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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.
Highlights
The very first large-gap Kane-Mele quantum spin Hall insulator was predicted to be monolayer jacutingaite (Pt2HgSe3), a naturally occurring exfoliable mineral discovered in Brazil in 2008
The 001-surface states have been shown to be topologically protected by a mirror Chern number CM = −2, associated with a nodal line gapped by spinorbit interactions
By using maximally localized Wannier functions, we identify a large nontrivial second nearest-layer hopping term that breaks the standard paradigm of weak topological insulators
Summary
Antimo Marrazzo ,1 Nicola Marzari ,1 and Marco Gibertini 2 1Theory and Simulation of Materials (THEOS), and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland 2Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest Ansermet, CH-1211 Geneva, Switzerland (Received 13 September 2019; accepted 6 February 2020; published 13 March 2020). The experimental isolation of graphene [2] inspired Kane and Mele to assert that by doubling Haldane’s model and introducing spins one could describe intrinsic spin-orbit coupling (SOC) in graphene, leading to a novel gapped topological phase [3,4] Such phase, identified by a Z2 topological invariant, is named quantum spin Hall insulator (QSHI) and it is protected by time-reversal symmetry. Recent first-principles simulations confirmed this weak topological classification [14,15,16], but at the same time surprisingly predicted the presence of basal surface states associated with a nontrivial mirror Chern number CM, promoting bulk jacutingaite to a dual topological material [19,20] with both weak and crystalline topological properties Such (001) surface states have been demonstrated independently through angle-resolved photoemission spectroscopy (ARPES) experiments on synthetic jacutingaite single crystals [14]. Even and odd layers are approximately independent and can be separately described by a 3D KM model where the novel hopping term drives a band inversion, giving rise to a nodal
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