Prediction of the quantum spin Hall effect in monolayers of transition-metal carbides MC (M=Ti, Zr, Hf)

Wereport the existence of the quantum spin Hall effect (QSHE) in monolayers of transition-metal carbidesMC(M=Zr, Hf). Under ambient conditions, the ZrC monolayer exhibits QSHE with an energy gap of 54 meV, in which topological helical edge states exist. Enhanced d_xy-d_xy interaction induces band inversion, resulting in nontrivial topological features. By applying in-plane strain, the HfC monolayer can be tuned from a trivial insulator to a quantum spin Hall insulator with an energy gap of 170 meV, three times that of the ZrC monolayer. The strong stability of MC monolayers provides a new platform for QSHE and spintronic applications.