Hall Conductivity of Two-Dimensional Electrons in an Abrikosov Magnetic Flux Lattice

We study, both theoretically and experimentally, the Hall transport of two-dimensional electrons exposed to a magnetic field produced by an Abrikosov flux lattice. Our experiments on monolayer graphene-hBN-NbSe2 heterostructure demonstrate a substantial reduction in the Hall conductivity as the temperature is reduced from above the superconducting critical temperature of NbSe2, when the magnetic field is uniform, to below, where the magnetic field bunches into an Abrikosov flux lattice. We provide a quantitative explanation of this phenomenon by evaluating the cumulative Berry curvature of occupied states using a lattice model, while also taking account of disorder, and extrapolating to the continuum limit. A fundamental role is played by a correlation between the Berry curvature and the energy within Landau levels broadened by the non-uniform magnetic field.