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By using density-functional theory-based GW method, we studied the valley degree of freedom of Janus monolayer VSSe. The GW corrections lead to a doubling of the band gap and change the band dispersion considerably, indicating significant many-body effects. VSSe is confirmed to be ferromagnetic, which breaks the time-reversal symmetry and the odd parity of the Berry curvature in momentum space. The dissimilar magnitudes of Berry curvatures of the inequivalent valleys give rise to appreciable anomalous Hall conductivity (AHC). The calculated valley optical response of VSSe exhibits a clear valley-selective circular dichroism. The ferromagnetism induces large valley-Zeeman splitting, making it possible to realize the selective valley excitation even by unpolarized light. The Janus VSSe is more tunable by external fields because of symmetry breaking. Due to the relief of time-reversal symmetry, the valley-Zeeman splitting can be continuously tuned by varying the magnetization direction. The loss of mirror symmetry in VSSe enables a bidirection modulation of the band gap by changing the direction of electric field. The strain can linearly tune the valley gap in a considerable range. The Berry curvature and AHC can be effectively regulated in the external fields.
Luo et al. (Mon,) studied this question.