Multicomponent Skyrmion lattices and their excitations

TL;DR

This paper investigates multicomponent Skyrmion lattices in quantum Hall ferromagnets, analyzing their formation, symmetry breaking, and excitation spectra, with implications for experimental systems like AlAs quantum wells.

Contribution

It provides an analytical study of Skyrmion lattice formation, symmetry breaking, and excitation spectra in multicomponent quantum Hall systems, including effects of anisotropy.

Findings

Hexagonal Skyrmion lattice breaks SU(d) symmetry.

Charge density modulation vanishes exponentially with d.

Identifies a transition from triangular to square lattice due to anisotropy.

Abstract

We study quantum Hall ferromagnets with a finite density topologically charged spin textures in the presence of internal degrees of freedom such as spin, valley, or layer indices, so that the system is parametrised by a $d$-component complex spinor field. In the absence of anisotropies, we find formation of a hexagonal Skyrmion lattice which completely breaks the underlying SU(d) symmetry. The ground state charge density modulation, which inevitably exists in these lattices, vanishes exponentially in $d$. We compute analytically the complete low-lying excitation spectrum, which separates into $d^{2}-1$ gapless acoustic magnetic modes and a magnetophonon. We discuss the role of effective mass anisotropy for SU(3)-valley Skyrmions relevant for experiments with AlAs quantum wells. Here, we find a transition, which breaks a six-fold rotational symmetry of a triangular lattice, followed by a formation of a square lattice at large values of anisotropy strength.