Discovery of a ferroelastic topological insulator in a two-dimensional tetragonal lattice.

Ferroelasticity and band topology are two intriguing yet distinct quantum states of condensed matter materials. Their coexistence in a single two-dimensional (2D) lattice, however, has never been observed. Here, we found that the 2D tetragonal HfC monolayer allowed simultaneous presence of ferroelastic and topological orders. By using first-principles calculations, we found that it could allow a low switching barrier with reversible strain of 17.4%, indicating that the anisotropic properties are achievable experimentally for a 2D tetragonal lattice. More interestingly, the tuning of topological behaviors with strain led to spin-separated and gapless edge states, that is, the quantum spin Hall effect. These findings from the coupling of two quantum orders offer insights into ferroelastic control over topological edge states for achieving multifunctional properties in next-generation 2D nanodevices.