Valley and charge pumping in time-modulated moiré of semiconductors

Long range moiré patterns can emerge by vertically stacking two monolayer semiconductors with a small twist angle. In such moiré lattices, electrons gain a layer pseudospin internal degree of freedom. The spatially periodic moiré potential effectively introduces a pseudo-Zeeman field, which exhibits vortex/antivortex textures. In the adiabatic regime, the layer pseudospin of an electron moving in the moiré adapts to the local direction of the pseudo-Zeeman field constantly. Such dynamics of the layer pseudospin can be understood through an emergent magnetic field acting on the electron. When the moiré is time-modulated, the magnetic field changes dynamically and a sizable emergent electric field can emerge due to Faraday's law of induction. In this work, we study the emergent fields and the resultant transport responses in time-modulated moiré by applying, for example, interlayer bias or THz pulses. We show that valley/spin and charge currents can be pumped between different domains. Our study offers a simple scheme to realize emergent electrodynamics for valley/spintronics applications.