Hall effect for Dirac electrons in graphene exposed to an Abrikosov flux lattice

¹ Department of Physics, 104 Davey Lab, The Pennsylvania State University - University Park, PA 16802, USA
² Department of Physics, Indian Institute of Science - Bangalore 560012, India
³ Tata Institute of Fundamental Research - Homi Bhabha Road, Colaba, Mumbai 400 005, India
⁴ National Institute for Materials Science - Namiki 1-1, Ibaraki 305-0044, Japan

Received: 7 October 2020
Accepted: 20 October 2020

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 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.