Quadrupolar photovoltaic effect in the terahertz range in a two-dimensional spin-32 hole system

The quantum kinetic approach based on the density matrix offers a complete quantum mechanical description of dynamical optical and transport currents in solid-state systems. Starting from the quantum Liouville equation for the density matrix in an external electric field, we identify a strong photovoltaic response due to the nonlinear optical transition between heavy and light hole sub-bands enabled by Td symmetry in a quantum well, which we term the quadrupolar photovoltaic effect (QPE). The photovoltaic current exhibits a strong resonance in the vicinity of the heavy hole-light hole splitting, with a magnitude governed by the momentum relaxation time, which can reach nanoseconds in GaAs holes. Since the heavy hole-light hole splitting can be tuned from a few meV to nearly 100 meV, the QPE could serve as the basis for a terahertz photodetector, addressing the famous terahertz gap. We discuss experimental observation and device applications.