Low and high-energy localization landscapes for tight-binding Hamiltonians in 2D lattices

TL;DR

This paper extends the localization landscape theory to 2D lattice Hamiltonians, enabling accurate prediction of localized states' locations and energies in materials like graphene, thus advancing understanding of disorder effects in these systems.

Contribution

It introduces a systematic extension of localization landscape theory to discrete 2D lattices and higher dimensions, providing a new tool for analyzing localization in tight-binding models.

Findings

Accurately predicts localization sites and energies in 2D lattices.

Works for low and high energy regimes in honeycomb and hexagonal lattices.

Extends LL theory from continuous to discrete lattice systems.

Abstract

Localization of electronic wave functions in modern two-dimensional (2D) materials such as graphene can impact drastically their transport and magnetic properties. The recent localization landscape (LL) theory has brought many tools and theoretical results to understand such localization phenomena in the continuous setting, but with very few extensions so far to the discrete realm or to tight-binding Hamiltonians. In this paper, we show how this approach can be extended to almost all known 2D~lattices, and propose a systematic way of designing LL even for higher dimension. We demonstrate in detail how this LL theory works and predicts accurately not only the location, but also the energies of localized eigenfunctions in the low and high energy regimes for the honeycomb and hexagonal lattices, making it a highly promising tool for investigating the role of disorder in these materials.