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Register a new userNon-divergent Fermi velocity for interacting graphene at the Dirac point
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Recent experiments reveal a significant increase in the graphene Fermi velocity close to charge neutrality. This has widely been interpreted as a confirmation of the logarithmic divergence of the graphene Fermi velocity predicted by a perturbative approach. In this work, we reconsider this problem using functional bosonization techniques calculating the effects of electron interactions on the density of states non-perturbatively. We find that the renormalized velocity is {it finite} and independent of the high energy cut-off, and we argue that the experimental observations are better understood in terms of an anomalous dimension. Our results also represent a bosonized solution for interacting Weyl fermions in (2+1) dimensions at half-filing.
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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).
We have investigated the behavior of the resistance of graphene at the $n=0$ Landau Level in an intense magnetic field $H$. Employing a low-dissipation technique (with power $P<$3 fW), we find that, at low temperature $T$, the resistance at the Dirac point $R_0(H)$ undergoes a 1000-fold increase from $sim$10 k$Omega$ to 40 M$Omega$ within a narrow interval of field. The abruptness of the increase suggests that a transition to an insulating, ordered state occurs at the critical field $H_c$. Results from 5 samples show that $H_c$ depends systematically on the disorder, as measured by the offset gate voltage $V_0$. Samples with small $V_0$ display a smaller critical field $H_c$. Empirically, the steep increase in $R_0$ fits acccurately a Kosterlitz-Thouless-type correlation length over 3 decades. The curves of $R_0$ vs. $T$ at fixed $H$ approach the thermal-activation form with a gap $Deltasim$15 K as $Hto H_c^{-}$, consistent with a field-induced insulating state.
The electronic properties of graphene have been intensively investigated over the last decade, and signatures of the remarkable features of its linear Dirac spectrum have been displayed using transport and spectroscopy experiments. In contrast, the orbital magnetism of graphene, which is one of the most fundamental signature of the characteristic Berry phase of graphenes electronic wave functions, has not yet been measured in a single flake. In particular, the striking prediction of a divergent diamagnetic response at zero doping calls for an experimental test. Using a highly sensitive Giant Magnetoresistance sensor (GMR) we have measured the gate voltage-dependent magnetization of a single graphene monolayer encapsulated between boron nitride crystals. The signal exhibits a diamagnetic peak at the Dirac point whose magnetic field and temperature dependences agree with theoretical predictions starting from the work of Mc Clure cite{McClure1956}. Our measurements open a new field of investigation of orbital currents in graphene and 2D topological materials, offering a new means to monitor Berry phase singularities and explore correlated states generated by combined effects of Coulomb interactions, strain or moire potentials.
The electronic properties of non-interacting particles moving on a two-dimensional bricklayer lattice are investigated numerically. In particular, the influence of disorder in form of a spatially varying random magnetic flux is studied. In addition, a strong perpendicular constant magnetic field $B$ is considered. The density of states $rho(E)$ goes to zero for $Eto 0$ as in the ordered system, but with a much steeper slope. This happens for both cases: at the Dirac point for B=0 and at the center of the central Landau band for finite $B$. Close to the Dirac point, the dependence of $rho(E)$ on the system size, on the disorder strength, and on the constant magnetic flux density is analyzed and fitted to an analytical expression proposed previously in connection with the thermal quantum Hall effect. Additional short-range on-site disorder completely replenishes the indentation in the density of states at the Dirac point.
A Dirac-Fermi liquid (DFL)--a doped system with Dirac spectrum--is an important example of a non-Galilean-invariant Fermi liquid (FL). Real-life realizations of a DFL include, e.g., doped graphene, surface states of three-dimensional (3D) topological insulators, and 3D Dirac/Weyl metals. We study the optical conductivity of a DFL arising from intraband electron-electron scattering. It is shown that the effective current relaxation rate behaves as $1/tau_{J}propto left(omega^2+4pi^2 T^2right)left(3omega^2+8pi^2 T^2right)$ for $max{omega, T}ll mu$, where $mu$ is the chemical potential, with an additional logarithmic factor in two dimensions. In graphene, the quartic form of $1/tau_{J}$ competes with a small FL-like term, $proptoomega^2+4pi^2 T^2$, due to trigonal warping of the Fermi surface. We also calculated the dynamical charge susceptibility, $chi_mathrm{c}({bf q},omega)$, outside the particle-hole continua and to one-loop order in the dynamically screened Coulomb interaction. For a 2D DFL, the imaginary part of $chi_mathrm{c}({bf q},omega)$ scales as $q^2omegaln|omega|$ and $q^4/omega^3$ for frequencies larger and smaller than the plasmon frequency at given $q$, respectively. The small-$q$ limit of $mathrm{Im} chi_mathrm{c}({bf q},omega)$ reproduces our result for the conductivity via the Einstein relation.
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