Condensed Matter Theory

Condensed Matter Theory

  • Fushan Zhou added an answer:
    26
    How do you visualize the two kinds of spin of an electron?

    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.

    Fushan Zhou

    What is the spin of an electron? All textbooks say something like "the intrinsic angular momentum of an electron". Beyong that, I  don't believe there is anybody that can explain why and how an electrons possess such kind of thing.

    Here,I just suggest that we look for the answer in another direction -- classical mechanics. Yes! Classical mechanics, Specifically, generalized elasticity of continua with microstructures, which sadly for various reasons, is virtually an unknown field to theoretically physicists.

  • Sergei Sergeenkov added an answer:
    5
    What is the typical range of the critical current in a SQUID?

    Some experiments in circuit QED have reported it to be 1-2 micro Ampere. Can it be one order of magnitude larger?

    Sergei Sergeenkov

    Here is the so-called SQUID gradiometer (for measuring inhomogeneous magnetic fields) with Ic=10mA.

  • Sitansh Sharma asked a question:
    New
    Can we use optB86b-vdw functional along with SOC?

    Dear RG user,

    Greetings,

    I am working in 2D materials and new to the use of VASP software.

    For my studies i want to use OptB86b-vdw functional along with SOC. But, when i am using this functional + SOC, in my vasp output file, i am not able to find neither "Total vdW correction in eV" nor vdw_kernel.dat file is read during the calculation. But the keywords related to OptB86b-vdw
    GGA = MK
    PARAM1 = 0.1234
    PARAM2 = 1.0000
    LUSE_VDW = .TRUE.
    AGGAC = 0.0000

    are read during the vasp calculations.

    But when i am using this functional without SOC, i am able to find both of them in my output file.

    Please help me to resolve this problem.

    Many thanks for help.

    with best regards,

    Sitansh

  • Cenap Özel added an answer:
    1
    How is the transversal intersection of manifolds and warped product structures?

    How is the transversal intersection of manifolds and warped product structures?

    Cenap Özel

    Let M = M_1 \cap M_2,  where  M_1 = M`_1 \times_{f_1} M``_1. and M_1 = M`_2\times_{f_1} M``_2, be transversal intersection of manifold with some structures..

    How are the warped product submanifolds in transversal intersection of of warped product manifolds... 

  • Amrit Sorli added an answer:
    11
    Who is studying the equivalence between inertial mass and gravitational mass?

    In one of our usual daily round table discussions at the Coaltso team we had glimpsed the solution to the problem of equivalence between the inertial mass and the gravitational mass regarding the existence of a physical experiment which can be used to distinguish them.

    We think that this problem has a shortcut path. We hope for interested collaboratorsto join us.

    Amrit Sorli

    Which is inertial mass of the pra-kilogram from Paris on the Mars surface? We know that the amount of matter of pra-kilogram on the Earth surface and on the Mars surface is the same. Which is value of inertial mass of pra-kilogram on the Mars surface?

  • Hou sj added an answer:
    5
    How can I calculate elastic constants of SQS structures using VASP ?

    I am using vasp 5.2 version where the elastic constants for a symmetric structure is automatically calculated by IBRION = 6 tag.

    Since, I am interested in SQS structure which is basically having very low symmetry. Now, my question is does vasp still keep symmetry of the structure (let say, bcc) while calculating elastic constants?

    What if I want to calculate elastic constants of a SQS-54 structure (bcc) which is basically way to expensive to calculate from computational point of view and if by a bain path transformation I reduce it to let say SQS-36 having tetragonal structure, then in that case will the elastic constants of the SQS-36 (tetragonal) structure be equivalent to that of SQS-54 (bcc) structure?

    Basically, all I want to reduce my giant SQS-54 bcc structure to some tetragonal structure of having small atoms and in that case can I consider the elastic constants of the tetragonal structure be equivalent to SQS-54 bcc structure?

    Any idea would be greatly acknowledged.

    Hou sj

    In my opinion, if you set isym=0 , vasp  will give reasonable result.  I do not know if you have solve this problem. Could you share your newest results with us?  I think many people are interested in this .

  • Vladimir V. Lugovoi added an answer:
    15
    What is the magnetic field, created by ion of Fe^{+2} (for electron of conductivity), if the ion magnetic moment equals 5.1 Bohr's magneton?

