Moiré-pattern fluctuations and electron-phason coupling in twisted bilayer graphene

In twisted bilayer graphene, long-wavelength lattice fluctuations are dominated by phasons: acoustic collective modes resulting from coherent superpositions of optical phonons. At 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 elastic and adhesion forces governing lattice relaxation. Shear deformations of the beating pattern dominate the electron-phason coupling. This coupling lifts the layer degeneracy of the Dirac cones at the corners of the moiré Brillouin zone, which could explain the observed fourfold (instead of eightfold) Landau level degeneracy. Electron-phason scattering gives rise to a linear-T resistivity that increases with decreasing twist angle due to the reduction of the stiffness of the soliton network. This contribution alone cannot explain the huge enhancement of the resistivity of the normal state close to the magic angle. I will discuss the connection between these soft collective modes and the widespread presence of twist angle disorder in the samples.