Frequency-dependent superconducting states revealed using the dynamical linear response theory*

The standard method to investigate superconducting order parameters from the normal state is to inspect the linear response to a static pairing field. We generalize this method to frequency-dependent fields in order to compute the dynamical pairing susceptibility. This generalization allows to capture the full frequency-dependance of the

eigenvectors of the pairing susceptibility, and in particular it gives access to odd-frequency solutions. Within the dynamical mean-field theory framework, we benchmarked this method on the single-site attractive Hubbard model. We then investigated the local solutions of single-site three-orbital strontium ruthenate (Sr₂RuO₄) in the absence of spin-orbit coupling. Finally, we used this method to revealed that transition to an odd-frequency state in the two-channel Kondo model was of first order. This method has potential application to magnetic and charge ordered states in the  particle-hole channel.