Hall Effect for Dirac Electrons in Graphene Exposed to an Abrikosov Flux Lattice

TL;DR

This study investigates how an Abrikosov flux lattice affects the Hall effect in graphene, revealing a density-dependent reduction in Hall conductivity due to Berry curvature levitation caused by non-uniform magnetic fields.

Contribution

The paper combines theoretical analysis and experimental measurements to show how non-uniform magnetic fields from an Abrikosov flux lattice influence the Hall effect in Dirac electrons in graphene, highlighting a novel Berry curvature effect.

Findings

Density-dependent reduction of Hall conductivity in graphene

Berry curvature levitation within broadened Landau levels

Experimental confirmation of Hall resistivity reduction below superconducting transition

Abstract

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.