    For example, to get answer, could we use classical formula (44.4) from the book Landau,Lifshitz "Theory of field" (see the attached photo) ?
    It's because, we suppose, the distance between the electron of conductivity and the atom is equal approximately the distance between two neighbor atoms which can be in interval from R = 10^{-5} cm to R = 10^{-7} cm, whereas the radius of electron orbit is r = 10{-8} cm. Thus (see photo) R >> r. Just in that approximation the formula (44.4) was obtained.
    Am I right?
    What is magnetic field?
    Thank you in advance.

    Vladimir V. Lugovoi

    Seems, in two-dimensional (like a graphene) flat surface, it could be formed one-dimensional, filamentary, long-range ordered structures, formed by any number of n of charged fermions (see red circles in added fig.1 from http://dx.doi.org/10.4236/jmp.2015.67103 ).

    The properties of this structure are like the properties of condensate

    (see added fig.2, where \Delta y_{n}  is the averaged distance between the particles in filamentary structure) : 

    -  the linear density of particles (in filamentary structure) grows with the number (n) of particles of structure,    

    - the linear density of particles (in filamentary structure) grows with the magnitude of external magnetic field ,

    - energy per one electron of filamentary structure is reduced with growing number of n of electrons. 

    One structure (with any fixed number of n of particles) is described by one wave function; therefore, the particles, which form structure, are indistinguishable. 

    Could this be connected also and with exchange interaction? (Perhaps, with interaction between two filamentary structures, which are the same each other and have the same quantum nature …) Any opinions would be important for me.  Thanks.

    + 1 more attachment

  • Alexander Pisch added an answer:
    3
    How can I calculate the sublimation enthalpy at different temperatures?

    Please help me, if anyone has any materials or suggestion of how to get the value of sublimation enthalpy at different temperatures, say 298K, when we have one of the value at 398 K?

    Alexander Pisch

    As a first order, you can take it constant, i.e. that the sublimation enthalpy at 298K is close to the one at 398K. However, this is only the case, if the gas species are the same at the two temperatures. 

  • Tahir Nawaz Khan added an answer:
    28
    How to calculate lattice constant from XRD spectrum?
    Lattice Constant formula.
    Tahir Nawaz Khan

    Cullity book link : https://archive.org/details/elementsofxraydi030864mbp

  • Anees P added an answer:
    6
    Any advice on free energy calculations for unstable high temperature phase ?

    Hi,

    I am having unstable high temperature phases and I want to calculate free energy of those structures, what is the best and efficient method to calculate it?

    I know there are ways to calculate it such as:

    Quasi harmonic Debye model, SCAILD method, AIMD method and fast free energy calculations, but I am bit confused which one I should chose?

    Every method has some limitations for example, Debye model is kind of analytic, SCAILD and AIMD is too computationally expensive, but no idea about fast free energy. So, under such circumstance, it would be really good if anyone has some experience regarding these methods and can suggest something.

    Thanks in advance.

    Anees P

    I am not an expert in PLUMED. PLUMED have interface with most of the popular ab-inito and MD packages. For more details please visit their website

    http://plumed.github.io/doc-v2.2/user-doc/manual.pdf

  • Eva Majerníková added an answer:
    18
    Higg's mechanism in condensed matter physics?
    Alledgelly, there exists a paper by P.W. Anderson where he proposed for a condensed matter problem a mechanism analogical to the Higgs mechanism in particle physics before the last had appeared.

    Do anybody know the reference of that paper by P.W. Anderson?
    Eva Majerníková

    Thank You for the  reference. on Greiter's paper.  The ref. on Anderson's paper I have  already found .

  • Lawrence Dunne added an answer:
    11
    Is there any concept of quasi-particle in classical systems?

    By quasi-particle I mean in the sense of particles dressed with their interactions/correlations? If yes, any references would be helpful. 

    Lawrence Dunne

    Dear Sandipan,

    It can be very easy to misunderstand some of the subtle points and differences about what I will call 'classical' and 'quantum' quasiparticles.

    Firstly. we can say that a classical quasiparticle is 

    real particle + clothing = quasiparticle.

    We have numerous examples from an ion surrounded by counter ions in an electrolyte solution to vibrational modes in a classical dynamical system.

