- Letter
- Open Access
Spin-projected charge conductance in SNN junctions with noncentrosymmetric superconductors
Phys. Rev. Research 5, L012022 – Published 17 February, 2023
DOI: https://doi.org/10.1103/PhysRevResearch.5.L012022
Abstract
A superconductor–normal-metal–normal-metal junction in which the superconducting potential is a mixture between -wave and -wave potentials is investigated using the Usadel equation equipped with Tanaka-Nazarov boundary conditions. This Research Letter provides several ways to distinguish between -wavechiral -wave superconductors and -wavehelical -wave superconductors and a way to determine whether a superconductor has a mixed pair potential. Thus it is of great importance in the determination of the pair potential of superconductors. It is shown that the different spin sectors satisfy independent equations and can thus be calculated separately even if the vector depends on the direction of momentum. This greatly simplifies the equations to be solved. It was found that a difference in conductance for sectors with opposite spins arises if both an -wave component and a -wave component are present, even in the absence of a magnetic field. It is shown that the spin-projected charge conductance for -wave chiral -wave junctions and -wave helical -wave junctions is qualitatively similar. A setup containing two superconductor–normal-metal junctions is shown to give a clear difference between the two types of superconductivity.
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References (73)
- P. G. de Gennes, Boundary effects in superconductors, Rev. Mod. Phys. 36, 225 (1964).
- F. Steglich, J. Aarts, C. D. Bredl, W. Lieke, D. Meschede, W. Franz, and H. Schäfer, Superconductivity in the Presence of Strong Pauli Paramagnetism: , Phys. Rev. Lett. 43, 1892 (1979).
- L. J. Buchholtz and G. Zwicknagl, Identification of -wave superconductors, Phys. Rev. B 23, 5788 (1981).
- J. G. Bednorz and K. A. Müller, Possible high superconductivity in the Ba–La–Cu–O system, Z. Phys. B: Condens. Matter 64, 189 (1986).
- L. Fu and C. L. Kane, Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator, Phys. Rev. Lett. 100, 096407 (2008).
- M. Sigrist and K. Ueda, Phenomenological theory of unconventional superconductivity, Rev. Mod. Phys. 63, 239 (1991).
- Y. Maeno, S. Kittaka, T. Nomura, S. Yonezawa, and K. Ishida, Evaluation of spin-triplet superconductivity in , J. Phys. Soc. Jpn. 81, 011009 (2012).
- M. Sigrist, Review on the chiral -wave phase of , Prog. Theor. Phys. Suppl. 160, 1 (2005).
- A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Classification of topological insulators and superconductors in three spatial dimensions, Phys. Rev. B 78, 195125 (2008).
- C. Kallin and A. Berlinsky, Is a chiral p-wave superconductor? J. Phys.: Condens. Matter 21, 164210 (2009).
- M. Eschrig, Spin-polarized supercurrents for spintronics: A review of current progress, Rep. Prog. Phys. 78, 104501 (2015).
- J. Linder and J. W. Robinson, Superconducting spintronics, Nat. Phys. 11, 307 (2015).
- H. G. Suh, H. Menke, P. M. R. Brydon, C. Timm, A. Ramires, and D. F. Agterberg, Stabilizing even-parity chiral superconductivity in , Phys. Rev. Res. 2, 032023(R) (2020).
- F. S. Bergeret, A. F. Volkov, and K. B. Efetov, Odd triplet superconductivity and related phenomena in superconductor-ferromagnet structures, Rev. Mod. Phys. 77, 1321 (2005).
- Y. Tanaka, M. Sato, and N. Nagaosa, Symmetry and topology in superconductors–odd-frequency pairing and edge states–, J. Phys. Soc. Jpn. 81, 011013 (2012).
- J. Linder and A. V. Balatsky, Odd-frequency superconductivity, Rev. Mod. Phys. 91, 045005 (2019).
- J. Cayao, C. Triola, and A. M. Black-Schaffer, Odd-frequency superconducting pairing in one-dimensional systems, Eur. Phys. J.: Spec. Top. 229, 545 (2020).
