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 (${\gamma }_3$), 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 ${\sigma }_0=8e^2/\left(\pi h\right)$ being the result in the absence of trigonal warping, ${\gamma }_3=0$]. We demonstrate that ${\gamma }_4\ne 0$ leads to the divergent conductivity ($\sigma \to \infty$) if ${\gamma }_3\ne 0$, or to the vanishing conductivity ($\sigma \to 0$) if ${\gamma }_3=0$. For realistic values of the tight-binding model parameters, ${\gamma }_3=0.3\mathrm{eV},{\gamma }_4=0.15\mathrm{eV}$ (and ${\delta }_{AB}=0$), the conductivity values are in the range $\sigma /{\sigma }_0\approx 4-5$ for $100\text{nm}<L<1\mu \mathrm{m}$, 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 $\sigma =\sigma \left(L\right)$ is no longer universal, the Fano factor approaches the pseudodiffusive value ($F\to 1/3$ for $L\to \infty$) in any case with nonvanishing $\sigma$ (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 ${\delta }_{AB}={\delta }_{AB}\left(T\right)$ showing that, for $0<T⩽T_c\approx 12\mathrm{K}$ and ${\delta }_{AB}\left(0\right)=1.5\mathrm{meV},\sigma \left(L\right)$ is noticeably affected by $T$ for $L\gtrsim 100$ nm.

• Received 9 December 2019
• Accepted 11 March 2020

DOI:https://doi.org/10.1103/PhysRevB.101.125425

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Published by the American Physical Society