Effects of relaxation on photovoltaic effect and possibility of photocurrent within transparent region

We theoretically study photocurrents in metals that break both inversion $\mathcal{P}$ and $\mathcal{T}$ symmetries within the transparent region. We find that the system under the ac electric fields is well described with an effective Hamiltonian and the photocurrent is of the order of $\mathcal{O}(\omega_J/\gamma)$ if the frequency of the induced current $\omega_J$ and the scattering rate $\gamma$ satisfy $\omega_J/\gamma \ll 1$, and vanishes in the limit of $\omega_J/\gamma\to 0$. On the other hand, the effective Hamiltonian description indicates that nonvanishing photocurrent can appear even in the transparent region if the system is thin enough compared to the mean free path in the direction of the induced current (where $\gamma$ can be effectively regarded as 0). Candidate materials for the such photovoltaic effect within the transparent region include multiferroics breaking both $\mathcal{P}$ and $\mathcal{T}$ symmetries.