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

Abstract

Semiclassical spin-coherent kinetic equations can be derived from quantum theory by manydifferent approaches (Liouville equation based approaches, nonequilibrium Green’s functiontechniques, etc). The collision integrals turn out to be formally different, but coincidein textbook examples as well as for systems where the spin–orbit coupling isonly a small part of the kinetic energy like in related studies on the spin Halleffect. In Dirac cone physics (graphene, surface states of topological insulators likeBi1 − xSbx,Bi2Te3 etc), where this coupling constitutes the entire kinetic energy, the difference manifests itselfin the precise value of the electron–hole coherence originated quantum correction tothe Drude conductivity . The leading correction is derived analytically for single and multilayer graphene withgeneral scalar impurities. The often neglected principal value terms in the collision integralare important. Neglecting them yields a leading correction of order , whereas including them can give a correction of order . The latter opens up a counterintuitive scenario with finite electron–hole coherent effects atFermi energies arbitrarily far above the neutrality point regime, for example in the form of a shiftδσ ∼ e2/h that only depends on the dielectric constant. This residual conductivity, possibly related tothe one observed in recent experiments, depends crucially on the approach and could offera setting for experimentally singling out one of the candidates. Concerning the differentformalisms we notice that the discrepancy between a density matrix approach and aGreen’s function approach is removed if the generalized Kadanoff–Baym Ansatzin the latter is replaced by an anti-ordered version. This issue of Ansatz mayalso be important for Boltzmann type treatments of graphene beyond a linearresponse.