    However, none of these examples captures the essence of a quantum quasiparticle for example a 'dressed' electron in a metal. The conduction electrons are quasiparticles which behave the way they do because of screening. The plasmon modes are the reason for this.  This separation demonstrated firstly by Bohm and Pines is purely quantum mechanical and I do not think there is a classical analogue. If there is, I would be interested to learn about it.

    Best wishes-Lawrence Dunne

  • Pius Augustine added an answer:
    2
    Why, whilst depositing PMN-PT on LSCO buffered platinised silicon substrate, on and off, is the film conducting?

    What could be the possible reason? 

    Pius Augustine

    Thank you Tarun.

    Sometimes between two points on the surface of the film shows very low resistance. 

    Also between the bottom platinum electrode and top surface of PMN-PT film. 

    Is it because of the O2 partial pressure ? 

  • Anton Nikonov added an answer:
    4
    How to solve the problem with Nb-Ti-Al potential in LAMMPS?

    I'm trying to simulate the structure of B2 alloy Ti-Nb using the potential http://www.ctcms.nist.gov/potentials/Nb.html#Nb-Ti-Al

    Created structure collapses with a large release of energy during relaxation. The lattice parameters were taken from the test report. The LAMMPS script is attached.

    Anton Nikonov

    Thank you.

    This structure is shown in the table with the test results of the interatomic potential.

    The same result is obtained when using the NVT.

  • Konrad Gruszka added an answer:
    5
    "relax" or "vc-relax", which one for optimization of primary cell in QE (or generally other DFT codes)?

    Hello.

    Let's suppose I have some unit cell for example Hexagonal Yttrium. I would like now to introduce a defect in the form of substitution of one of the atoms by let's say bigger one. Before doing further calculations I know, that first I should lead to minimize the forces acting on the atoms inside the cell. Quantum Espresso lets me do this by two ways: one using older 'relax' optimization where cell parameters don't change and a second one where I can optimize not only positions of atoms inside cell but also other things like eg. cell size or angles, possibly leading to a lower total energy.

    Which option should I use, to ensure that my calculations would be physicaly right? Does forcing the system to remain in a particular unit cell is appropriate? What if I do not know the true unit cell due to the lack of experimental data?

    Konrad Gruszka

    Thank You all for your answers.

    I can see now, that this case  is more of my assumptions than 'only one good path' that I should follow..

    Ang Feng: I can imagine that when only isolated defect is present, the latter will "arrange" to fit this inclusion, so relaxation of whole cell is needed .  I think that also a much bigger supercell is appropriate. 

  • Carlos Paz de Araujo added an answer:
    7
    The averaged energy of two-electrons repulsion U - What is it?

    As is well-known, the so-called averaged energy of two-electrons Coulomb repulsion U has been introduced both in quantum theory of atoms / molecules and of condensed matter, which is typically defined, as is shown in the attached figure (a), - where the integral written there is taken over the whole 6-dimensional configurational space (r1=(x1, y1, z1) and r2 = (x2, y2, z2)).

    For instance, the on-site two-electrons repulsion energy U appears in superexchange theory, where the antiferromagnetic contribution to exchange integral is obtained as: Jaf ~ b2/U (where b is a hopping integral), it appears in LDA+U approach intended to reproduce the band structure of strongly correlated crystalline systems correctly, and so on.

    As far, as I can judge, the U energy is introduced as was shown (or in equivalent way) in manifold textbooks and papers.

    But it is absolutely evident, that the integral defined so diverges, in other words, is equal to infinity, except the trivial and physically insignificant case, if at least one of one-electron orbitals is identically zero at the whole space. Actually, most probably no other physically reasonable form of one-electron orbitals can be proposed to eliminate the singularity in the denominator at ANY point of "line" r1 = r2 in 6-dimensional space (see also attached figure (b), where this point is symbolically depicted for the case of "one-dimensional" electrons).

    Note, that the approach like "Let`s deviate from "line" r1 = r2, next, take the integral over the whole space except the deviation vicinity (see also figure (b)), and finally calculate the limit of the result approaching the measure of deviation to zero".. so, something like that evidently is not valid - because it also does not eliminate the singularity, actually, the integral over the whole space except the deviation vicinity might be arbitrarily large (keeping its sign to be invariable), as depends on the deviation measure value.

