Conductivity scaling and the effects of symmetry-breaking terms in bilayer graphene Hamiltonian

Abstract

We study the ballistic conductivity of bilayer graphene in the presence of symmetry-breaking terms in an effective Hamiltonian for low-energy excitations, such as the trigonal-warping term (γ3), the electron-hole symmetry-breaking interlayer hopping (γ4), and the staggered potential (δAB). Earlier, it was shown that for γ3≠0, in the absence of remaining symmetry-breaking terms (i.e., γ4=δAB=0), the conductivity (σ) approaches the value of 3σ0 for the system size L→∞ [with σ0=8e2/(πh) being the result in the absence of trigonal warping, γ3=0]. We demonstrate that γ4≠0 leads to the divergent conductivity (σ→∞) if γ3≠0, or to the vanishing conductivity (σ→0) if γ3=0. For realistic values of the tight-binding model parameters, γ3=0.3eV,γ4=0.15eV (and δAB=0), the conductivity values are in the range σ/σ0≈4-5 for 100nm