Formula of Weak-Field Magnetoresistance in Graphene

Abstract

The formula of weak-field magnetoconductivity ∆σ(B) proportional to B 2 , with B the strength of a magnetic field, is derived for systems corresponding to monolayer and bilayer graphenes. It is represented by Feynman diagrams given by three hexagons. In order to see qualitative features of the magnetoconductivity, it is calculated for monolayer graphene in a constant broadening approximation, in which a single imaginary self-energy is introduced. The results show that −∆σ(B) is exactly the same as the counter term due to the Hall current in the energy region away from zero energy, leading to the vanishing magnetoresistance in the Hall bar geometry. In the vicinity of zero energy, −∆σ(B) exhibits a prominent double-peak structure similar to that of the counter term. However, its absolute value becomes slightly smaller than the counter term, giving negative magnetoresistance having double-dip structure.

Theory of Weak-Field Magnetoresistance in Bilayer Graphene

“…The formula of the magnetoconductivity ∆σ proportional to B 2 has been derived in a previous paper, 15 -0.5 0.0 0.5 by extending the procedure used for the weak-field Hall effect. 34,35 It is given by Eq.…”

“…(41) of Ref. 15 and described by the Feynman diagrams given by three hexagons shown in Fig. 1 of Ref.…”

“…1 of Ref. 15. It was explicitly calculated in monolayer graphene first within a constant broadening approximation 15 and then in a more elaborate selfconsistent Born approximation.…”

“…15. It was explicitly calculated in monolayer graphene first within a constant broadening approximation 15 and then in a more elaborate selfconsistent Born approximation. 22 In the following, we use the same approximations and therefore cannot discuss interference effects such as described by maximally crossed diagrams, [36][37][38] leading to weak localization behavior.…”

“…[7][8][9][10][11][12][13][14] The purpose of this paper is to calculate the weak-field magnetoconductivity, correction to the conductivity proportional to B 2 with magnetic field B, in bilayer graphene within a self-consistent Born approximation, using a formula derived previously. 15 In monolayer graphene conduction and valence bands with linear dispersion cross at the K and K' points located at a Brillouin-zone corner. 16,17 In bilayer graphene, this band structure is modified by interlayer interactions.…”