Spectroscopic and optical response of odd-frequency Berezinskii superconductors

By using a simple model with a parabolic dispersion law and a non-magnetic disorder, the spectral function, the electron density of states, and the optical conductivity are calculated in clean and disordered Berezinskii superconductors for a few gap ansatzes. The strong dependence of the spectral function and the electron DOS on the frequency profile of the gap is rather unusual and could explain why it is experimentally hard to identify the Berezinskii state. It is found also that the OF pairing allows for peaks in the real part of the optical conductivity, whose form and position depend on the specific frequency profiles of the gap. For the frequencies that correspond to these peaks, sharp cusps appear in the imaginary part. The form of these cusps is nontrivial for the OF pairing. In particular, the imaginary part of the optical conductivity can become negative allowing for the optical transparency windows.