Finite Cluster Typical Medium Theory for Disordered Electronic Systems

TL;DR

This paper applies the typical medium dynamical cluster approach to study Anderson localization in three-dimensional disordered systems, highlighting the importance of spatial correlations and environment effects, and confirming the universality of the critical exponent.

Contribution

The study extends TMDCA to various disorder distributions, demonstrating its effectiveness and efficiency in accurately characterizing the Anderson transition with finite clusters.

Findings

TMDCA accurately reproduces the mobility edge re-entrance behavior.

Critical disorder strengths are correctly identified by TMDCA.

The critical exponent for the transition is universal across distributions.

Abstract

We use the recently developed typical medium dynamical cluster (TMDCA) approach~[Ekuma \etal,~\textit{Phys. Rev. B \textbf{89}, 081107 (2014)}] to perform a detailed study of the Anderson localization transition in three dimensions for the Box, Gaussian, Lorentzian, and Binary disorder distributions, and benchmark them with exact numerical results. Utilizing the nonlocal hybridization function and the momentum resolved typical spectra to characterize the localization transition in three dimensions, we demonstrate the importance of both spatial correlations and a typical environment for the proper characterization of the localization transition in all the disorder distributions studied. As a function of increasing cluster size, the TMDCA systematically recovers the re-entrance behavior of the mobility edge for disorder distributions with finite variance, obtaining the correct critical disorder strengths, and shows that the order parameter critical exponent for the Anderson localization transition is universal. The TMDCA is computationally efficient, requiring only a small cluster to obtain qualitative and quantitative data in good agreement with numerical exact results at a fraction of the computational cost. Our results demonstrate that the TMDCA provides a consistent and systematic description of the Anderson localization transition.