Symmetry-dependent antiferromagnetic proximity effects on valley splitting

A typical valley material, such as the transition-metal dichalcogenide (TMD) monolayer, is characterized by two degenerate valley states protected by time-reversal symmetry (TS). In order to achieve emergent valley-contrasting physics with broken valley degeneracy resulting from TS breaking, previous studies have focused on ferromagnetic proximity effect. In the present work, we investigate the antiferromagnetic (AFM) proximity effect on the valley degeneracy. We construct composite systems consisting of a TMD monolayer and a proximity layer with specific intra-plane AFM configurations. Using an extended three-band model to describe the valley states of such systems, we show that "time-reversal" plus either "fractional translation" or "mirror" symmetry can protect the valley degeneracy. In addition, first-principles calculations and symmetry analysis are used to verify the results obtained from the extended tight-binding model. The corresponding mechanism of the valley splitting/degeneracy is also revealed through nondegenerate perturbation method.