Universal applicability of the odd-frequency pairing condition

Establish whether the condition [\hat{h},\hat{\Delta}]_* \neq 0, originally formulated for multiband bulk superconductors, applies universally to all superconducting systems, including superconducting hybrid structures.

Background

The paper discusses a previously established leading-order criterion for odd-frequency pairing in multiband bulk superconductors, expressed through the nonvanishing generalized commutator [\hat{h},\hat{\Delta}]_* = \hat{h}\hat{\Delta} - \hat{\Delta}\hat{h}^*. This condition is also related to superconducting fitness and the suppression of the critical temperature.

Before presenting its generalized derivation, the paper identifies as unresolved whether this bulk-superconductor criterion remains valid in other settings, particularly superconducting hybrid structures. The paper subsequently claims to resolve this question by proving that the generalized condition is necessary and sufficient for odd-frequency pairing in all superconducting systems; therefore, this is the explicitly stated motivating open question rather than an unresolved conclusion of the paper.