Odd-frequency pairing state in superconducting junctions

We have theoretically studied the induced odd-frequency pairing states in ballistic normal metal/superconductor (N/S) junctions where a superconductor has even-frequency symmetry in the bulk. We demonstrate that the pair amplitude in the junction has an admixture of an odd-frequency component due to the breakdown of translational invariance near the N/S interface [1]. We have also studied about the proximity effect in junctions between diffusive normal metals (DN) and superconductors. It is revealed for spin-triplet superconductor that the resulting symmetry in DN is always odd-frequency spin-triplet [2]. The resulting quasiparticle density of state in DN has a zero energy peak [3]. This unusual proximity effect due to the generation of odd-frequency state is also expected in ferromagnet / superconductor junctions [4]. \newline [1] Y. Tanaka, et al, Phys. Rev. Lett. 99, 037005 (2007), M. Eschirig, et al, J. Low Temp. Phys. \textbf{147} 457 (2007). \newline [2] Y. Tanaka and A.A. Golubov, Phys. Rev. Lett. 98 037003 (2007). \newline [3] Y. Tanaka and S. Kashiwaya, Phys. Rev. B, 70, 012507 (2004). \newline [4] Y. Asano, Y. Tanaka and A. A. Golubov, Phys. Rev. Lett., 98, 107002 (2007).