Based on first-principles calculations, we have found a family of two-dimensional (2D) transition-metal chalcogenides MX$_5$ (M = Zr, Hf and X = S, Se and Te) can host quantum spin Hall (QSH) effect. The molecular dynamics (MD) simulation indicate that they are all thermal-dynamically stable at room temperature, the largest band gap is 0.19 eV. We have investigated the electronic and topological properties and they have very similar properties. For the single-layer ZrX$_5$, they are all gapless semimetals without consideration of spin-orbit coupling (SOC). The consideration of SOC will result in insulating phases with band gaps of 49.5 meV (direct), 0.18 eV (direct) and 0.13 eV (indirect) for ZrS$_5$, ZrSe$_5$ to ZrTe$_5$, respectively. The evolution of Wannier charge centers (WCC) and edge states confirm they are all QSH insulators. The mechanisms for QSH effect in ZrX$_5$ originate from the special nonsymmorphic space group features. In addition, the QSH state of ZrS$_5$ survives at a large range of strain as long as the interchain coupling is not strong enough to reverse the band ordering. The single-layer ZrS$_5$ will occur a TI-to-semimetal (metal) or metal-to-semimetal transition under certain strain. The realization of pure MX$_5$ monolayer should be readily obtained via mechanical exfoliation methods, thus holding great promise for nanoscale device applications and stimulating further efforts on transition metal (TM) based QSH materials.
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