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

TL;DR

This paper reveals the emergence of dual topological phases in bulk jacutingaite, a layered material, by extending the Kane-Mele model and identifying a non-trivial second nearest-layer hopping term that explains experimental surface states.

Contribution

The study extends the Kane-Mele model to bulk jacutingaite, uncovering the microscopic origin of its topological order and explaining experimental surface states through a novel interlayer hopping mechanism.

Findings

Identification of a large non-trivial second nearest-layer hopping term.

Agreement between extended Kane-Mele model predictions and experiments.

Discovery of crystalline topological order in bulk jacutingaite.

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.