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

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 ($γ_3$), the electron-hole symmetry breaking interlayer hopping ($γ_4$), and the staggered potential ($δ_{AB}$). Earlier, it was shown that for $γ_3\neq{}0$, in the absence of remaining symmetry-breaking terms (i.e., $γ_4=δ_{AB}=0$), the conductivity ($σ$) approaches the value of $3σ_0$ for the system size $L\rightarrow{}\infty$ (with $σ_0=8e^2/(πh)$ being the result in the absence of trigonal warping, $γ_3=0$). We demonstrate that $γ_4\neq{}0$ leads to the divergent conductivity if $γ_3\neq{}0$, or to the vanishing conductivity if $γ_3=0$. For realistic values of the tight-binding model parameters, $γ_3=0.3\,$eV, $γ_4=0.15\,$eV (and $δ_{AB}=0$), the conductivity values are in the range of $σ/σ_0\approx{}4-5$ for $100\,$nm$\ <L<1\,μ$m, in agreement with existing experimental results. The staggered potential ($δ_{AB}\neq{}0$) suppresses zero-temperature transport, leading to $σ\rightarrow{}0$ for $L\rightarrow{}\infty$. Although $σ=σ(L)$ is no longer universal, the Fano factor approaches the pseudodiffusive value ($F\rightarrow{}1/3$ for $L\rightarrow{}\infty$) in any case with non-vanishing $σ$ (otherwise, $F\rightarrow{}1$) signaling the transport is ruled by evanescent waves. Temperature effects are briefly discussed in terms of a phenomenological model for staggered potential $δ_{AB}=δ_{AB}(T)$ showing that, for $0<T\leqslant{}T_c\approx{}12\,$K and $δ_{AB}(0)=1.5\,$meV, $σ(L)$ is noticeably affected by $T$ for $L\gtrsim{}100\,$nm.