- Non-centrosymmetric Superconductors: Introduction and Overview, edited by E. Bauer and M. Sigrist, Lecture Notes in Physics Vol. 847 (Springer, Berlin, 2012).
- E. Bauer, G. Hilscher, H. Michor, C. Paul, E.-W. Scheidt, A. Gribanov, Y. Seropegin, H. Noël, M. Sigrist, and P. Rogl, Heavy Fermion Superconductivity and Magnetic Order in Noncentrosymmetric , Phys. Rev. Lett. 92, 027003 (2004).
- G. Amano, S. Akutagawa, T. Muranaka, Y. Zenitani, and J. Akimitsu, Superconductivity at 18 K in yttrium sesquicarbide system, , J. Phys. Soc. Jpn. 73, 530 (2004).
- T. Akazawa, H. Hidaka, H. Kotegawa, T. C. Kobayashi, T. Fujiwara, E. Yamamoto, Y. Haga, R. Settai, and Y. Ōnuki, Pressure-induced superconductivity in UIr, J. Phys. Soc. Jpn. 73, 3129 (2004).
- K. Togano, P. Badica, Y. Nakamori, S. Orimo, H. Takeya, and K. Hirata, Superconductivity in the Metal Rich Li-Pd-B Ternary Boride, Phys. Rev. Lett. 93, 247004 (2004).
- N. Tateiwa, Y. Haga, T. D. Matsuda, S. Ikeda, T. Yasuda, T. Takeuchi, R. Settai, and Y. Ōnuki, Novel pressure phase diagram of heavy fermion superconductor investigated by ac calorimetry, J. Phys. Soc. Jpn. 74, 1903 (2005).
- N. Kimura, K. Ito, K. Saitoh, Y. Umeda, H. Aoki, and T. Terashima, Pressure-Induced Superconductivity in Noncentrosymmetric Heavy-Fermion , Phys. Rev. Lett. 95, 247004 (2005).
- I. Sugitani, Y. Okuda, H. Shishido, T. Yamada, A. Thamizhavel, E. Yamamoto, T. D. Matsuda, Y. Haga, T. Takeuchi, R. Settai, and Y. Ōnuki, Pressure-induced heavy-fermion superconductivity in antiferromagnet without inversion symmetry, J. Phys. Soc. Jpn. 75, 043703 (2006).
- F. Honda, I. Bonalde, K. Shimizu, S. Yoshiuchi, Y. Hirose, T. Nakamura, R. Settai, and Y. Ōnuki, Pressure-induced superconductivity and large upper critical field in the noncentrosymmetric antiferromagnet , Phys. Rev. B 81, 140507 (2010).
- R. Settai, I. Sugitani, Y. Okuda, A. Thamizhavel, M. Nakashima, Y. Ōnuki, and H. Harima, Pressure-induced superconductivity in without inversion symmetry, J. Magn. Magn. Mater. 310, 844 (2007).
- E. Bauer, G. Rogl, X.-Q. Chen, R. T. Khan, H. Michor, G. Hilscher, E. Royanian, K. Kumagai, D. Z. Li, Y. Y. Li, R. Podloucky, and P. Rogl, Unconventional superconducting phase in the weakly correlated noncentrosymmetric compound, Phys. Rev. B 82, 064511 (2010).
- W. Xie, P. Zhang, B. Shen, W. Jiang, G. Pang, T. Shang, C. Cao, M. Smidman, and H. Yuan, CaPtAs: A new noncentrosymmetric superconductor, Sci. China Phys. Mech. Astron. 63, 237412 (2020).
- G. Annunziata, D. Manske, and J. Linder, Proximity effect with noncentrosymmetric superconductors, Phys. Rev. B 86, 174514 (2012).
- Y. Tanaka, T. Kokkeler, and A. Golubov, Theory of proximity effect in -wave superconductor junctions, Phys. Rev. B 105, 214512 (2022).
