  Various physical phenomena have been discovered by tuning degrees of freedom,
among which there is the degree of freedom (DOF) -- "valley". The typical
valley materials are characterized by two degenerate valley states protected by
time-reversal symmetry (TS). 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 resulted from TS
breaking, previous studies mainly focused on magnetic proximity effect provided
by ferromagnetic (FM) layer. Nevertheless, the anti-ferromagnetic (AFM)
proximity effect on the valley degeneracy has never been investigated
systematically. In this work, we construct the composites consisting of a
transitionmetal dichalcogenide (TMD) monolayer and a proximity layer with
specific intra-plane 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 has been proved
to protect 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 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 expand the range of qualified proximity layers for valley
splitting, enabling more flexible manipulation of valley degree.
