Time-reversal invariant topological skyrmion phases

TL;DR

This paper introduces time-reversal invariant topological skyrmion phases, revealing a hidden bulk-boundary correspondence via a $ ext{Z}_2$ spin skyrmion invariant, and discusses experimental detection methods.

Contribution

It defines topological skyrmion phases in TRI systems and uncovers a novel bulk-boundary correspondence not captured by traditional classification schemes.

Findings

Presence of a non-trivial $ ext{Z}_2$ spin skyrmion invariant

Hidden bulk-boundary correspondence in 2D TRI systems

Potential detection via ARPES and transport measurements

Abstract

Topological phases realized in time-reversal invariant (TRI) systems are foundational to experimental study of the broader canon of topological condensed matter as they do not require exotic magnetic orders for realization. We therefore introduce topological skyrmion phases of matter realized in TRI systems as a foundational step towards experimental realization of topological skyrmion phases. A novel bulk-boundary correspondence hidden from the ten-fold way classification scheme is revealed by the presence of a non-trivial value of a $\mathbb{Z}_2$ spin skyrmion invariant. This quantized topological invariant gives a finer description of the topology in 2D TRI systems as it indicates the presence or absence of robust helical edge states for open boundary conditions, in cases where the $\mathbb{Z}_2$ invariant computed with projectors onto occupied states takes a trivial value. Physically, we show this hidden bulk-boundary correspondence derives from additional spin-momentum-locking of the helical edge states associated with the topological skyrmion phase. ARPES techniques and transport measurements can detect these signatures of topological spin-momentum-locking and helical gapless modes. Our work therefore lays the foundation for experimental study of these phases of matter.