Localization in the Incommensurate Systems: A Plane Wave Study via Effective Potentials

TL;DR

This paper introduces a plane wave method to analyze localization and spectral properties of incommensurate systems using effective potentials, offering a new computational approach in condensed matter physics.

Contribution

The study develops a novel plane wave approach for effective potentials in incommensurate systems, enabling analysis of localization and spectrum distribution.

Findings

Effective potentials can infer electron localization.

Spectrum distribution can be derived from effective potentials.

Numerical experiments validate the method's effectiveness.

Abstract

In this paper, we apply the effective potentials in the localization landscape theory (Filoche et al., 2012, Arnold et al., 2016) to study the spectral properties of the incommensurate systems. We uniquely develop a plane wave method for the effective potentials of the incommensurate systems and utilize that, the localization of the electron density can be inferred from the effective potentials. Moreover, we show that the spectrum distribution can also be obtained from the effective potential version of Weyl's law. We perform some numerical experiments on some typical incommensurate systems, showing that the effective potential provides an alternative tool for investigating the localization and spectrum distribution of the systems.