Magnetic skyrmion crystal at a topological insulator surface

TL;DR

This paper investigates the electronic properties of magnetic skyrmion crystals on topological insulator surfaces, revealing how different skyrmion textures influence band topology and proposing a tight-binding model capturing these effects.

Contribution

It introduces a detailed analysis of exchange interactions between Dirac surface states and skyrmion textures, providing explicit Wannier functions and a tight-binding model for low-energy bands.

Findings

Distinct qualitative differences between Ne9el and Bloch skyrmions.

Explicit construction of Wannier orbitals resembling chiral bound states.

A two-band tight-binding model capturing topological features.

Abstract

We consider a magnetic skyrmion crystal formed at the surface of a topological insulator. Incorporating the exchange interaction between the helical Dirac surface states and the periodic N\'eel or Bloch skyrmion texture, we obtain the resulting electronic band structure and discuss the constraints that symmetries impose on the energies and Berry curvature. We find substantive qualitative differences between the N\'eel and Bloch cases, with the latter generically permitting a multiband low energy tight-binding representation whose parameters are tightly constrained by symmetries. We explicitly compute the associated Wannier orbitals, which resemble the ringlike chiral bound states of helical Dirac fermions coupled to a single skyrmion in a ferromagnetic background. We construct a two-band tight-binding model with real nearest-neighbor hoppings which captures the salient topological features of the low-energy bands. Our results are relevant to magnetic topological insulators (TIs), as well as to TI-magnetic thin film heterostructures, in which skyrmion crystals may be stabilized.