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ABSTRACT: We investigate the effect of an applied uniaxial strain on the ferromagnetic
instability due to long- range Coulomb interaction between Dirac fermions in
graphene. In case of undeformed graphene the ferromagnetic exchange instability
occurs at sufficiently strong interaction within the Hartree- Fock
approximation. In this work we show that using the same theoretical framework
but with an additional applied uniaxial strain, the transition can occur for
much weaker interaction, within the range in suspended graphene. We also study
the consequence of strain on the formation of localized magnetic states on
adatoms in graphene. We systematically analyze the interplay between the
anisotropic (strain- induced) nature of the Dirac fermions in graphene, on-
site Hubbard interaction at the impurity and the hybridization between the
graphene and impurity electrons. The polarization of the electrons in the
localized orbital is numerically calculated within the mean- field self-
consistent scheme. We obtain complete phase diagram containing non- magnetic as
well as magnetic regions and our results can find prospective application in
the field of carbon- based spintronics.
01/2013;
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ABSTRACT: We study the role of long-range electron-electron interactions in a system of
two-dimensional anisotropic Dirac fermions, which naturally appear in
uniaxially strained graphene, graphene in external potentials, some strongly
anisotropic topological insulators, and engineered anisotropic graphene
structures. We find that while for small interactions and anisotropy the system
restores the conventional isotropic Dirac liquid behavior, strong enough
anisotropy can lead to the formation of a quasi-one dimensional electronic
phase with dominant charge order (anisotropic excitonic insulator).
06/2012;
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ABSTRACT: We consider the quantum phase transition between a Néel antiferromagnet and a valence-bond solid (VBS) in a two-dimensional system of S = 1/2 spins. Assuming that the excitations of the critical ground state are linearly dispersing deconfined spinons obeying Bose statistics, we derive expressions for the specific heat C and the magnetic susceptibility χ at low temperature T in terms of a correlation length ξ(T). Comparing with quantum Monte Carlo results for the J-Q model, which is a candidate for a deconfined Néel-VBS transition, we obtain an almost perfect consistency between C, χ, and ξ. The corresponding expressions for magnon (triplet) excitations are not internally consistent, however, lending strong support for spinon excitations in the J-Q model.
Physical Review Letters 05/2011; 106(20):207203. · 7.37 Impact Factor
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ABSTRACT: We review the problem of electron-electron interactions in graphene. Starting
from the screening of long range interactions in these systems, we discuss the
existence of an emerging Dirac liquid of Lorentz invariant quasi-particles in
the weak coupling regime, and strongly correlated electronic states in the
strong coupling regime. We also analyze the analogy and connections between the
many-body problem and the Coulomb impurity problem. The problem of the magnetic
instability and Kondo effect of impurities and/or adatoms in graphene is also
discussed in analogy with classical models of many-body effects in ordinary
metals. We show that Lorentz invariance plays a fundamental role and leads to
effects that span the whole spectrum, from the ultraviolet to the infrared. The
effect of an emerging Lorentz invariance is also discussed in the context of
finite size and edge effects as well as mesoscopic physics. We also briefly
discuss the effects of strong magnetic fields in single layers and review some
of the main aspects of the many-body problem in graphene bilayers. In addition
to reviewing the fully understood aspects of the many-body problem in graphene,
we show that a plethora of interesting issues remain open, both theoretically
and experimentally, and that the field of graphene research is still exciting
and vibrant.
12/2010;
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ABSTRACT: We argue that our analysis of the J-Q model, presented in Phys. Rev. B 80, 174403 (2009), and based on a field-theory description of coupled dimers, captures properly the strong quantum fluctuations tendencies, and the objections outlined by L. Isaev, G. Ortiz, and J. Dukelsky, arXiv:1003.5205, are misplaced.
09/2010;
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ABSTRACT: We examine the 1/N expansion, where N is the number of two-component Dirac
fermions, for Coulomb interactions in graphene with a gap of magnitude $\Delta
= 2 m$. We find that for $N\alpha\gg1$, where $\alpha$ is graphene's "fine
structure constant", there is a crossover as a function of distance $r$ from
the usual 3D Coulomb law, $V(r) \sim 1/r$, to a 2D Coulomb interaction, $V(r)
\sim \ln(N\alpha/mr)$, for $m^{-1} \ll r \ll m^{-1} N \alpha/6$. This effect
reflects the weak "confinement" of the electric field in the graphene plane.
