Electron-phonon scattering and in-plane electric conductivity in twisted bilayer graphene

TL;DR

This paper investigates how the in-plane electrical conductivity of twisted bilayer graphene varies with twist angle and temperature, revealing distinct regimes and the influence of electron-phonon interactions and external electric fields.

Contribution

It provides a comprehensive analysis of transport properties across different twist angles using a combined theoretical approach, highlighting the impact of topological transitions.

Findings

Conductivity is angle-dependent, with three distinct regimes identified.

At large angles, conductivity is temperature-independent below 10 K.

Small angles show a significant drop in conductivity and complex energy dependence.

Abstract

We have surveyed the in-plane transport properties of the graphene twist bilayer using (i) a low-energy effective Hamiltonian for the underlying electronic structure, (ii) an isotropic elastic phonon model, and (iii) the linear Boltzmann equation for elastic electron-phonon scattering. We find that transport in the twist bilayer is profoundly sensitive to the rotation angle of the constituent layers. Similar to the electronic structure of the twist bilayer the transport is qualitatively different in three distinct angle regimes. At large angles ($\theta > \,\approx\!\!10^\circ$) and at temperatures below an interlayer Bloch-Gr\"uneisen temperature of $\approx 10$~K the conductivity is independent of the twist angle i.e. the layers are fully decoupled. Above this temperature the layers, even though decoupled in the ground state, are re-coupled by electron-phonon scattering and the transport is different both from single layer graphene as well as the Bernal bilayer. In the small angle regime $\theta <\,\approx\!\!2^\circ$ the conductivity drops by two orders of magnitude and develops a rich energy dependence, reflecting the complexity of the underlying topological changes (Lifshitz transitions) of the Fermi surface. At intermediate angles the conductivity decreases continuously as the twist angle is reduced, while the energy dependence of the conductivity presents two sharp transitions, that occur at specific angle dependent energies, and that may be related to (i) the well studied van Hove singularity of the twist bilayer and (ii) a Lifshitz transition that occurs when trigonally placed electron pockets decorate the strongly warped Dirac cone. We examine the role of a layer perpendicular electric field finding that it affects the conductivity strongly at low temperatures whereas this effect is washed out by Fermi smearing at room temperatures.