Multicomponent Skyrmion lattices and their excitations

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.

4.5 pages, 3 figures

References in corpus (18)

• Skyrmion Lattice in a Chiral Magnet
• Electronic Properties of Graphene in a Strong Magnetic Field
• Spontaneous Inter-layer Coherence in Double-Layer Quantum-Hall Systems I: Charged Vortices and Kosterlitz-Thouless Phase Transitions
• Skyrmion Lattice in Two-Dimensional Chiral Magnet
• Chiral CP^2 skyrmions in three-band superconductors
• Observation of Quantum Hall Valley Skyrmions
• Nematic Valley Ordering in Quantum Hall Systems
• Integer quantum Hall effect on a six valley hydrogen-passivated silicon (111) surface
• Designing Topological Bands in Reciprocal Space
• Entanglement Skyrmions in multicomponent quantum Hall systems
• Skyrmions in the quantum Hall effect at finite Zeeman coupling
• Exact Tkachenko modes and their damping in the vortex lattice regime of rapidly rotating bosons
• Collective modes of CP(3) Skyrmion crystals in quantum Hall ferromagnets
• Mixed phases in U(N) superconductivity
• Neutral skyrmion configurations in the low-energy effective theory of spinor condensate ferromagnets
• Valley degeneracy in biaxially strained aluminum arsenide quantum wells
• Skyrme crystal in bilayer and multilayer graphene
• Symmetry analysis of crystalline spin textures in dipolar spinor condensates

Cited by in corpus (11)

• Geometric stability of topological lattice phases
• Engineering geometrically flat Chern bands with Fubini-Study Kähler structure
• Magnus-Induced Dynamics of Driven Skyrmions on a Quasi-One-Dimensional Periodic Substrate
• SU(4) Skyrmions in the $\nu =\pm 1$ Quantum Hall State of Graphene
• Stability of a skyrmion and interaction of magnons
• Demonstration of $\mathbb{C}{P}^2$ skyrmions in three-band superconductors by self-consistent solutions to a Bogoliubov-de Gennes model
• Riemann meets Goldstone: magnon scattering off quantum Hall skyrmion crystals probes interplay of symmetry breaking and topology
• Order by Disorder and by Doping in Quantum Hall Valley Ferromagnets
• Large and exact quantum degeneracy in a Skyrmion magnet
• Entanglement smectic and stripe order
• Topological Electrostatics