Skyrme and Wigner crystals in graphene

TL;DR

This paper investigates electron crystal phases in graphene under magnetic fields, showing Skyrme crystals are energetically favorable over Wigner crystals in certain conditions and predicting distinct collective modes for experimental identification.

Contribution

It introduces a detailed Hartree-Fock analysis of Skyrme and Wigner crystals in graphene, highlighting the stability of Skyrme crystals and their unique collective excitations.

Findings

Skyrme crystals have lower energy than Wigner crystals near certain filling factors.

Skyrme crystals exhibit three linearly-dispersing Goldstone modes.

Wigner crystals have a single quadratic Goldstone mode.

Abstract

At low-energy, the band structure of graphene can be approximated by two degenerate valleys $(K,K^{\prime})$ about which the electronic spectra of the valence and conduction bands have linear dispersion relations. An electronic state in this band spectrum is a linear superposition of states from the $A$ and $B$ sublattices of the honeycomb lattice of graphene. In a quantizing magnetic field, the band spectrum is split into Landau levels with level N=0 having zero weight on the $B(A)$ sublattice for the $% K(K^{\prime})$ valley. Treating the valley index as a pseudospin and assuming the real spins to be fully polarized, we compute the energy of Wigner and Skyrme crystals in the Hartree-Fock approximation. We show that Skyrme crystals have lower energy than Wigner crystals \textit{i.e.} crystals with no pseudospin texture in some range of filling factor $\nu $ around integer fillings. The collective mode spectrum of the valley-skyrmion crystal has three linearly-dispersing Goldstone modes in addition to the usual phonon mode while a Wigner crystal has only one extra Goldstone mode with a quadratic dispersion. We comment on how these modes should be affected by disorder and how, in principle, a microwave absorption experiment could distinguish between Wigner and Skyrme crystals.