Novel in-gap bulk current rectification mechanisms

We develop a unified formalism for current rectification processes of electronic Bloch bands in response to oscillatory electric fields that accounts microscopically for relaxation processes by including the coupling to a physical heat bath. This allows us to describe the impact of inelastic energy relaxation processes on intra-band phenomena such as the non-linear Hall effect and on inter-band phenomena such as shift and injection current effects. Moreover, we describe the conditions under which these effects survive even when the frequency of the impinging radiation is inside the optical absorption band-gap and discuss when these effects are allowed to produce a rectified current and perform work on an external circuit without violating the fundamental laws of thermodynamics. These considerations will allow us to uncover novel facet of the non-linear Hall effect as an efficient amplifier of circularly polarized light.