Optical conductivity of a metal-insulator transition for the Anderson-Hubbard model in 3 dimensions away from 1/2 filling

TL;DR

This study numerically investigates the Anderson-Hubbard model in three dimensions away from half-filling, revealing how disorder and interactions influence the metal-insulator transition and ac conductivity behavior.

Contribution

It provides a detailed numerical analysis of the Anderson-Hubbard model, highlighting the role of magnetic moments and disorder in the metal-insulator transition.

Findings

Weak interactions increase the density of states and conductivity at low frequencies.

Large disorder and interactions suppress the density of states and conductivity, inducing a transition.

Magnetic moments are crucial for the suppression of the density of states and the transition.

Abstract

We have completed a numerical investigation of the Anderson-Hubbard model for three-dimensional simple cubic lattices using a real-space self-consistent Hartree-Fock decoupling approximation for the Hubbard interaction. In this formulation we treat the spatial disorder exactly, and therefore we account for effects arising from localization physics. We have examined the model for electronic densities well away 1/2 filling, thereby avoiding the physics of a Mott insulator. Several recent studies have made clear that the combined effects of electronic interactions and spatial disorder can give rise to a suppression of the electronic density of states, and a subsequent metal-insulator transition can occur. We augment such studies by calculating the ac conductivity for such systems. Our numerical results show that weak interactions enhance the density of states at the Fermi level and the low-frequency conductivity, there are no local magnetic moments, and the ac conductivity is Drude-like. However, with a large enough disorder strength and larger interactions the density of states at the Fermi level and the low-frequency conductivity are both suppressed, the conductivity becomes non-Drude-like, and these phenomena are accompanied by the presence of local magnetic moments. The low-frequency conductivity changes from a sigma-sigma_dc omega^{1/2} behaviour in the metallic phase, to a sigma omega^2 behaviour in the nonmetallic regime. Our numerical results show that the formation of magnetic moments is essential to the suppression of the density of states at the Fermi level, and therefore essential to the metal-insulator transition.