Emergent dual topology in the three-dimensional Kane-Mele Pt2HgSe3

Abstract

Recently, 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 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 CM = −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:1909.05050v1 [cond-mat.mes-hall]

Gate-tunable imbalanced Kane-Mele model in encapsulated bilayer jacutingaite

“…The sublattice asymmetry is responsible for a large trivial (ν bi = 0 + 0 = 0) band-gap of 290 meV at the K point. The same level of displacement is found in trilayer jacutingaite, however, the trilayer is semimetallic owing to a large second-nearest layer hopping between the outer layers, similarly to what happens in the bulk [29]. See Table I for an overview of the Hg positions and bandgaps of the different studied structures.…”

“…1 for the top layer when E ext = 0. While for the external sublattice the WF is similar to the one of the monolayer [23] and it is well localized on just one layer, the inner WF has significant contributions from orbitals in the opposite layer, signaling a strong hybridization between the layers similarly to what happens in bulk jacutingaite [29]. As a result, the center of the inner WFs is significantly shifted in the z-direction such that the center of the top WF of the bottom layer is higher than the one of the bottom WF of the top layer.…”

“…In bulk jacutingaite, the layers can not be considered as nearly independent, so that this scenario is expected to break down. Indeed, first-principles simulations have shown that nearby layers are strongly hybridized, giving rise to a large second-nearest layer hopping [29]. This strong coupling drives bulk jacutingaite into a semimetallic state endowed with a dual topology [29][30][31] that combines a non-zero mirror Chern number with a weak topology.…”

“…Indeed, first-principles simulations have shown that nearby layers are strongly hybridized, giving rise to a large second-nearest layer hopping [29]. This strong coupling drives bulk jacutingaite into a semimetallic state endowed with a dual topology [29][30][31] that combines a non-zero mirror Chern number with a weak topology. Recent experiments have verified both the semimetallic nature of bulk Pt 2 HgSe 3 [32] and the presence of surface states protected by the crystalline mirror symmetry [33].…”

Van der Waals Heterostructure Pt$_{2}$HgSe$_{3}$/CrI$_3$ for Topological Valleytronics

“…In the absence of spin-orbit coupling, linear dispersion exists around K and K ′ points by dashed lines. When the spin-orbit coupling is further included, a large band gap opens as plotted by solid lines, which indicates that Pt 2 HgSe 3 can be considered as a Kane-Mele type topological insulator [44][45][46].…”