- W. Belzig, F. K. Wilhelm, C. Bruder, G. Schön, and A. Zaikin, Quasiclassical Green's function approach to mesoscopic superconductivity, Superlattices Microstruct. 25, 1251 (1999).
- V. Chandrasekhar, An introduction to the quasiclassical theory of superconductivity for diffusive proximity-coupled systems, in The Physics of Superconductors, edited by K.-H. Bennemann and J. Ketterson (Springer, Berlin, 2004), pp. 55–110.
- G. Eilenberger, Transformation of Gorkov's equation for type II superconductors into transport-like equations, Z. Phys. A 214, 195 (1968).
- A. Larkin and Y. Ovchinnikov, Quasiclassical method in the theory of superconductivity, Zh. Eksp. Teor. Fiz. 55, 2262 (1968) [Sov. Phys. JETP 28, 1200 (1969)].
- K. D. Usadel, Generalized Diffusion Equation for Superconducting Alloys, Phys. Rev. Lett. 25, 507 (1970).
- B. Josephson, Possible new effects in superconductive tunnelling, Phys. Lett. 1, 251 (1962).
- B. Josephson, Coupled superconductors, Rev. Mod. Phys. 36, 216 (1964).
- B. Josephson, Supercurrents through barriers, Adv. Phys. 14, 419 (1965).
- A. I. Larkin and Y. U. N. Ovchinnikov, Nonlinear effects during the motion of vortices in superconductors, Zh. Eksp. Teor. Fiz. 73, 7 (1977) [Sov. Phys. JETP 46, 155 (1978)].
- A. Kastalsky, A. W. Kleinsasser, L. H. Greene, R. Bhat, F. P. Milliken, and J. P. Harbison, Observation of Pair Currents in Superconductor-Semiconductor Contacts, Phys. Rev. Lett. 67, 3026 (1991).
- A. Volkov, A. Zaitsev, and T. Klapwijk, Proximity effect under nonequilibrium conditions in double-barrier superconducting junctions, Phys. C (Amsterdam) 210, 21 (1993).
- A. Volkov, The proximity effect and subgap conductivity in superconductor-barrier-normal metal contacts, Phys. B (Amsterdam) 203, 267 (1994).
- B. J. van Wees, P. de Vries, P. Magnée, and T. M. Klapwijk, Excess Conductance of Superconductor-Semiconductor Interfaces Due to Phase Conjugation Between Electrons and Holes, Phys. Rev. Lett. 69, 510 (1992).
- Y. V. Nazarov, Circuit Theory of Andreev Conductance, Phys. Rev. Lett. 73, 1420 (1994).
- S. Yip, Conductance anomalies for normal-metal–insulator–superconductor contacts, Phys. Rev. B 52, 15504 (1995).
- V. Schmidt, The Physics of Superconductors (Springer, Berlin, 1997).
- Y. Tanaka and S. Kashiwaya, Anomalous charge transport in triplet superconductor junctions, Phys. Rev. B 70, 012507 (2004).
- M. Eschrig, C. Iniotakis, and Y. Tanaka, Properties of interfaces and surfaces in non-centrosymmetric superconductors, in Non-centrosymmetric Superconductors, edited by E. Bauer and M. Sigrist, Lecture Notes in Physics Vol. 847 (Springer, Berlin, 2012), pp. 313–357.
- P. Gentile, C. Noce, A. Romano, G. Annunziata, J. Linder, and M. Cuoco, Odd-frequency triplet pairing in mixed-parity superconductors, arXiv:1109.4885.
- Y. Rahnavard, D. Manske, and G. Annunziata, Magnetic Josephson junctions with noncentrosymmetric superconductors, Phys. Rev. B 89, 214501 (2014).
- V. Mishra, Y. Li, F.-C. Zhang, and S. Kirchner, Effects of spin-orbit coupling in superconducting proximity devices: Application to heterostructures, Phys. Rev. B 103, 184505 (2021).
- Y. Tanaka, Y. V. Nazarov, and S. Kashiwaya, Circuit Theory of Unconventional Superconductor Junctions, Phys. Rev. Lett. 90, 167003 (2003).
