Odd-frequency superconducting states with different types of Meissner response: Problem of coexistence

TL;DR

This paper investigates the coexistence of odd-frequency superconducting states with different Meissner responses, revealing that the diamagnetic odd-dia state is unphysical and cannot be realized in practice.

Contribution

It demonstrates that the odd-dia superconducting state cannot be physically realized due to the absence of a Hamiltonian description and the unphysical nature of the mixed state.

Findings

The superfluid density of the mixed state has non-physical imaginary parts.

Josephson currents between odd-para and odd-dia states are unphysical.

The odd-dia state lacks a Hamiltonian description, implying it cannot be realized physically.

Abstract

We consider physical properties of a superconductor with a recently proposed type of odd-frequency pairing that exhibits diamagnetic Meissner response ("odd-dia state"). Such a state was suggested in order to address stability issues arising in an odd-frequency superconducting state with paramagnetic Meissner response ("odd-para state"). Assuming the existence of an odd-dia state (due to a proper retarded interaction), we study its coexistence with an odd-para state. The latter is known to be generated as an induced superconducting component in, e.g., singlet superconductor/ferromagnet proximity structures or triplet superconductor/normal metal systems. Calculating the superfluid density of the mixed odd-para/odd-dia state and the Josephson current between the odd-para and odd-dia states, we find that the expressions for the currents in both cases have non-vanishing imaginary contributions and are therefore unphysical. We show that a realization of the odd-dia state implies the absence of a Hamiltonian description of the system, and suggest that there exists no physically realizable perturbation that could give rise to the spontaneous symmetry breaking necessary for an actual realization of the odd-dia superconducting state.