# DC conductivity of twisted bilayer graphene: Angle-dependent transport properties and effects of disorder

## TL;DR

This study calculates the in-plane DC conductivity of twisted bilayer graphene across various angles, electric fields, and disorder levels, revealing angle-dependent transport behaviors and the role of chiral boundary states, aligning with recent experiments.

## Contribution

It provides a detailed analysis of how twist angle, electric field, and vacancies influence the DC conductivity of TBLG, highlighting the preservation of chiral symmetry at high angles and boundary state contributions at low angles.

## Key findings

- High-angle TBLG shows doubled minimum conductivity similar to monolayer graphene.
- Low-angle TBLG conductivity depends on twist angle and disorder, losing protection.
- Chiral boundary states contribute to conductivity under electric fields at low angles.

## Abstract

The in-plane DC conductivity of twisted bilayer graphene (TBLG) is calculated using an expansion of the real-space Kubo-Bastin conductivity in terms of Chebyshev polynomials. We investigate within a tight-binding (TB) approach the transport properties as a function of rotation angle, applied perpendicular electric field and vacancy disorder. We find that for high-angle twists, the two layers are effectively decoupled, and the minimum conductivity at the Dirac point corresponds to double the value observed in monolayer graphene. This remains valid even in the presence of vacancies, hinting that chiral symmetry is still preserved. On the contrary, for low twist angles, the conductivity at the Dirac point depends on the twist angle and is not protected in the presence of disorder. Furthermore, for low angles and in the presence of an applied electric field, we find that the chiral boundary states emerging between AB and BA regions contribute to the DC conductivity, despite the appearance of strongly localized states in the AA regions. The results agree with recent conductivity experiments on twisted bilayer graphene.