In-plane polarization induced ferroelectrovalley coupling in a two-dimensional rare-earth halide

We propose a mechanism where the valley splitting is caused by an in-plane electric polarization and the coupling between the two makes it possible for an electric field to control the valley degree of freedom. We demonstrate this by considering Gd-substituted EuCl$_2$ monolayer in its 1T-phase using first-principles calculations. This monolayer exhibits an in-plane polarization which breaks the inversion symmetry of the monolayer leading to a spontaneous valley splitting. The resulting valley polarization is strongly coupled with the electric polarization and, hence, the valley degree of freedom can be switched by an external electric field in this case, instead of the conventional magnetic field. We show that a similar ferroelectric-ferrovalley (FE-FV) coupling can also exist in the previously reported ferroelectric (CrBr$_3$)$_2$Li monolayer. This mechanism opens up a new avenue for electric field control of valley polarization in two-dimensional materials.