Typical medium dynamical cluster approximation for the study of Anderson localization in three dimensions

Abstract

We develop a systematic typical medium dynamical cluster approximation that provides a proper description of the Anderson localization transition in three dimensions (3D). Our method successfully captures the localization phenomenon both in the low and large disorder regimes, and allows us to study the localization in different momenta cells, which renders the discovery that the Anderson localization transition occurs in a cell-selective fashion. As a function of cluster size, our method systematically recovers the reentrance behavior of the mobility edge and obtains the correct critical disorder strength for Anderson localization in 3D.

Study of off-diagonal disorder using the typical medium dynamical cluster approximation

“…35 In Ref. 35 we confirmed that the typical density of states vanishes for states which are localized and it is finite for extended states.…”

“…To include the effects of off-diagonal disorder, Gonis 27 extended the Molecular CPA, which uses a selfconsistently embedded finite size cluster to capture nonlocal corrections to the CPA. However, he criticized the MCPA for violating translational invariance and other critical properties of a valid quantum cluster theory 15,35 . In order to take into account such non-local effects on offdiagonal disorder models while maintaining translational invariance, we extend the BEB formalism using the DCA scheme [29][30][31] .…”

“…So far, the typical medium analysis has been applied to systems with only diagonal disorder 35,45 . In this paper, we develop a typical medium dynamical cluster approximation formalism capable of characterizing the localization transition in systems with both diagonal and off-diagonal disorder.…”

“…35 The TMDCA provides an accurate description of the Anderson localization transition for modest cluster sizes in three-dimensional models with diagonal disorder while recovering the TMT for a one-site cluster. In this work, we generalize our recently proposed TMDCA scheme to address the question of electron localization in systems with both diagonal and off-diagonal disorder.…”

“…These mean field approaches describe the effective medium using the average density of states which is not critical at the tran-sition 12,[35][36][37] . Thus, theories which rely on such averaged quantities will fail to properly characterize Anderson localization.…”