Low-energy dynamical response of an Anderson insulator with local attraction

TL;DR

This paper investigates how local attraction affects the low-energy dynamical response of an Anderson insulator, revealing that interactions mainly quantitatively suppress conductivity without changing its fundamental low-frequency behavior.

Contribution

It demonstrates that local attraction modifies the Mott resonances in Anderson insulators, preserving the asymptotic form of conductivity but reducing its magnitude.

Findings

Low-energy response is suppressed by local attraction.

Mott formula's asymptotic behavior remains unchanged.

Reduction in response is mainly quantitative, not qualitative.

Abstract

The low-frequency dynamical response of an Anderson insulator is dominated by so-called Mott resonances: hybridization of pairs of states close in energy, but separated spatially. We study the effect of interaction on Mott resonances in the model of spinful fermions (electrons) with local attraction. This model is known to exhibit a so-called pseudogap: a suppression of the low-energy single-particle excitations. Correspondingly, the low-energy dynamical response is also reduced. However this reduction has mostly quantitative character. In particular, the Mott formula for frequency-dependent conductivity preserves its functional asymptotic behavior at low frequencies, but with a small numerical prefactor. This result can be explained in terms of Mott resonances for electron pairs instead of single electrons.