Article,
Magnon scattering off quantum Hall skyrmion crystals probes interplay of topology and symmetry breaking
Phys. Rev. B, 108 (10): 104401 (Sep 1, 2023)
DOI: 10.1103/PhysRevB.108.104401
Abstract
We introduce a model to study magnon scattering in skyrmion crystals, sandwiched between ferromagnets,
which act as the source of magnons. Thanks to recent experimental advances, such a set-up can be realised
in quantum Hall heterojunctions, and it is interesting as skyrmions are topological objects while the skyrmion
crystals break internal and translational symmetries, thus allowing to study the interplay of topological and
symmetry breaking physics. Starting from a basis of holomorphic theta functions, we construct an appropriate
analytical ansatz for such a junction with finite spatially modulating topological charge density in the central
region and vanishing in the leads. We then construct a suitably defined energy functional for the junction in
terms of these spinors and derive the resulting equations of motion, which take the form of a Bogoliubov-de
Gennes-like equation. Using a combination of analytical techniques, field theory, heuristic models, and fully
microscopic recursive transfer-matrix numerics, we calculate the spectra and magnon transmission properties
of the skyrmion crystal. We find that magnon transmission can be understood via a combination of low-energy
Goldstone modes and effective emergent Landau levels at higher energies. The presence of the former manifests
in discrete low-energy peaks in the transmission spectrum and we show how the these features reflect the nature
of the Goldstone modes arising from symmetry breaking. In turn, the effective Landau levels, which reflect the
topology of the skyrmion crystal, lead to band-like transmission features, from the structure of which further de-
tails of the excitation spectrum of the skyrmion crystal can be inferred. Such characteristic transmission features
are not present in competing phases of either the quantum Hall phase diagram or in metallic magnets, and hence
provide direct and unique signatures of skyrmion crystal phases and their properties. We discuss experimental
considerations regarding the realisation of our model, which most directly apply to heterojunctions in monolayer
graphene with the central region doped slightly away from unit filling and the two ends exactly at unit filling, a
ν = 1 : 1 ± δν : 1 junction. Such physics is also relevant to junctions formed by metallic magnets, which host
skyrmion crystal phases, or partly in junctions with artificially realized and periodically modulated gauge fields.
