Generalized Multiband Typical Medium Dynamical Cluster Approximation: Application to (Ga,Mn)N

TL;DR

This paper extends the multiband typical medium dynamical cluster approximation to handle complex disordered systems, applying it to (Ga,Mn)N to analyze localization and potential metallic behavior at certain doping levels.

Contribution

The authors introduce a generalized formalism for multiband disordered systems with improved numerical stability, and apply it to a real material to study localization phenomena.

Findings

Impurity band in (Ga,Mn)N is fully localized for Mn concentration x<0.03.

For 0.03<x<0.10, impurity states are delocalized but at the mobility edge.

System remains insulating within experimental doping limits due to Anderson localization.

Abstract

We generalize the multiband typical medium dynamical cluster approximation and the formalism introduced by Blackman, Esterling and Berk so that it can deal with localization in multiband disordered systems with both diagonal and off-diagonal disorder with complicated potentials. We also introduce a new ansatz for the angle resolved typical density of states that greatly improves the numerical stability of the method while preserving the independence of scattering events at different frequencies. Starting from the first-principles effective Hamiltonian, we apply this method to the diluted magnetic semiconductor Ga$_{1-x}$Mn$_x$N, and find the impurity band is completely localized for Mn concentrations $x<0.03$ while for $0.03 <x<0.10$ the impurity band has delocalized states but the chemical potential resides at or above the mobility edge. So, the system is always insulating within the experimental compositional limit ($x\approx 0.10$) due to Anderson localization. However, for $0.03 <x<0.10$ hole doping could make the system metallic allowing double exchange mediated, or enhanced, ferromagnetism. The developed method is expected to have a large impact on first-principles studies of Anderson localization.