Dielectric response of Anderson and pseudogapped insulators

TL;DR

This paper investigates the dielectric response of Anderson insulators across dimensions, revealing a proportionality to the square of the localization length, and explores how electron-electron interactions influence dielectric properties in various materials.

Contribution

It provides a detailed analysis combining analytic and numerical methods to challenge previous effective-medium approximations and examines interaction effects on dielectric constants in disordered insulators.

Findings

Dielectric polarizability scales with the square of the localization length.

Electron-electron interactions modify the dielectric constant in large localization length materials.

Phonon-mediated attraction affects dielectric response, detectable via magnetic field response.

Abstract

Using a combination of analytic and numerical methods, we study the polarizability of a (non-interacting) Anderson insulator in one, two, and three dimensions and demonstrate that, in a wide range of parameters, it scales proportionally to the square of the localization length, contrary to earlier claims based on the effective-medium approximation. We further analyze the effect of electron-electron interactions on the dielectric constant in quasi-1D, quasi-2D and 3D materials with large localization length, including both Coulomb repulsion and phonon-mediated attraction. The phonon-mediated attraction (in the pseudogapped state on the insulating side of the Superconductor-Insulator Transition) produces a correction to the dielectric constant, which may be detected from a linear response of a dielectric constant to an external magnetic field.