Time-reversal invariant topological skyrmion phases

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.

References in corpus (13)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Quantum Spin Hall Effect and Topological Field Effect Transistor in Two-Dimensional Transition Metal Dichalcogenides
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Spin-orbit gap of graphene: First-principles calculations
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Robustness of the Spin-Chern number
• New Family of Robust 2D Topological Insulators in van der Waals Heterostructures
• Robustness of quantized transport through edge states of finite length: Imaging current density in Floquet topological vs. quantum spin and anomalous Hall insulators
• Topological skyrmion phases of matter
• Defect bulk-boundary correspondence of topological skyrmion phases of matter

Cited by in corpus (4)

• Quantum skyrmion Hall effect
• Type-II topological phase transitions of topological skyrmion phases
• Observable-enriched entanglement
• Multiplicative Chern insulator