Diamagnetism of Graphene with Long-Range Scatterers

Abstract

The diamagnetic susceptibility of disordered monolayer graphene containing scatterers with long-range potential is calculated in a self-consistent Born approximation. Explicit numerical results are obtained for a Gaussian potential. The results show that the delta-function susceptibility in the ideal graphene is broadened by disorder and that the broadening is determined by the condition that states can be mixed with those at the Dirac point. For charged impurities, the susceptibility exhibits a double-peak structure as a function of the Fermi energy at zero temperature, due to the rapid decrease in effective scattering strength with the increase of the Fermi level.

Theory of Valley Hall Conductivity in Graphene with Gap

“…Figure 3 shows some examples of valley Hall conductivity in the clean limit in the case of scatterers with Gaussian potential for varying potential range d. We have assumed dk c = 10 in actual calculations. In this case, the results become a function of ε(γ/d) −1 , because there is only a single relevant energy scale γ/d corresponding to range d. [55][56][57] In the short-range limit d(γ/∆) −1 ≪ 1, the enhancement over the ideal conductivity is maximum and with the increase of d the enhancement is reduced. Even in the long-range limit d(γ/∆) −1 ≫ 1 the conductivity is larger and exhibits distinct double-peak structure, i.e., the maximum absolute value is larger than g s e 2 /(2h) outside the gap region.…”

“…The dependence on the direction of k can be eliminated in various ways as has previously been shown. [55][56][57][58] We shall briefly review such a method for the purpose of deriving explicit expressions for the valley Hall conductivity and its analytic result in the clean limit. We consider the system containing scatterers, described by the Hamiltonian:…”

Diamagnetism of Graphene with Gap in Nonuniform Magnetic Field

“…[68][69][70] However, calculations of susceptibility in nonuniform magnetic fields within this scheme are not feasible, because they involve considerable numerical computations.…”

Formula of Weak-Field Magnetoresistance in Graphene

“…The situation is essentially the same as in the case of the derivation of the diamagnetic susceptibility, 43 which has been used in many systems, including graphene, 17,18,24,37,38,44,45 molecular conductors, 27 and giant Rashba systems. 46 By taking the average, we haveĴ µ (R) →Ĵ µ /L 2 , with L being the linear dimension of the system, i.e.,…”