  We introduce the concept of valley-layer coupling (VLC) in two-dimensional
materials, where the low-energy electronic states in the emergent valleys have
valley-contrasted layer polarization such that each state is spatially
localized on the top or bottom super-layer. The VLC enables a direct coupling
between valley and gate electric field, opening a new route towards
electrically controlled valleytronics. We analyze the symmetry requirements for
the system to host VLC, demonstrate our idea via first-principles calculations
and model analysis of a concrete 2D material example, and show that an
electric, continuous, wide-range, and switchable control of valley polarization
can be achieved by VLC. Furthermore, we find that systems with VLC can exhibit
other interesting physics, such as valley-contrasting linear dichroism and
optical selection of the electric polarization of interlayer excitons.