The crossover also leads to unusual renormalization of the quasiparticle
velocity and gap at low momenta. We also discuss the differences between the
interaction potential in gapped graphene and usual QED for different coupling
regimes.
03/2009;
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ABSTRACT: We review the problem of adatoms in graphene under two complementary points of view, scattering theory and strong correlations. We show that in both cases impurity atoms on the graphene surface present effects that are absent in the physics of impurities in ordinary metals. We discuss how to observe these unusual effects with standard experimental probes such as scanning tunneling microscopes, and spin susceptibility. Comment: For the Proceedings of the "Graphene Week 2008" at the ICTP in Trieste, Italy. 8 pages, 8 figures
12/2008;
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ABSTRACT: We examine the conditions necessary for the presence of localized magnetic moments on adatoms with inner shell electrons in graphene. We show that the low density of states at the Dirac point, and the anomalous broadening of the adatom electronic level, lead to the formation of magnetic moments for arbitrarily small local charging energy. As a result, we obtain an anomalous scaling of the boundary separating magnetic and nonmagnetic states. We show that, unlike any other material, the formation of magnetic moments can be controlled by an electric field effect.
Physical Review Letters 08/2008; 101(2):026805. · 7.37 Impact Factor
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ABSTRACT: We study the distribution of vacuum polarization charge induced by a Coulomb impurity in massive graphene. By analytically computing the polarization function, we show that the charge density is distributed in space in a non-trivial fashion, and on a characteristic length-scale set by the effective Compton wavelength. The density crosses over from a logarithmic behavior below this scale, to a power law variation above it. Our results in the continuum limit are confirmed by explicit diagonalization of the corresponding tight-binding model on a finite-size lattice. Electron-electron interaction effects are also discussed.
07/2008;
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ABSTRACT: We study the problem of Coulomb field-induced charging of the ground state in a system of 2D massive Dirac particles (gapped graphene). As in its 3D QED counterpart, the critical Coulomb coupling is renormalized to higher values, compared to the massless case. We find that in gapped graphene a novel supercritical regime is possible, where the screening charge is comparable to the impurity charge, thus leading to suppression of the Coulomb field at nanometer scales. We corroborate this with numerical solution of the tight-binding problem in the honeycomb lattice.
04/2008;
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ABSTRACT: We calculate exactly the vacuum polarization charge density in the field of a subcritical Coulomb impurity, Z|e|/r, in graphene. Our analysis is based on the exact electron Green's function, obtained by using the operator method, and leads to results that are exact in the parameter Zalpha, where alpha is the "fine-structure constant" of graphene. Taking into account also electron-electron interactions in the Hartree approximation, we solve the problem self-consistently in the subcritical regime, where the impurity has an effective charge Z(eff), determined by the localized induced charge. We find that an impurity with bare charge Z=1 remains subcritical, Z(eff)alpha<1/2, for any alpha, while impurities with Z=2, 3 and higher can become supercritical at certain values of alpha.
Physical Review Letters 02/2008; 100(7):076803. · 7.37 Impact Factor
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ABSTRACT: The weak ferromagnetism present in insulating La_{2}CuO_4 at low doping leads to a spin flop transition, and to transverse (interplane) hopping of holes in a strong external magnetic field. This results in a dimensional crossover 2D $\to$ 3D for the in-plane transport, which in turn leads to an increase of the hole's localization length and increased conduction. We demonstrate theoretically that as a consequence of this mechanism, a frequency-dependent jump of the in-plane ac hopping conductivity occurs at the spin flop transition. We predict the value and the frequency dependence of the jump. Experimental studies of this effect would provide important confirmation of the emerging understanding of lightly doped insulating La_{2-x}Sr_xCuO_4.
08/2007;
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ABSTRACT: We discuss the effect of electron-electron interactions on the static polarization properties of graphene beyond RPA. Divergent self-energy corrections are naturally absorbed into the renormalized coupling constant $\alpha$. We find that the lowest order vertex correction, which is the first non-trivial correlation contribution, is finite, and about 30% of the RPA result at strong coupling $\alpha \sim 1$. The vertex correction leads to further reduction of the effective charge. Finite contributions to dielectric screening are expected in all orders of perturbation theory.
