Magnetic skyrmion crystal at a topological insulator surface

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 Néel 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 Néel 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.

21 pages, 7 figures

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• Giant proximity exchange and flat Chern band in 2D magnet-semiconductor heterostructures
• Designer Meron Lattice on the Surface of a Topological Insulator
• Magnetic warping in topological insulators
• Anisotropic planar Hall effects in Bi${}_2$Se${}_3$/EuS interfaces: Deciphering the role of proximity induced spin canting and topological spin texture
• Giant resonant skew scattering of plasma waves in a two-dimensional electron gas
• Interface-Induced Stability of Nontrivial Topological Spin Textures: Unveiling Room-Temperature Hopfions and Skyrmions
• A $C^{\ast }$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals
• Disorder-Induced Topological Phases in a Two-Dimensional Chern Insulator with Strong Magnetic Disorder
• Chiral electronic network within skyrmionic lattice on topological insulator surfaces
• Charge ordering and spontaneous topological Hall effect in bilayer skyrmion crystals
• Dilute Paramagnetism and Non-Trivial Topology in Quasicrystal Approximant Fe${}_4$Al${}_{13}$