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.

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双层石墨烯哈密顿量中的电导率定标和对称破缺项的影响

我们研究了在低能量激发的有效哈密顿量中存在对称破坏项的情况下双层石墨烯的弹道电导率，例如三角翘曲项（${\gamma }_3$），破坏电子空穴对称性的层间跳变（${\gamma }_4$），以及交错的电位（${\delta }_{\mathrm{一种}乙}$）。先前显示，对于${\gamma }_3\ne 0$，而没有剩余的破坏对称性的术语（例如， ${\gamma }_4={\delta }_{\mathrm{一种}乙}=0$），电导率（$\sigma$）接近 $3{\sigma }_0$ 对于系统大小 $\mathrm{大号}\to \infty$ [与 ${\sigma }_0=8{Ë}^2/（\pi H）$ 是没有三角翘曲的结果， ${\gamma }_3=0$]。我们证明${\gamma }_4\ne 0$ 导致电导率发散（$\sigma \to \infty$）如果 ${\gamma }_3\ne 0$，或消失的电导率（$\sigma \to 0$）如果 ${\gamma }_3=0$。对于紧密绑定模型参数的实际值，${\gamma }_3=0.3\mathrm{电子伏特}，{\gamma }_4=0.15\mathrm{电子伏特}$ （和 ${\delta }_{\mathrm{一种}乙}=0$），电导率值在范围内 $\sigma /{\sigma }_0\approx 4-5$ 对于 $100\text{纳米}<\mathrm{大号}<\mathrm{1个}\mu \mathrm{米}$，与现有实验结果一致。交错的潜力（${\delta }_{\mathrm{一种}乙}\ne 0$）抑制零温度传输，导致 $\sigma \to 0$ 对于 $\mathrm{大号}\to \infty$。虽然$\sigma =\sigma （\mathrm{大号}）$ 不再通用，则Fano因子接近伪扩散值（$F\to \mathrm{1个}/3$ 对于 $\mathrm{大号}\to \infty$）在任何情况下都不会消失 $\sigma$ （除此以外， $F\to \mathrm{1个}$），表示传输受by逝波控制。就现象电位的现象学模型简要讨论了温度效应${\delta }_{\mathrm{一种}乙}={\delta }_{\mathrm{一种}乙}（Ť）$ 显示， $0<Ť⩽{Ť}_C\approx 12\mathrm{ķ}$ 和 ${\delta }_{\mathrm{一种}乙}（0）=1.5\mathrm{病毒}，\sigma （\mathrm{大号}）$ 受到明显影响 $Ť$ 对于 $\mathrm{大号}\gtrsim 100$ 纳米