安德森局域化的Landau-Ginzburg理论
Landau-Ginzburg Theory for Anderson localization
摘要：
典型介质理论通过自洽地计算几何平均（典型）局域态密度（LDOS），在概念上提供了安德森局域化的最简单的序参量描述。在这里，我们展示了如何空间相关性也可以在这样一个自洽的理论，利用标准的朗道方法，允许（慢）空间波动的序参量，并进行适当的梯度展开。我们的理论结果提供了洞察到最近的STM实验，这是用来可视化附近的金属绝缘体过渡$Ga_{1-x}Mn_{x}As.$的空间波动的电子波函数。我们表明，在我们的理论，实验的所有功能可以考虑的无序重整化的长程库仑相互作用的模型。这包括赝能隙的形成，$C(R)\sim\frac{1}{R}$形式的LDOS自相关函数，和$ζ\sim\frac{1}{E}$能量依赖的相关长度在临界状态。
英文摘要：
The Typical Medium Theory provides conceptually the simplest order parameter description of Anderson localization by self-consistently calculating the geometrically-averaged (typical) local density of states (LDOS). Here we show how spatial correlations can also be captured within such a self-consistent theory, by utilizing the standard Landau method of allowing for (slow) spatial fluctuations of the order parameter, and performing an appropriate gradient expansion. Our theoretical results provide insight into recent STM experiments, which were used to visualize the spatially fluctuating electronic wave functions near the metal insulator transition in $Ga_{1-x}Mn_{x}As.$ We show that, within our theory, all features of the experiment can be accounted for by considering a model of disorder renormalized by long-range Coulomb interactions. This includes the pseudogap formation, the $C(R)\sim\frac{1}{R}$ form of the LDOS autocorrelations function, and the $ζ\sim\frac{1}{E}$ energy dependence of the correlation length at criticality.
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