07/2007;
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ABSTRACT: We study a Heisenberg S=1/2 ring-exchange antiferromagnet which exhibits a quantum phase transition from a spontaneously dimerized (valence bond solid) phase to a magnetically ordered (Neel) phase. We argue that the quantum transition is of unconventional nature; both singlet and triplet modes of high density condense as the transition is approached from the dimer side, signaling restoration of lattice symmetry. These features are consistent with "deconfined quantum criticality", of which the present model is believed to be the only example so far.
05/2007;
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ABSTRACT: We study the S=1/2 Heisenberg antiferromagnet on a square lattice with nearest-neighbor and plaquette four-spin exchanges (introduced by A.W. Sandvik, Phys. Rev. Lett. {\bf 98}, 227202 (2007).) This model undergoes a quantum phase transition from a spontaneously dimerized phase to N\'eel order at a critical coupling. We show that as the critical point is approached from the dimerized side, the system exhibits strong fluctuations in the dimer background, reflected in the presence of a low-energy singlet mode, with a simultaneous rise in the triplet quasiparticle density. We find that both singlet and triplet modes of high density condense at the transition, signaling restoration of lattice symmetry. In our approach, which goes beyond mean-field theory in terms of the triplet excitations, the transition appears sharp; however since our method breaks down near the critical point, we argue that we cannot make a definite conclusion regarding the order of the transition. Comment: 6 pages, 4 figures; published version
04/2007;
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ABSTRACT: We show that, due to the weak ferromagnetism of La$_{2-x}$Sr$_x$CuO$_4$, an
external magnetic field leads to a dimensional crossover 2D $\to$ 3D for the
in-plane transport. The crossover results in an increase of the hole's
localization length and hence in a dramatic negative magnetoresistance in the
variable range hopping regime. This mechanism quantitatively explains puzzling
experimental data on the negative magnetoresistance in the N\'eel phase of
La$_{2-x}$Sr$_x$CuO$_4$.
10/2006;
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ABSTRACT: We discuss the spiral spin density wave model and its application to explain properties of underdoped La$_{2-x}$Sr$_x$CuO$_4$. We argue that the spiral picture is theoretically well justified in the context of the extended $t-J$ model, and then show that it can explain a number of observed features, such as the location and symmetry of the incommensurate peaks in elastic neutron scattering, as well as the in-plane resistivity anisotropy. A consistent description of the low doping region (below 10% or so) emerges from the spiral formulation, in which the holes show no tendency towards any type of charge order and the physics is purely spin driven.
11/2005;
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ABSTRACT: We study the in-plane resistivity anisotropy in the spin-glass phase of the high-$T_{c}$ cuprates, on the basis of holes moving in a spiral spin background. This picture follows from analysis of the extended $t-J$ model with Coulomb impurities. In the variable-range hopping regime the resistivity anisotropy is found to have a maximum value of around 90%, and it decreases with temperature, in excellent agreement with experiments in La$_{2-x}$Sr$_x$CuO$_4$. In our approach the transport anisotropy is due to the non-collinearity of the spiral spin state, rather than an intrinsic tendency of the charges to self-organize.
07/2005;
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ABSTRACT: The main feature in the elastic neutron scattering of La2-xSrxCuO4 is the existence of incommensurate peaks with positions that jump from 45 degrees to 0 degrees at 5% doping. We show that the spiral state of the t-t(')-t('')-J model with realistic parameters describes these data perfectly. We explain why in the insulator the peak is at 45 degrees while it switches to 0 degrees precisely at the insulator-metal transition. The calculated positions of the peaks are in agreement with the data in both phases.
Physical Review Letters 04/2005; 94(9):097005. · 7.37 Impact Factor
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ABSTRACT: We analyze the t-t′-t″-J model at low doping δ⪡1 by chiral perturbation theory and show that the (1,0) spiral state is stabilized by the presence of t′, t″ above critical values around 0.2J, assuming t∕J=3.1. We find that the (magnon mediated) hole-hole interactions have an important effect on the region of charge stability in the space of parameters t′, t″, generally increasing stability, while the stability in the magnetic sector is guaranteed by the presence of spin quantum fluctuations (order from disorder effect). These conclusions are based on perturbative analysis performed up to two loops, with very good convergence.
Phys. Rev. B. 11/2004; 70(19).
