Perturbative analysis of the conductivity in disordered monolayer and bilayer graphene

Abstract

The DC conductivity of monolayer and bilayer graphene is studied perturbatively for different types of disorder. In the case of monolayer, an exact cancellation of logarithmic divergences occurs for all disorder types. The total conductivity correction for a random vector potential is zero, while for a random scalar potential and a random gap it acquires finite corrections. We identify the diagrams which are responsible for these corrections and extrapolate the finite contributions to higher orders which gives us general expressions for the conductivity of weakly disordered monolayer graphene. In the case of bilayer graphene, a cancellation of all contributions for all types of disorder takes place. Thus, the minimal conductivity of bilayer graphene turns out to be very robust against disorder.

4 pages, 2 figures + supplementary material. Final version as published with PRB

References in corpus (10)

• Chiral tunneling and the Klein paradox in graphene
• Giant Intrinsic Carrier Mobilities in Graphene and Its Bilayer
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Charged Impurity Scattering in Graphene
• Measurement of Scattering Rate and Minimum Conductivity in Graphene
• Absence of interaction corrections in graphene conductivity
• Random gap model for graphene and graphene bilayers
• Diffusion in the random gap model of mono- and bilayer graphene
• Long-range correlations in disordered graphene
• Optical conductivity of graphene in the presence of random lattice deformations

Cited by in corpus (5)

• Renormalized transport properties of randomly gapped 2D Dirac fermions
• Dynamical symmetry breaking in a 2D electron gas with a spectral node
• Finite-size scaling in a 2D disordered electron gas with spectral nodes
• Linear response peculiarity of a two--dimensional Dirac electron gas at weak scattering
• Electron-electron interactions in non-equilibrium bilayer graphene