Emergent dual topology in the three-dimensional Kane-Mele Pt${}_2$HgSe${}_3$

Abstract

Recently, the very first large-gap Kane-Mele quantum spin Hall insulator was predicted to be monolayer jacutingaite (Pt${}_2$HgSe${}_3$), a naturally-occurring exfoliable mineral discovered in Brazil in 2008. The stacking of quantum spin Hall monolayers into a van-der-Waals layered crystal typically leads to a (0;001) weak topological phase, which does not protect the existence of surface states on the (001) surface. Unexpectedly, recent angle-resolved photoemission spectroscopy experiments revealed the presence of surface states dispersing over large areas of the 001-surface Brillouin zone of jacutingaite single crystals. The 001-surface states have been shown to be topologically protected by a mirror Chern number $C_M=-2$, associated with a nodal line gapped by spin-orbit interactions. Here, we extend the two-dimensional Kane-Mele model to bulk jacutingaite and unveil the microscopic origin of the gapped nodal line and the emerging crystalline topological order. By using maximally-localized Wannier functions, we identify a large non-trivial second nearest-layer hopping term that breaks the standard paradigm of weak topological insulators. Complemented by this term, the predictions of the Kane-Mele model are in remarkable agreement with recent experiments and first-principles simulations, providing an appealing conceptual framework also relevant for other layered materials made of stacked honeycomb lattices.

arXiv commentmain text: 7 pages, 3 figures; supplementary: 3 pages, 2 figures

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• Signature of large-gap quantum spin Hall state in the layered mineral jacutingaite
• Conductance of quantum spin Hall edge states from first principles: the critical role of magnetic impurities and inter-edge scattering
• Jacutingaite-family: a class of topological materials
• Second-Order Topological Insulator in van der Waals Heterostructures of CoBr${}_2$/Pt${}_2$HgSe${}_3$/CoBr${}_2$
• Probing topological phases in a perturbed Kane-Mele model via RKKY interaction: Application to monolayer jacutingaite Pt${}_2$HgSe${}_3$
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• Gate-tunable imbalanced Kane-Mele model in encapsulated bilayer jacutingaite
• STM observation of the hinge-states of bismuth nanocrystals
• Dual topological insulator with mirror symmetry protected helical edge states
• Topological insulating phase arising in transition metal dichalcogenide alloy
• Exploring Topological Transport in Pt${}_2$HgSe${}_3$ Nanoribbons: Insights for Spintronic Device Integration
• Emerging nonlinear Hall effect in Kane-Mele two-dimensional topological insulators