Ubiquitous presence of odd-frequency pairing state in superconducting junctions

We predict generation of the odd-frequency pairing state near interfaces in conventional even-frequency superconductors. Using the quasiclassical Greenʹs function formalism, we show that the pair amplitude can be decomposed into even and odd-frequency components. We demonstrate that, quite generally, the spin-singlet even-parity (spin-triplet odd-parity) pair potential in a superconductor induces the odd-frequency pairing component with spin-singlet odd-parity (spin-triplet even-parity) near interfaces. The magnitude of the induced odd-frequency component is enhanced in the presence of the midgap Andreev resonant state due to the sign change of the anisotropic pair potential at the interface. The Josephson effect should therefore occur between odd- and even-frequency superconductors, contrary to the standard wisdom. A method to probe the odd-frequency superconductors is proposed.