Theory of moire twist angle disorder

Twist angle disorder (TAD) occurs ubiquitously in twist bilayer Van-der-Waals materials. Starting with a simple model of twisted hetero-bilayer transition metal dichalcogenides, which is described in the continuum limit by fermions experiencing a moiré potential, we propose a theory of weak TAD. Specifically, we model weak TAD as slow classical (quenched) fields that vary at a length scale much larger than the moiré lattice constant, and which couple to fermions through a phase factor. We obtain the disorder-induced correlation in the limits of both weak and strong moiré potential, and derive the resulting scattering time and transport properties.