Collective Modes and Skyrmion Excitations in Graphene SU(4) Quantum Hall Ferromagnets

TL;DR

This paper investigates the collective excitations and skyrmion states in graphene's SU(4) quantum Hall ferromagnets, revealing their properties, energies, and the nature of their excitations, including skyrmion lattice modes.

Contribution

It provides a comprehensive analytical and wave function-based study of SU(4) quantum Hall states, their excitations, and skyrmion properties in graphene.

Findings

Skyrmions carry charge ±1 at all integer fillings.

Skyrmions are lowest energy charged excitations for |n| ≤ 3.

Skyrmion lattice states support four gapless modes with full SU(4) symmetry.

Abstract

Graphene exhibits quantum Hall ferromagnetism in which an approximate SU(4) symmetry involving spin and valley degrees of freedom is spontaneously broken. We construct a set of integer and fractional quantum Hall states that break the SU(4) spin/valley symmetry, and study their neutral and charged excitations. Several properties of these ferromagnets can be evaluated analytically in the SU(4) symmetric limit, including the full collective mode spectrum at integer fillings. By constructing explicit wave functions we show that the lowest energy skyrmion states carry charge $\pm 1$ for {\em any} integer filling, and that skyrmions are the lowest energy charged excitations for graphene Landau level index $|n| \le 3$. We also show that the skyrmion lattice states which occur near integer filling factors support four gapless collective mode branches in the presence of full SU(4) symmetry. Comparisons are made with the more familiar SU(2) quantum Hall ferromagnets studied previously.