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 the 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 (NbSe₂) 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 NbSe₂, when the magnetic field is uniform, to below, where the magnetic field bunches into an Abrikosov flux lattice.

通过将量子霍尔效应耦合到超导性来实现外来粒子的建议涉及空间不均匀的磁场。为了朝这个目标迈进，我们在理论上和实验上都研究了暴露于Abrikosov通量晶格的Dirac电子系统。从理论上讲，我们发现非均匀磁场会导致载流子密度随霍尔电导率的降低而降低。我们的研究表明，这种降低源于一个相当微妙的效应：由于不均匀的磁场而使Landau能级内的Berry曲率悬浮。通过实验，我们测量了单层石墨烯-六方氮化硼-二硒化铌（NbSe ₂）异质结构，并发现当温度从均匀磁场的NbSe ₂的超导临界温度之上降至低于该温度的磁场时，石墨烯的霍尔电阻密度随密度的降低而降低，在此之下磁场聚束成Abrikosov通量格子。