Weak localization as a probe of intervalley coherent order in graphene systems

Spontaneous intervalley coherent order is widely conjectured in many graphene multilayer systems, especially in moiré systems with twist induced flat bands. This type of order is hard to be confirmed, however, mainly because experimental signatures are limited. We find that when the valley number conservation in a graphene system is spontaneously broken by time-reversal invariant intervalley coherent order, interference between the time-reversed paths of mean-field quasiparticles can yield a quantum correction to the Drude conductivity. Intervalley coherent states can exhibit weak localization or antilocalization depending on whether they belong to the orthogonal or symplectic symmetry class. Quantum interference corrections to transport can be a smoking gun for intervalley coherence, provided that intervalley scattering induced by atomically sharp defects is negligible. Our analysis motivates low-temperature weak-field magnetoresistance measurements in graphene mutlilayers in which time-reversal invariant intervalley coherent order is suspected.