Symmetry-dependent antiferromagnetic proximity effects on valley splitting

Abstract

Various physical phenomena have been discovered by tuning degrees of freedom, among which there is the ``valley'' degree of freedom (DOF). The typical valley materials are characterized by two degenerate valley states protected by time-reversal symmetry ($\mathcal{T}\mathrm{S}$). These states indexed by valley DOF have been measured and manipulated for emergent valley-contrasting physics with the broken valley degeneracy. To achieve the valley splitting resulting from $\mathcal{T}\mathrm{S}$ breaking, previous studies have mainly focused on the magnetic proximity effect provided by the ferromagnetic layer. In contrast, the antiferromagnetic (AFM) proximity effect on the valley degeneracy has not been widely investigated systematically. In this work, we construct the composite systems consisting of a transition-metal dichalcogenide monolayer and a proximity layer with specific intraplane AFM configurations. We extend the three-band model to describe the valley states of such systems. It is shown that either ``time-reversal $+$ fractional translation'' or ``mirror'' symmetry can protect the valley degeneracy. Additionally, first-principles calculations based on density functional theory (DFT) have been performed to verify the results obtained from the extended tight-binding (TB) model. The corresponding mechanism of the valley splitting/degeneracy is revealed through the nondegenerate perturbation. Meanwhile, an extra condition is proposed to keep the well-defined valley states disentangled from each other through two negative examples based on degenerate perturbation. Further DFT studies on the effects of the ${U}_{\mathrm{eff}}$ and interlayer distance are performed. Manipulating the magnetization of Mo is shown to be feasible and effective for controlling the valley splitting with the direct overlap tuned by ${U}_{\mathrm{eff}}$ and the interlayer distance. The TB method introduced in the present work can properly describe the low-energy physics of valley materials that couple to the proximity with complex magnetic configurations. The results considerably expand the range of qualified proximity layers for valley splitting, enabling more flexible manipulation of valley degree.