynes-modified McMillan formula is model dependent formula, where the model describes only real materials which satisfy 4 approximations. The isotropic approximation is one of them. If, in a system, the isotropic approximation failed then is it possible to apply the formalism to estimate the superconducting transition temperature?
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@Behanam Farid Sir.....Thank you.
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anyone who knows 
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Dr.chien can you please refer some related paper. it will be help to further understanding for me
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In our work , we reported the estimation method for calculating the optical band gap and determining the type of inter band transition. The empirical fitting of experimental data to the law requires the assumption of a value for (3/2 , 1/2 , 2 , 3 )  
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