Influence of Trigonal Warping on Interference Effects in Bilayer Graphene

Bilayer graphene (two coupled graphitic monolayers arranged according to Bernal stacking) is a two-dimensional gapless semiconductor with a peculiar electronic spectrum different from the Dirac spectrum in the monolayer material. In particular, the electronic Fermi line in each of its valleys has a strong $\mathbf{p}\to -\mathbf{p}$ asymmetry due to trigonal warping, which suppresses the weak localization effect. We show that weak localization in bilayer graphene may be present only in devices with pronounced intervalley scattering, and we evaluate the corresponding magnetoresistance.

Figure 1

Fermi lines (solid lines) in the vicinity of two inequivalent valleys ${\mathbf{K}}_{+}$ and ${\mathbf{K}}_{-}$ of the hexagonal Brillouin zone (dashed line). Trigonal warping produces asymmetry of the dispersion at each valley $ϵ({\mathbf{K}}_{\pm },\mathbf{p})\ne ϵ({\mathbf{K}}_{\pm },-\mathbf{p})$, where momentum $\mathbf{p}$ is determined with respect to the center of the valley, but the effects of warping in the valleys have opposite signs, $ϵ({\mathbf{K}}_{\pm },\mathbf{p})=ϵ({\mathbf{K}}_{\mp },-\mathbf{p})$. The bilayer lattice configuration is described in detail in 12.