Effective continuum model of twisted bilayer GeSe and origin of emerging one-dimensional mode

TL;DR

This paper develops an effective continuum model for twisted bilayer GeSe, revealing how moiré patterns induce one-dimensional flat bands and exploring the potential for dimensional crossover in this system.

Contribution

It introduces a local approximation-based continuum model for twisted bilayer GeSe and links moiré potential effects to atomic alignment and flat band formation.

Findings

Flat bands appear at larger angles due to large effective mass.

The flat bands are more strongly flattened in one direction.

The model suggests potential for exploring dimensional crossover.

Abstract

The electric structure of twisted bilayer GeSe, which shows a rectangular moir\'{e} pattern, is analyzed using a $\bm{k}\cdot\bm{p}$ type effective continuum model. The effective model is constructed on the basis of the the local approximation method, where the local lattice structure of a twisted bilayer system is approximated by its untwisted bilayer with parallel displacement, and the required parameters are fixed with the help of the first-principles method. By inspecting the twist angle dependence of the physical properties, we reveal a relation between the effective potential under moir\'{e} pattern and the alignment of the Ge atoms, and also the resultant one-dimensional flat band, where the band is flattened stronger in a specific direction than the perpendicular direction. Due to the relatively large effective mass of the original monolayers, the flat band with its band width as small as a few meV appear in a relatively large angle. This gives us an opportunity to explore the dimensional crossover in the twisted bilayer platform.