- Y. V. Nazarov, Novel circuit theory of Andreev reflection, Superlattices Microstruct. 25, 1221 (1999).
- Y. Tanaka and A. A. Golubov, Theory of the Proximity Effect in Junctions with Unconventional Superconductors, Phys. Rev. Lett. 98, 037003 (2007).
- Y. Tanaka, Y. V. Nazarov, A. A. Golubov, and S. Kashiwaya, Theory of charge transport in diffusive normal metal/unconventional singlet superconductor contacts, Phys. Rev. B 69, 144519 (2004).
- Y. Tanaka, S. Kashiwaya, and T. Yokoyama, Theory of enhanced proximity effect by midgap Andreev resonant state in diffusive normal-metal/triplet superconductor junctions, Phys. Rev. B 71, 094513 (2005).
- Y. Asano, Y. Tanaka, A. A. Golubov, and S. Kashiwaya, Conductance Spectroscopy of Spin-Triplet Superconductors, Phys. Rev. Lett. 99, 067005 (2007).
- T. Yokoyama, Y. Tanaka, and A. A. Golubov, Resonant proximity effect in normal metal/diffusive ferromagnet/superconductor junctions, Phys. Rev. B 73, 094501 (2006).
- Y. Sawa, T. Yokoyama, Y. Tanaka, and A. A. Golubov, Quasiclassical Green's function theory of the Josephson effect in chiral -wave superconductor/diffusive normal metal/chiral -wave superconductor junctions, Phys. Rev. B 75, 134508 (2007).
- S.-I. Suzuki, A. A. Golubov, Y. Asano, and Y. Tanaka, Effects of phase coherence on local density of states in superconducting proximity structures, Phys. Rev. B 100, 024511 (2019).
- S.-I. Suzuki, A. A. Golubov, Y. Asano, and Y. Tanaka, Quasiparticle spectrum in mesoscopic superconducting junctions with weak magnetization, in Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2019), JPS Conference Proceedings Vol. 30 (Physical Society of Japan, Tokyo, 2020), p. 011045.
- T. Kokkeler, Usadel equation for a four terminal junction, Master's thesis, University of Twente, 2021.
- G. E. Volovik, The Universe in a Helium Droplet, International Series of Monographs on Physics Vol. 117 (Oxford University Press, Oxford, 2003).
- C. Iniotakis, N. Hayashi, Y. Sawa, T. Yokoyama, U. May, Y. Tanaka, and M. Sigrist, Andreev bound states and tunneling characteristics of a noncentrosymmetric superconductor, Phys. Rev. B 76, 012501 (2007).
- X.-L. Qi, T. L. Hughes, S. Raghu, and S.-C. Zhang, Time-Reversal-Invariant Topological Superconductors and Superfluids in Two and Three Dimensions, Phys. Rev. Lett. 102, 187001 (2009).
- Y. Tanaka, T. Yokoyama, A. V. Balatsky, and N. Nagaosa, Theory of topological spin current in noncentrosymmetric superconductors, Phys. Rev. B 79, 060505 (2009).
- M. Matsumoto and M. Sigrist, Quasiparticle states near the surface and the domain wall in a -wave superconductor, J. Phys. Soc. Jpn. 68, 994 (1999).
- N. Read and D. Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect, Phys. Rev. B 61, 10267 (2000).
- A. Furusaki, M. Matsumoto, and M. Sigrist, Spontaneous Hall effect in a chiral -wave superconductor, Phys. Rev. B 64, 054514 (2001).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L012022 for an explicit calculation.
- P. Burset, F. Keidel, Y. Tanaka, N. Nagaosa, and B. Trauzettel, Transport signatures of superconducting hybrids with mixed singlet and chiral triplet states, Phys. Rev. B 90, 085438 (2014).
- S.-P. Chiu, C. Tsuei, S.-S. Yeh, F.-C. Zhang, S. Kirchner, and J.-J. Lin, Observation of triplet superconductivity in heterostructures, Sci. Adv. 7, eabg6569 (2021).