  Anomalous valley Hall (AVH) effect is a fundamental transport phenomenon in
the field of condensed-matter physics. Usually, the research on AVH effect is
mainly focused on 2D lattices with ferromagnetic order. Here, by means of model
analysis, we present a general design principle for realizing AVH effect in
antiferromagnetic monolayers, which involves the introduction of nonequilibrium
potentials to break of PT symmetry. Using first-principles calculations, we
further demonstrate this design principle by stacking antiferromagnetic
monolayer MnPSe3 on ferroelectric monolayer Sc2CO2 and achieve the AVH effect.
The AVH effect can be well controlled by modulating the stacking pattern. In
addition, by reversing the ferroelectric polarization of Sc2CO2 via electric
field, the AVH effect in monolayer MnPSe3 can be readily switched on or off.
The underlying physics are revealed in detail. Our findings open up a new
direction of research on exploring AVH effect.
