Design and realization of topological Dirac fermions on a triangular lattice

Abstract

Large-gap quantum spin Hall insulators are promising materials for room-temperature applications based on Dirac fermions. Key to engineer the topologically non-trivial band ordering and sizable band gaps is strong spin-orbit interaction. Following Kane and Mele’s original suggestion, one approach is to synthesize monolayers of heavy atoms with honeycomb coordination accommodated on templates with hexagonal symmetry. Yet, in the majority of cases, this recipe leads to triangular lattices, typically hosting metals or trivial insulators. Here, we conceive and realize “indenene”, a triangular monolayer of indium on SiC exhibiting non-trivial valley physics driven by local spin-orbit coupling, which prevails over inversion-symmetry breaking terms. By means of tunneling microscopy of the 2D bulk we identify the quantum spin Hall phase of this triangular lattice and unveil how a hidden honeycomb connectivity emerges from interference patterns in Bloch px ± ipy-derived wave functions.

Topological phase diagram and materials realization in triangular lattice with multiple orbitals

“…Here, we demonstrate real material systems that can fully capture this multiorbital model and exhibit large-gap QSH states. Especially, recent experiments demonstrated the successful growth of In monolayer on SiC surface, which has a triangular lattice and shows nontrivial topological properties, as observed by STM/STS and ARPES [29]. We thus resort to the epi-taxial growth of In monolayer on a series of semiconductor substrates, including diamond, SiC, Si, Ge, and InAs.…”

“…Importantly, the DFT calculated results capture well the salient features of the mapped topological phase diagram in the TB parameter space. As the proposed systems are experimentally available [29], we expect the present study to stimulate immediate attention to regulate the properties of semiconductor-supported topological materials via carrier doping, external strain, electrical and magnetic fields.…”

Recipe for higher-order topology on the triangular lattice

“…The QSHI phase shown in Fig. 1b was recently realized in indenene, where symmetry breaking is provided by a SiC substrate [28][29][30][31].…”

“…By breaking either reflection symmetry, σ h or σ v , a ν = 1 QSHI phase can be reached: in the former case, the hybridization between the p z and the in-plane orbitals dominates over the SOC term along the nodal line, stabilizing an indenene-like QSHI phase (Fig. 1b) [31]. The other QSHI phase is characterized by a strong local orbital angular momentum polarization at the valley momenta, which gaps the in-plane Dirac bands (" σ v QSHI", Fig.…”

“…Our approach is very general and may be realized in many compounds by depositing adatoms onto the threefold symmetric (111) surface of a zincblende/diamond substrate. We identified by first-principles calculations the Z 2 -trivial analogues of the recently synthesized QSHI indenene [31], namely B, Ga and Al on SiC, as potential candidates and showed explicitly for the case of Al a full finite-size study: it is bulk insulating and has gapped edges and localized corner charge on a finite-sized triangular flake. Given the abundance of zincblende/diamond substrates (Si, C, GaAs, and InSb, for example), and a variety of potential adsorbates, we expect many other material combinations will also realize the HOTI phase.…”