Theory of Coulomb drag in spatially inhomogeneous 2D materials

Coulomb drag is a favored experimental probe of Coulomb interactions between layers of 2D materials. In reality, these layers display spatial charge density fluctuations known as puddles due to various imperfections. A theoretical formalism for incorporating density inhomogeneity into calculations has however not been developed, making the understanding of experiments difficult. Here, we remedy this by formulating an effective medium theory of drag that applies in all 2D materials. We show that a number of striking features at zero magnetic field in graphene drag experiment which have not been explained by existing literature emerge naturally within this theory. Applying the theory to a phenomenological model of exciton condensation, we show that the expected divergence in drag resistivity is replaced by a peak that diminishes with increasing puddle strength. Given that puddles are ubiquitous in 2D materials, this work will be useful for a wide range of future studies.