    Sorry for a long text, but it is related to my question directly. On the one hand - I cannot find the logical errors in argumentation given above, as well, as cannot find the explanation in textbooks and publications I have ever seen. On the other hand, manifold sources deal with the definitely FINITE values of U (typically, some eV).

    Can someone explain me, how this contradiction could be solved?

    I would be VERY grateful.

    Carlos Paz de Araujo

    U is the screened potential. So, you should pick RPA or Thomas-fermi to described the dressed quasi-particle and then, the integral will not diverge. There is no sense for the integral if the potential energy does not get screened within a few lattice sites, or is in the case of the Hubbard model, screening within a distance slightly larger than the Bohr radius. Thus, when you see U, understand that it is really Vexternal/dielectric function.

  • Henry Tregillus added an answer:
    3
    How to define a theoretical room-temperature quantum state storage device?

    The coherence time of quantum dots is largely linked to their electromagnetic susceptibility (environmental interaction strength). Topological quantum computing is based upon the long coherence time of anyon pseudoparticle states.

    Is there some known material which exhibits stable quasiparticle behavior in response to photonic excitation?

    Or if not, what might such a material look like?

    Henry Tregillus

    Arijit, Franz:

    I am attempting to build such a statistical description of quantum mechanics within a solid, such that the movement and behavior of large-scale quantized behavior can be understood and applied. As it stands, the best we have in this regard is NMR, but it relies on something different than what I have in mind.

    NMR uses electromagnetic pulses to target specific magnetic moments of complex molecules in a strong magnetic field; given the known resonance of a particular section, it can be manipulated, and the molecule can be used as a circuit of some sort. Operations result due to inner-molecular interactions, and as these are probabilistic, the final measurement has to be done many times - or just over a lot of samples.

    Like Arijit is saying, NMR is NOT scalable. We just don't have the resolution necessary, nor the magnetic field strengths desired. It's also slow. The principles behind it however, of using molecules themselves as storage and logic gate structures, is a big part of what I'm trying to learn, just from the perspective of condensed matter, rather than molecular dynamics.

    I'll be sure to check out more NMR papers though, it is certainly a good building block. Thank you both :)

  • Tanmoy Chakraborty added an answer:
    1
    What is the equation that describes the directional dependent shear modulus of orthorhombic crystals in polar co-ordinates?

    May be the question is bit specific, but I want to know if anyone has any idea about it, just in case. I know the relations for bulk modulus and Young's modulus from the paper (J. Appl. Phys. 109, 023507 (2011), Eq. 16 & 17), but they didn't calculate directional dependent shear modulus.

    So, in case if anyone knows, kindly let me know. Thanks in advance.

    Tanmoy Chakraborty

    Alright, I found the answer by myself from a paper:

    AIP Advances 5, 087102 (2015)

    The equation is given on pg. no.-13 (Eq.-10)

    So, in case anybody is interested, can follow the above reference.

  • Manuel Morales added an answer:
    10
    Is the Standard Model incomplete in light of String-Net theory?

    I have a doubt regarding String-Net theory. Prof. Xiao-Gang Wen stresses upon the point that all fermions must carry gauge charges. The Standard Model contain composite fermions that are neutral for U(1) × SU(2) × SU(3) gauge theory. So, according to string-net theory the Standard Model of particle physics is incomplete, and the correct/complete model should contain extra gauge theory, such as a Z_2 gauge theory. But, Coleman-Mandula theorem states, more or less, that space time symmetries (which determine spin) cannot mix with gauge symmetries in anyway. The Haag-Lopuszanski-Sohnius (HLS) extension of this theorem states that the only possible loophole to the Coleman-Mandula theorem is SUSY, as far as I understood. So, is the Standard Model incomplete from the point of view of string-net theory or is string-net theory radically inconsistent with what we see in nature, and must therefore be wrong in its present form? Also, is it meaningful to call something a Z_2 gauge theory (because, as far as I understand, discrete symmetries can at best act as "large" gauge transformations)? PS: To get an understanding/gist of what Prof. Wen is saying (as I mentioned in the first half of my question) please refer to this paper: http://arxiv.org/abs/cond-mat/0302460

    Manuel Morales

    "Experiments are the judges."

