Quantum corrections in the Boltzmann conductivity of graphene and their sensitivity to the choice of formalism

Abstract

Semiclassical spin-coherent kinetic equations can be derived from quantum theory with many different approaches (Liouville equation based approaches, nonequilibrium Green's functions techniques, etc.). The collision integrals turn out to be formally different, but coincide in textbook examples as well as for systems where the spin-orbit coupling is only a small part of the kinetic energy like in related studies on the spin Hall effect. In Dirac cone physics (graphene, surface states of topological insulators like Bi_{1-x}Sb_x, Bi_2Te_3 etc.), where this coupling constitutes the entire kinetic energy, the difference manifests itself in the precise value of the electron-hole coherence originated quantum correction to the Drude conductivity $\sim e^2/h\ast \ell k_F$. The leading correction is derived analytically for single and multilayer graphene with general scalar impurities. The often neglected principal value terms in the collision integral are important. Neglecting them yields a leading correction of order $(\ell k_F{)}^{-1}$, whereas including them can give a correction of order $(\ell k_F{)}^0$. The latter opens up a counterintuitive scenario with finite electron-hole coherent effects at Fermi energies arbitrarily far above the neutrality point regime, for example in the form of a shift $\sim e^2/h$ that only depends on the dielectric constant. This residual conductivity, possibly related to the one observed in recent experiments, depends crucially on the approach and could offer a setting for experimentally singling out one of the candidates. Concerning the different formalisms we notice that the discrepancy between a density matrix approach and a Green's function approach is removed if the Generalized Kadanoff-Baym Ansatz in the latter is replaced by an anti-ordered version.

31 pages, 1 figure. An important sign error has been rectified in the principal value terms in equation (52) in the vN & NSO expression. It has no implications for the results on the leading quantum correction studied in this paper. However, for the higher quantum corrections studied in arXiv:1304.3929 (see comment in the latter) the implications are crucial

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• Inter-band Coherence Response to Electric Fields in Crystals
• Finite Conductivity Minimum in Bilayer Graphene without Charge Inhomogeneities
• Relaxation mechanisms of the persistent spin helix
• Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling: I. Kinetic equation and anomalous Hall and spin-Hall effects
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• Theory of Conductivity of Chiral Particles