# Lattice relaxation and energy band modulation in twisted bilayer graphenes

## TL;DR

This paper develops a continuum theory to analyze lattice relaxation in twisted bilayer graphene and demonstrates how relaxation significantly alters electronic properties, including band gaps and Fermi velocity enhancements.

## Contribution

It introduces a new effective continuum model for lattice relaxation in TBG and reveals its impact on electronic band structure, especially at small twist angles.

## Key findings

- Relaxed lattice reduces AA-stacking area and forms a triangular domain structure.
- Energy gaps up to 20meV open at superlattice subband edges due to relaxation.
- Lattice relaxation enhances the Fermi velocity compared to non-relaxed models.

## Abstract

We theoretically study the lattice relaxation in the twisted bilayer graphene (TBG) and its effect on the electronic band structure. We develop an effective continuum theory to describe the lattice relaxation in general TBGs and obtain the optimized structure to minimize the total energy. At small rotation angles $< 2^{\circ}$, in particular, we find that the relaxed lattice drastically reduces the area of AA-stacking region, and form a triangular domain structure with alternating AB and BA stacking regions. We then investigate the effect of the domain formation on the electronic band structure. The most notable change from the non-relaxed model is that an energy gap up to 20meV opens at the superlattice subband edges on the electron and hole sides. We also find that the lattice relaxation significantly enhances the Fermi velocity, which was strongly suppressed in the non-relaxed model.