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

Triangular lattice, with each site coordinating with six neighbors, is one most common network in two-dimensional (2D) limit. Manifestations of peculiar properties in the lattice, including magnetic frustration and quantum spin liquid, have been restricted to single-orbital tight-binding (TB) model so far, while the orbital degree of freedom is largely overlooked. Here, by combining TB modeling with first-principles calculations, we demonstrate the rich electronic structures of triangular lattice with multiple (px,py,pz)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(p_{x}, p_{y}, p_{z})$\end{document} orbitals. Type I/II Dirac point, quadratic nodal point and nodal-loops are observed, and the topological phase diagram is mapped out by manipulating the horizontal mirror symmetry, spin-orbit coupling and energy position of relevant orbitals. Remarkably, we show that large-gap quantum spin Hall phase (∼0.2 eV) can be realized in experimentally achievable systems by growing indium monolayer on a series of semiconducting substrates, such as C/Si/Ge(111) and SiC(0001) surfaces, and the proposed materials capture the TB parameter space well. Our work not only provides physical insights into the orbital physics in 2D lattices, but also sheds light on the integration of novel quantum states with conventional semiconductor technology for potential applications, such as dissipationless interconnects for electronic circuits.