Valley-dependent properties in two-dimensional Cr2COF MXene predicted from first principles

The search for valley-dependent exotic properties could enable quantum device applications and therefore attracts rapidly increasing attention. Here, using first principles, we predict existence of the intrinsic valley-related multiple Hall effect in two-dimensional (2D) ${\mathrm{Cr}}_{2}\mathrm{COF}$ MXene. ${\mathrm{Cr}}_{2}\mathrm{COF}$ MXene is a ferromagnetic semiconductor with a direct bandgap locating at the edges of the hexagonal Brillouin zone, endowing it with valley physics. Protected by time-reversal symmetry breaking and out-of-plane magnetization, the valleys are polarized spontaneously. Moreover, the valley polarization is sizeable in both the valence and conduction bands, benefiting the observation of the anomalous valley Hall effect. More remarkably, due to strong spin-orbit interaction, the valley-dependent band inversion occurs naturally, and thus, the valley-polarized quantum anomalous Hall effect can be realized simultaneously in ${\mathrm{Cr}}_{2}\mathrm{COF}$ MXene, giving rise to the intriguing intrinsic valley-related multiple Hall effect. In addition, this multiple Hall effect can be effectively engineered under strain. Our findings greatly enrich the research on valley-dependent physical properties in 2D systems.