It is known that so-called odd-frequency pairing is possible where Cooper pair is formed between two electrons with different times and pair amplitude (pair function) has a sign change with the exchange of times of two electrons [1]. We have clarified that odd-frequency pairing ubiquitously presents in superconductor junctions [2-3] and it is amplified at the edge or interface in the presence of zero energy surface Andreev bound state (ZESABS) and  Majorana zero mode(MZM) [2-3].

One of the remarkable properties generated by odd-frequency spin-triplet s-wave pairing is the anomalous proximity effect in diffusive normal metal (DN) / spin-triplet p-wave superconductor junctions where quasiparticle density of states in DN has a zero energy peak (ZEP) of LDOS due to the penetration of odd-frequency spin-triplet s-wave pairing[7,8]. Also in 1d  or 2d junctions with flat band ZESABS or MZM, the zero voltage conductance is quantized [5-6].

Recently it has been proven that the anomalous proximity effect is robust against the inclusion of the spin-singlet s-wave pairing, as far as p-wave pairing is dominant.[7-8]

This implies that odd-frequency pairing can be detected in non-centrosymmetric superconductors. It is also noted that the anomalous proximity effect is possible in the Rashba superconductor realized by nano-wire on the surface of a conventional spin-singlet s-wave superconductor with spin-orbit coupling and Zeeman field [6]. As regards the verification of the anomalous proximity effect, our prediction has been observed in the tunneling experiments of CoSi₂/TiSi₂ heterojunctions [9].

References

1.V. L. Berezinskii, Pis’ma Zh. Eksp. Teor. Fiz. 20, 628 (1974).
2. Y. Tanaka, M. Sato and N. Nagaosa, J. Phys. Soc. Jpn. 81, 011013 (2012).
3.  Y. Tanaka, Y. Tanuma, and A. A. Golubov. Phys. Rev. B, 76, 054522 (2007).
4. Y. Tanaka and A.A. Golubov, Phys. Rev. Lett. 98, 037003 (2007),
5. Y. Tanaka and S. Kashiwaya, Phys. Rev. B 70, 012507 (2004).
6. Y. Asano and Y. Tanaka, Phys. Rev. B 87, 104513 (2013).
7. Y. Tanaka, T. Kokkeler, and A. Golubov, Phys. Rev. B 105, 214512 (2022).
8. T. H. Kokkeler, Y. Tanaka, and A. A. Golubov, Phys. Rev. Res. 5, L012022 (2022).
9.  S.-P. Chiu, et al, Science Advances 7, eabg6569 (2021), Nanoscale, 15, 9179　(2023).

Please contact phweb@ust.hk should you have questions about the talk.