# Moir\'e-pattern fluctuations and electron-phason coupling in twisted bilayer graphene

## TL;DR

This paper investigates how moiré-pattern fluctuations and electron-phason interactions in twisted bilayer graphene influence electronic properties, revealing mechanisms that affect Landau level degeneracy and resistivity, especially near magic angles.

## Contribution

It introduces a detailed analysis of electron-phason coupling in twisted bilayer graphene and its effects on electronic degeneracy and resistivity, highlighting the role of soliton network softness.

## Key findings

- Electron-phason coupling lifts Dirac cone degeneracy.
- Resistivity shows linear temperature dependence influenced by twist angle.
- Soliton network stiffness decreases near magic angles.

## Abstract

In twisted bilayer graphene, long-wavelength lattice fluctuations on the scale of the moir\'e period are dominated by phason modes, i.e., acoustic branches of the incommensurate lattice resulting from coherent superpositions of optical phonons. In the limit of small twist angles, these modes describe the sliding motion of stacking domain walls separating regions of partial commensuration. The resulting soliton network is a soft elastic manifold, whose reduced rigidity arises from the competition between intralayer (elastic) and interlayer (adhesion) forces governing lattice relaxation. Shear deformations of the beating pattern dominate the electron-phason coupling to the leading order in $t_{\perp}/t$, the ratio between interlayer and intralayer hopping parameters. This coupling lifts the layer degeneracy of the Dirac cones at the corners of the Moir\'e Brillouin zone, which could explain the observed 4-fold (instead of 8-fold) Landau level degeneracy. Electron-phason scattering gives rise to a linear-in-temperature contribution to the resistivity that increases with decreasing twist angle due to the reduction of the stiffness of the soliton network. This contribution alone, however, seems to be insufficient to explain the huge enhancement of the resistivity of the normal state close to the magic angle.