Photocurrent generation within the optical gap

The macroscopic directed flow of electrons in response to oscillating electric fields, or bulk rectified photocurrent, is a non-equilibrium phenomenon allowed in systems that break spatial inversion symmetry and is of significant practical and fundamental research interest. A question that has been debated for decades is whether an electric field with a frequency that lies within the optical gap of the crystal can generate a bulk photocurrent in the clean limit. We answer this question affirmatively by demonstrating that this is possible in metals and is consistent with the fundamental principles of thermodynamics. We also show that the Berry curvature dipole is a unique mechanism that behaves as an ideal reversible and dissipationless energy conveyor between the radiation and an external circuit. We will further demonstrate rigorously that the occupation of a periodic driven system does not have a simple Fermi-Dirac distribution function of the Floquet energy, and this generically leads to a finite rectified electric current within the optical gap of a metal even when the carrier relaxation rates vanish.