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Abstract

Topological phases realized in time-reversal invariant (TRI) systems are foundational to the 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 different bulk-boundary correspondence hidden from the tenfold way classification scheme is revealed by the presence of a nontrivial value of a Z2 spin skyrmion invariant. This quantized topological invariant gives a finer description of the topology in two-dimensional (2D) TRI systems as it indicates the presence or absence of robust helical edge states for open boundary conditions, in cases where the Z2 invariant computed with projectors onto occupied states takes a trivial value. Physically, we show that 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. © 2023 authors. Published by the American Physical Society.