Spin-valley entangled quantum Hall states in graphene

TL;DR

This paper explores interaction-driven quantum Hall states in graphene, revealing a competition of phases with spontaneous spin-valley entanglement influenced by Zeeman and substrate effects.

Contribution

It introduces the entangled-Kekulé-antiferromagnet phase and analyzes spin-valley entanglement in quantum Hall states beyond simplified models.

Findings

Identification of a new entangled-Kekulé-antiferromagnet phase.

Demonstration of spin-valley entanglement dependence on external potentials.

Quantification of entanglement using bipartite concurrence.

Abstract

We investigate interaction-driven integer quantum Hall states realized in Landau levels of monolayer graphene when two out of its four nearly degenerate spin-valley flavors are filled. By employing a model that accounts for interactions beyond pure delta-functions as well as Zeeman and substrate-induced valley potentials, we demonstrate the existence of a delicate competition of several phases with spontaneous generation of spin-valley entanglement, akin to the spontaneous appearance of spin-orbit coupling driven by interactions. We encounter a particular phase that we term the entangled-Kekul\'{e}-antiferromagnet (E-KD-AF) which only becomes spin-valley entangled under the simultaneous presence of Zeeman and substrate potentials, because it gains energy by simultaneously canting in the spin and valley spaces, by combining features of a canted anti-ferromagnet and a canted Kekul\'{e} state. We quantify the degree of spin-valley entanglement of the many competing phases by computing their bipartite concurrence.