Theory of Transport in Graphene with Long-Range Scatterers

Abstract

The density of states and conductivity are calculated for scatterers with nonzero range in monolayer graphene within a self-consistent Born approximation. For scatterers with a Gaussian potential, the minimum conductivity at the Dirac point remains universal in the clean limit, but increases with disorder and becomes nonuniversal for long-range scatterers. For charged impurities, we use the Thomas-Fermi approximation for the screening effect. The conductivity increases in proportion to the electron concentration in agreement with experiments and the minimum conductivity becomes about twice as large as the universal value.

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.…”

Diamagnetic Response of Disordered Graphene to Nonuniform Magnetic Field

“…[21][22][23][24][25] In this paper we use the self-consistent Born approximation assuming scatterers with potential range smaller than the typical electron wavelength (but larger than the lattice constant) in contrast to recent extensions to more general scatterers. 26,27) It should be mentioned that the orbital magnetism in uniform field was also studied for related materials, such as graphite intercalation compounds, [28][29][30] carbon nanotube, 11,[31][32][33] graphene ribbons, 34) few-layer graphenes, 3,19,35) bulk graphite, 36) bismuth, [37][38][39] and organic compounds having Dirac-like spectrum. 40) The paper is organized as follows: In x2, following a brief review on the electronic states, the diamagnetic susceptibility in ideal graphene, and a self-consistent Born approximation, we shall obtain an explicit expression for the susceptibility in the presence of disorder.…”

Bilayer Graphene with Long-Range Scatterers Studied in a Self-Consistent Born Approximation

“…This parameter is the same as that defined previously 13,15,16) for short-range scatterers with d ! 0 (W ¼ A À1 in refs.…”