Unfolding energy spectra of multi-periodicity materials

TL;DR

This paper introduces a novel multi-space unfolding scheme to analyze energy spectra of multi-periodic materials like twisted bilayer graphene, overcoming limitations of traditional single-cell methods and revealing velocity renormalization effects.

Contribution

The paper presents a new multi-space unfolding method that accurately analyzes complex energy spectra of multi-periodic systems, demonstrated on twisted bilayer graphene.

Findings

Conventional unfolding schemes fail for multi-periodic systems.

The new multi-space scheme successfully reveals velocity renormalization.

Validated the method's effectiveness on twisted bilayer graphene.

Abstract

We propose a new unfolding scheme to analyze energy spectra of complex large-scale systems which are inherently of multi-periodicity. Considering twisted bilayer graphene (tBLG) as an example, we first show that the conventional unfolding scheme in the past using a single primitive-cell representation causes serious problems in analyses of the energy spectra. We then introduce our multi-space representation scheme in the unfolding method and clarify its validity for tBLG. Velocity renormalization of Dirac electrons in tBLG is elucidated in the present unfolding scheme.