    Oh really? Think again...

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      ABSTRACT: The current scientific methodology is based on the paradigm of second cause logic by placing cause second to an observable physical effect, i.e., the existence of an effect causing the existence of an effect. The methodology of successfully predicting effects and the repetition of the predicted effects to serve as an indication of causality necessitates that causality is a singular mechanism in order for such a method to be valid. Conversely, the Tempt Destiny experimental model placed causality first by distinguishing which mutually exclusive selection variable caused the effects observed. The 'unambiguous' empirical evidence has shown that the second cause logic used as the foundation of scientific methodology cannot 'correctly' distinguish which first cause variables caused the effects observed.
      Full-text · Dataset · Jun 2014
  • Boris Sedunov added an answer:
    11
    What is the equivalent description of Van der Waals forces for a gas or supercritical fluid?

    In chemistry, a common method of calculating solute and solvent reaction rates in a liquid is through using the quantum mechanical descriptions of inter and intramolecular bonds. One of the intermolecular descriptions is that of Van der Waals interactions - that of the sum of electrical, quantized, yet weak bonding forces. These may include permanent dipole-dipole interactions (Keesom force), dipole-induced dipole interactions (Debye force), and spontaneous dipole interactions (London dispersion forces). Generally Van der Waals forces omit that of ionic bonds between molecules.

    As far as I know though, there isn't a model describing supercritical liquid/gas phases, such as that of CO2 which is often used to decaffeinate coffee beans. I know there are some models built to describe plasmas, but these are generally models designed for cross-section analysis used in fusion/fission reactors - they don't describe allowed energy levels in the same manner as say, a solid state semiconductor would.

    I'm not quite sure how to tackle this kind of problem. In a field theoretic condensed matter picture (or even many-body statistical Schrodinger equation) solids are generally described by phonon modes; quasiparticle states are evaluated with ladder operators, after setting up the problem with electron & ion density. Sometimes metallic conductors can be described by an electron gas - at sufficiently low temperatures, this is a Fermi liquid.

    Fermi liquids have energy levels described by momentum degeneracy and the Pauli exclusion principle. I assume something similar must apply to a gas, but there would be an absurd number of tightly packed available energy levels, and in terms of the Schrodinger equation, most particles would have a Hamiltonian of that similar to a free particle; bumping around other gases though, on the large scale, it's almost a classical description - and in fact, classical descriptions work pretty well. Is it just because the energy levels involved are so high that it's in the classical limit?

    Anyways. I can't seem to find any literature on this - all of the above is just my thinking on it. It's mostly a curiosity of mine :)

    Boris Sedunov

    Henry and all participants of this discussion. I have a new paper on this subject:

    http://www.scirp.org/Journal/PaperInformation.aspx?PaperID=61716

    Best regards,  Boris

  • Burhan Ullah added an answer:
    9
    How does the formation of oxygen vacancies affect the quality factor?

    As we know that the reduction of Ti+4 to Ti+3 ion, which is the consequence of the formation of oxygen vacancy. The Ti+3 ion can be viewed as a Ti+4 ion that trap an electron(T+4.e) which mean that  Ti+4.e-Voo - T+4.e  possible bond will be formed. The electron will be bound by the fully ionized oxygen vacancies(Voo). So what about the impact of quality factor in such conditions? How we can view the quality factor in terms of oxygen vacancies and the trapped electron?

    Burhan Ullah

    Thanks so much Respected Marcos Augusto Lima Nobre, i become very happy to see your comments on my question,  thanks for your kind suggestion and useful information. This give me a positive feedback to handle my problem.

    -------------------thanks once again to give me your time.--------------

  • Tanmoy Chakraborty added an answer:
    7
    What is the relationship between elastic constants and phonon spectra?

    Hi,

    I know it's bit fundamental question but I really want to understand the relationship between the various elastic constants and phonon branches? Can anyone suggest some review literature/notes/books where I can find some lucid and simple explanation regarding the relationship between the duo.

    May be the relationship holds for long wavelength limit (near to gamma point) but then why still some structures show elastic instability but dynamical stability (+ve phonon frequencies)? 

    Any kind advice would be acknowledged.

