大型金属正方形网络电导率的Al'tshuler-Aronov修正
Al'tshuler-Aronov correction to the conductivity of a large metallic square network
摘要：
考虑了电子-电子相互作用对弱无序金属电导率的修正（Al'tshuler-Aronov修正）$Δσ_\mathrm{ee}$。修正与拉普拉斯算子的谱行列式有关。被认为是一个大的正方形金属网络的情况下。发现$Δσ_\mathrm{ee}(L_T)$作为热长度$L_T$的函数的变化非常类似于弱局域化$Δσ_\mathrm{WL}(L_ϕ)$作为相位相干长度的函数的变化。我们对$Δσ_\mathrm{ee}$的结果在已知的一维和二维结果之间插值，但是进入$Δσ_\mathrm{ee}$表达式的相互作用参数保持一维行为。非常令人惊讶的是，结果非常接近$L_T\sim{a}/2$的2d对数行为，其中$a$是晶格参数。
英文摘要：
We consider the correction $Δσ_\mathrm{ee}$ due to electron-electron interaction to the conductivity of a weakly disordered metal (Al'tshuler-Aronov correction). The correction is related to the spectral determinant of the Laplace operator. The case of a large square metallic network is considered. The variation of $Δσ_\mathrm{ee}(L_T)$ as a function of the thermal length $L_T$ is found very similar to the variation of the weak localization $Δσ_\mathrm{WL}(L_ϕ)$ as a function of the phase coherence length. Our result for $Δσ_\mathrm{ee}$ interpolates between the known 1d and 2d results, but the interaction parameter entering the expression of $Δσ_\mathrm{ee}$ keeps a 1d behaviour. Quite surprisingly, the result is very close to the 2d logarithmic behaviour already for $L_T\sim{a}/2$, where $a$ is the lattice parameter.
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