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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.
We propose to engineer time-reversal-invariant topological insulators in two-dimensional (2D) crystals of transition metal dichalcogenides (TMDCs). We note that, at low doping, semiconducting TMDCs under shear strain will develop spin-polarized Landa
Quantum anomalous Hall (QAH) insulator is a topological phase which exhibits chiral edge states in the absence of magnetic field. The celebrated Haldane model is the first example of QAH effect, but difficult to realize. Here, we predict the two-dime
By using first-principles calculation, we have found that a family of 2D transition metal dichalcogenide haeckelites with square-octagonal lattice $MX_2$-4-8 ($M$=Mo, W and $X$=S, Se and Te) can host quantum spin hall effect. The phonon spectra indic
Symmetry, dimensionality, and interaction are crucial ingredients for phase transitions and quantum states of matter. As a prominent example, the integer quantum Hall effect (QHE) represents a topological phase generally regarded as characteristic fo
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