Quantum spin Hall phase in 2D trigonal lattice.

Z F Wang,Kyung-Hwan Jin,Feng Liu

doi:10.1038/ncomms12746

Abstract

The quantum spin Hall (QSH) phase is an exotic phenomena in condensed-matter physics. Here we show that a minimal basis of three orbitals (s, px, py) is required to produce a QSH phase via nearest-neighbour hopping in a two-dimensional trigonal lattice. Tight-binding model analyses and calculations show that the QSH phase arises from a spin–orbit coupling (SOC)-induced s–p band inversion or p–p bandgap opening at Brillouin zone centre (Γ point), whose topological phase diagram is mapped out in the parameter space of orbital energy and SOC. Remarkably, based on first-principles calculations, this exact model of QSH phase is shown to be realizable in an experimental system of Au/GaAs(111) surface with an SOC gap of ∼73 meV, facilitating the possible room-temperature measurement. Our results will extend the search for substrate supported QSH materials to new lattice and orbital types.

Highlights

The quantum spin Hall (QSH) phase is an exotic phenomena in condensed-matter physics
We consider a minimal basis of three orbitals (s, px, py) per lattice site of trigonal symmetry with nearestneighbour hopping, solve an effective tight-binding Hamiltonian and develop a generic phase diagram for the non-trivial band topology in the parameter space of orbital energy and spin–orbit coupling (SOC)
One is the transport measurement to measure the quantized conductance induced by topological edge state, and the other is scanning tunnelling spectroscopy measurement to image the real-space topological edge state within the energy window of SOC gap

Summary

Introduction

The quantum spin Hall (QSH) phase is an exotic phenomena in condensed-matter physics. Based on first-principles calculations, this exact model of QSH phase is shown to be realizable in an experimental system of Au/GaAs(111) surface with an SOC gap of B73 meV, facilitating the possible room-temperature measurement. In Kane–Mele model, the QSH phase is realized by any finite SOC-induced bandgap opening at Dirac point, as a generalization of Haldane’s model[4] to spinful system with time reversal symmetry in a hexagonal lattice. In BHZ model, the QSH phase is realized by SOC-induced band inversion at time reversal invariant momenta between two bands of different parities, originally derived from a square lattice of HgTe quantum-well system. Most remarkably, based on first-principles calculations, this exact QSH model is shown to be possibly realizable in an experimental system of Au/GaAs(111)[24] with a large non-trivial SOC gap of B73 meV

Methods

Results

Conclusion