  The proposals for realizing exotic particles through coupling of quantum Hall
effect to superconductivity involve spatially non-uniform magnetic fields. As a
step toward that goal, we study, both theoretically and experimentally, a
system of Dirac electrons exposed to an Abrikosov flux lattice. We
theoretically find that non-uniform magnetic field causes a carrier-density
dependent reduction of the Hall conductivity. Our studies show that this
reduction originates from a rather subtle effect: a levitation of the Berry
curvature within Landau levels broadened by the non-uniform magnetic field.
Experimentally, we measure the magneto-transport in a monolayer
graphene-hexagonal boron nitride - niobium diselenide (NbSe$_2$)
heterostructure, and find a density-dependent reduction of the Hall resistivity
of graphene as the temperature is lowered from above the superconducting
critical temperature of NbSe$_2$, when the magnetic field is uniform, to below,
where the magnetic field bunches into an Abrikosov flux lattice.
