Nearsightedness in Materials with Indirect Band Gaps

TL;DR

This paper analyzes the exponential decay of the density matrix in materials with indirect band gaps using a tight binding model, providing refined estimates for decay rates in homogeneous systems with localized perturbations.

Contribution

It offers a sharper estimate for the decay rate of the density matrix in materials with indirect band gaps, extending previous work to small band gap systems.

Findings

Established a sharp exponential decay estimate in reciprocal space.

Refined previous estimates for systems with small band gaps.

Applicable to homogeneous systems with localized perturbations.

Abstract

We investigate the nearsightedness property in the linear tight binding model at zero Fermi-temperature. We focus on the decay property of the density matrix for materials with indirect band gaps. By representing the density matrix in reciprocal space, we establish a qualitatively sharp estimate for the exponential decay rate in homogeneous systems, possibly with localized perturbations. This work refines the estimates presented in (Ortner, Thomas & Chen, 2020) for systems with small band gaps.