Fractional quantum Hall coexistence phases in higher Landau levels of graphene

TL;DR

This paper explores the complex coexistence of fractional quantum Hall phases in higher Landau levels of graphene, revealing a variety of symmetry-broken states including valley and spin entangled phases.

Contribution

It uncovers a richer set of symmetry-broken phases in higher Landau levels of graphene compared to the lowest level, including novel valley and spin entangled ferromagnetic and antiferromagnetic states.

Findings

Discovery of valley polarized and equatorial ferromagnets in higher Landau levels

Identification of spin-valley entangled phases with broken symmetries

Presence of multiple symmetry-broken phases beyond the lowest Landau level

Abstract

Monolayer graphene under a strong magnetic field near charge neutrality manifests the integer and fractional quantum Hall effects. Since only some of the four spin/valley flavors available to the electrons in each Landau level manifold are filled, they also exhibit spontaneous symmetry breaking the in spin/valley sector, a phenomenon known as quantum Hall ferromagnetism. In this work, we study quantum Hall ferromagnets in the higher Landau level manifolds of monolayer graphene and show that there is an even richer set of symmetry-broken phases than in the lowest Landau level manifold. Specifically, both valley polarized and valley equatorial (where the occupied Landau levels are in an equal superposition of both valleys) ferromagnets, antiferromagnets, and canted antiferromagnets are found. Several types of spin valley entangled phases are found, all of which manifest the simultaneous spontaneous symmetry breaking of both magnetic and lattice symmetries.