  In monolayer group-VI transition metal dichalcogenides (TMDC), charge
carriers have spin and valley degrees of freedom, both associated with magnetic
moments. On the other hand, the layer degree of freedom in multilayers is
associated with electrical polarization. Here, we show that TMDC bilayers offer
an unprecedented platform to realize a strong coupling between the spin, layer
pseudospin, and valley degrees of freedom of holes. Such coupling not only
gives rise to the spin Hall effect and spin circular dichroism in inversion
symmetric bilayer, but also leads to a variety of magnetoelectric effects
permitting quantum manipulation of these electronic degrees of freedom.
Oscillating electric and magnetic fields can both drive the hole spin resonance
where the two fields have valley-dependent interference, making possible a
prototype interplay between the spin and valley as information carriers for
potential valley-spintronic applications. We show how to realize quantum gates
on the spin qubit controlled by the valley bit.
