# The emergence of one-dimensional channels in marginal-angle twisted bilayer graphene

## TL;DR

This paper extends the continuum model for twisted bilayer graphene to include lattice relaxation and channel formation at very small twist angles, revealing complex quasi-one-dimensional electronic states under bias.

## Contribution

It introduces a comprehensive method combining atomic relaxation, projection of hopping parameters, and expanded harmonics to accurately describe electronic structures at marginal twist angles.

## Key findings

- Identification of complex quasi-one-dimensional states under bias.
- Demonstration of the importance of lattice relaxation in electronic structure.
- Enhanced continuum model accuracy at small twist angles.

## Abstract

We generalize the continuum model for Moir\'e structures made from twisted graphene layers, in order to include lattice relaxation and the formation of channels at very small (marginal) twist angles. We show that a precise description of the electronic structure at such small angles can be achieved by i) calculating first the relaxed atomic structure, ii) projecting the interlayer electronic hopping parameters using a suitable basis of Bloch states, and iii) increasing the number of harmonics in the continuum approximation to interlayer hopping. The results show a complex structure of quasi one dimensional states when a finite bias is applied.