Defect bulk-boundary correspondence of topological skyrmion phases of matter

TL;DR

This paper introduces a novel type of zero-energy bound state called cross zero-modes in topological skyrmion phases, revealing a new bulk-boundary correspondence and expanding the understanding of topological defects in quantum materials.

Contribution

It uncovers a new class of zero-modes with a cross structure in their wavefunctions, develops methods for modeling topological skyrmion phases, and introduces 3D skyrmion phases into the literature.

Findings

Discovery of cross zero-modes in skyrmion phases

Development of recipes for model Hamiltonians

Introduction of three-dimensional topological skyrmion phases

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.