The dynamical regime of layer-pseudospin ferromagnetism in biased bilayers.

Bilayer systems with narrow/flat electronic bands often host correlated states with inter-layer order, such as the layer-pseudospin ferromagnetism in quantum Hall bilayers. In equilibrium, the pseudospin vector lies on the easy plane of the Bloch sphere. Under a voltage bias applied by leads connected to the two layers, the pseudospin vector precesses in time on the Bloch sphere. Together with a nonzero electronic interlayer ​​tunneling, this realizes a non-equilibrium steady state like the AC Josephson effect, accompanied by AC and DC tunneling currents. In narrow/flat band bilayers made of graphene or transition metal dichalcogenides, the spin-valley degrees of freedom enable a rich manifold of layer-pseudospin ferromagnetic states, posting the question of which dynamical phase the system selects. We predict the dynamical phases in this regime using the ponderomotive​ force technique and compute the tunneling current.