Straintronics and twistronics in bilayer graphene

TL;DR

This paper explores how twist and strain in bilayer graphene can be engineered to control electronic properties, revealing strain as a powerful tool for tuning flat bands and topological phases.

Contribution

It introduces a global method for constructing supercells with arbitrary twist and strain, and analyzes their effects on band structure and topology using atomistic and continuum models.

Findings

Strain can significantly narrow bands beyond the magic angle.

Shear strain causes stronger lattice distortion than uniaxial strain.

Strain induces topological transitions and affects electron-electron interactions.

Abstract

The interplay of twist and strain in bilayer graphene enables the formation of moir\'e patterns and narrow bands that host correlated and topological phases. While magic-angle twisted bilayer graphene has been widely studied, strain provides an additional and realistic control knob for band engineering. In this work, we first generate a global method to construct commensurate supercells for arbitrary twist and heterostrain. Then, using atomistic tight-binding and strain-extended continuum models to study the commensurate structures, we identify configurations that minimize the bandwidth beyond the magic angle. The results reveal a strong dependence of band narrowing and topology on strain type, magnitude, direction and lattice relaxation. Particularly, shear strain produces a stronger distortion than uniaxial strain. Including electron-electron interactions through a self-consistent Hartree potential shows that strain broadens the bare bands while reducing electrostatic renormalization. Strain also drives topological transitions as the narrow and remote bands hybridize, establishing twisted and strained bilayer graphene as a tunable platform for flat-band and topological phenomena.