    Tanmoy Chakraborty

    Thanks Luis for your suggestions

  • Avaneesh Kumar added an answer:
    3
    Does anyone know why band structure and other properties of nano structure is different in spin and non-spin calculation of same structure?

    Hi, I'm new in the magnetic calculation. During simulation of Doped (single atom) bulk structure (Zinc-Blende) with and without spin polarized, i found band and other properties are different, Why is this so? Also help me to which atom (dopant or hosts atom) i will assign spin for spin calculation?    

    Avaneesh Kumar

    Thanks to both of you.

  • Yulia E. Shchadilova added an answer:
    5
    Are the superglass and the supersolid states observed experimentally? Or they still under debate?

    Why  the creation of such phases is  difficult?

    Because they require a dense regime with at least several particles within the interaction range, which can be difficult to achieve.

    Or there are other causes?

    Yulia E. Shchadilova

    Beyond experiments with liquid helium, the superfluid-to-supersolid phase transition was observed with the cold atomic gas in a cavity, e.g. Science 336, 1570 (2012). 

  • Shielo Namuco added an answer:
    8
    What will happen if you dope a magnetic material like manganese in a GdBCO bulk superconductor?
    Manganese has magnetic moment so I think it's magnetic moment might affect the superconductivity of the sample.
    Shielo Namuco

    Thank you very much for this answer Dr. Jardim. 

  • Xueheng Zheng added an answer:
    8
    How can I calculate phonon dispersion relations of structures with long range interactions using classical potentials?

    From my understanding, for long range interatomic interactions, not only the interactions of the unit cell with their nearest neighbors should be considered, other atoms around the unit cell should be taken into account as well. So when I tried to calculate the dispersion relation with classical potentials, I included the interactions to the 5th nearest neighbors. However the dynamical matrix is not Hermitian, i.e. some eigenvalues are negative numbers. Is it because the number of neighbors is not enough or is there any other way to calculate the dispersion relation when long range interactions are involved? Thanks.

    Xueheng Zheng

    I use a central force model, see Physica C 506 (2014) 100, available at my ResearchGate home.

  • Karel Carva added an answer:
    1
    How can i calculate the effective mass of electron and hole for solid solution?

    I know the effective mass of electron " me* "and hole " mh* " for ZnS and CdS separately and I want to know to calculate effective mass of electron and hole for solid solution ZnxCd1-xS ?

    Karel Carva

    For accurate solution I'd recommend ab initio calculation of this alloy, this would provide the band structure from which effective masses can be obtained. You should contact some group capable of employing the CPA approximation for alloys.

  • Remi Cornwall added an answer:
    2
    Can Fermi level go above top of the conduction band?

    Can Fermi level go above top of the conduction band?

  • Swapnali Dhanayat added an answer:
    4
    What is quantum confinement? How can I calculate bohr excitone radius of nanoparticle?

    How can we calculate the bohr excitone radius of nano-particle?

    Swapnali Dhanayat

    Thank you sir...

  • Behnam Farid added an answer:
    1
    What is Lifshitz transition and how are they different from Fermi level crossing?

    It seems Lifshitz transition refers to the change of Fermi surface without symmetry breaking. But I consider it is quite common that the Fermi surface changes as a function of doping, as in Fe-based superconductors. Furthermore, in semi-metals, doping can change the Fermi energy, resulting in Fermi surface change where electron bands cross the Fermi energy and the system become metallic. So how is the 'Lifshitz transition' different from these simple Fermi surface changing phenomena?

    Behnam Farid

    There is no fundamental difference. In fact, the Lifshitz transition was originally considered by Lifshitz (see the attached review article by Lifshitz and Kaganov) in the light described by you here above, for a given band structure. The issue that has come into prominence in recent years is that of the Lifshitz transition in strongly-correlated systems (in doped high-Tc compounds and heavy-fermion systems), where the notion of bands, and in particular of rigid bands to which electrons are added or from which electrons are removed (by appropriate doping), is of limited applicability, if at all. Due to strong electron-electron interaction, the electronic structure, as observed experimentally (say, by means of photo-emission spectroscopy) can substantially change upon doping, possibly in conjunction with changes in other parameters relevant to the system (such as temperature, pressure, etc.). As a result of interaction, Lifshitz transitions may be observed that are absent in mean-field treatments.

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