Defect bulk-boundary correspondence of topological skyrmion phases of matter
arXiv:2206.02251 · doi:10.1103/PhysRevB.107.235109
Abstract
Unpaired Majorana zero-modes are central to topological quantum computation schemes as building blocks of topological qubits, and are therefore under intense experimental and theoretical investigation. Their generalizations to parafermions and Fibonacci anyons are also of great interest, in particular for universal quantum computation schemes. In this work, we find a different generalization of Majorana zero-modes in effectively non-interacting systems, which are zero-energy bound states that exhibit a cross structure -- two straight, perpendicular lines in the complex plane -- composed of the complex number entries of the zero-mode wavefunction on a lattice, rather than a single straight line formed by complex number entries of the wavefunction on a lattice as in the case of an unpaired Majorana zero-mode. These cross zero-modes are realized for topological skyrmion phases under certain open boundary conditions when their characteristic momentum-space spin textures trap topological defects. They therefore serve as a second type of bulk-boundary correspondence for the topological skyrmion phases. In the process of characterizing this defect bulk-boundary correspondence, we develop recipes for constructing physically-relevant model Hamiltonians for topological skyrmion phases, efficient methods for computing the skyrmion number, and introduce three-dimensional topological skyrmion phases into the literature.
16 pages and 13 figures in main text, 15 pages and 1 figure in the supplementary materials
References in corpus (13)
- Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
- Non-Abelian Anyons and Topological Quantum Computation
- Classification of topological insulators and superconductors in three spatial dimensions
- Advances in the Physics of Magnetic Skyrmions and Perspective for Technology
- Topological Crystalline Insulators
- Spontaneous Skyrmion Ground States in Magnetic Metals
- Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
- Observation of phononic helical edge states in a mechanical 'topological insulator'
- Topological Defects and Gapless Modes in Insulators and Superconductors
- Realization of an anomalous Floquet topological system with ultracold atoms
- Topological surface states in three-dimensional magnetic insulators
- Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
- Unveiling quasiparticle dynamics of topological insulators through Bayesian modelling