Odd-frequency pairing state in superconducting junctions

Using a quasiclassical Green’s function formalism, we show that odd-frequency pairing state can be ubiquitously induced in the superconducting junctions. In ballistic normal metal–superconductor (N/S) junctions where a superconductor has even-frequency symmetry in the bulk, we show that odd-frequency pairing state can be induced at the interface. Even in the s-wave superconductor junction, the amplitude of the odd-frequency component is enhanced in the normal metal. The appearance of the midgap Andreev resonant states due to the sign change of the anisotropic pair potential at the interface is reinterpreted in terms of the generation of the odd-frequency pair amplitude.