Hierarchy of gaps and magnetic minibands in graphene in the presence of the Abrikosov vortex lattice

TL;DR

This paper investigates the electronic band structure of graphene under a magnetic field created by an Abrikosov vortex lattice, revealing unique miniband features and their implications for quantum Hall states.

Contribution

It provides a detailed analysis of the magnetic miniband spectrum in graphene influenced by a vortex lattice, highlighting the existence of non-dispersive bands and Dirac-type dispersions.

Findings

Presence of a non-dispersive zero-energy miniband.

Large gaps separating minibands suggest quantum Hall effect persistence.

Identification of miniband merging points with Dirac dispersion.

Abstract

We determine the structure of band and gaps in graphene encapsulated in hexagonal boron nitride and subjected to magnetic field of Abrikosov lattice of vortices in the underlying superconducting film. The spectrum features one non-dispersive magnetic miniband at zero energy, separated by the largest gaps in the miniband spectrum from a pair of minibands resembling slightly broadened first Landau levels in graphene, suggesting the persistence of $\nu = \pm 2$ quantum Hall effect states. Also, we identify occasional merging point of magnetic minibands which feature Dirac-type dispersion at the consecutive miniband edges.