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 effective Hamiltonian for low-energy excitations, such as the trigonal-warping term (${\gamma }_3$), the electron-hole symmetry breaking interlayer hopping (${\gamma }_4$), and the staggered potential (${\delta }_{AB}$). Earlier, it was shown that for ${\gamma }_3\ne 0$, in the absence of remaining symmetry-breaking terms (i.e., ${\gamma }_4={\delta }_{AB}=0$), the conductivity ($\sigma$) approaches the value of $3{\sigma }_0$ for the system size $L\to \infty$ (with ${\sigma }_0=8e^2/(\pi h)$ being the result in the absence of trigonal warping, ${\gamma }_3=0$). We demonstrate that ${\gamma }_4\ne 0$ leads to the divergent conductivity if ${\gamma }_3\ne 0$, or to the vanishing conductivity if ${\gamma }_3=0$. For realistic values of the tight-binding model parameters, ${\gamma }_3=0.3$eV, ${\gamma }_4=0.15$eV (and ${\delta }_{AB}=0$), the conductivity values are in the range of $\sigma /{\sigma }_0\approx 4-5$ for $100$nm$<L<1\mu$m, in agreement with existing experimental results. The staggered potential (${\delta }_{AB}\ne 0$) suppresses zero-temperature transport, leading to $\sigma \to 0$ for $L\to \infty$. Although $\sigma =\sigma (L)$ is no longer universal, the Fano factor approaches the pseudodiffusive value ($F\to 1/3$ for $L\to \infty$) in any case with non-vanishing $\sigma$ (otherwise, $F\to 1$) signaling the transport is ruled by evanescent waves. Temperature effects are briefly discussed in terms of a phenomenological model for staggered potential ${\delta }_{AB}={\delta }_{AB}(T)$ showing that, for $0<T⩽T_c\approx 12$K and ${\delta }_{AB}(0)=1.5$meV, $\sigma (L)$ is noticeably affected by $T$ for $L\gtrsim 100$nm.

RevTeX, 10 pages, 6 figures