- Access by Xinjiang University
Collective excitations and divergent spin currents in noncentrosymmetric superconductors
Phys. Rev. B 113, 134523 – Published 24 April, 2026
DOI: https://doi.org/10.1103/tsk3-m7v3
Abstract
We study the collective modes in a noncentrosymmetric superconductor with Rashba spin-orbit coupling under laser irradiation. The concept of Anderson Pseudospin Resonance allows us to reveal how laser driving gives rise not only to the established resonant enhancement of third harmonic response, but also to a resonant enhancement in the second-harmonic response of the spin current. We propose a theory that explains the phenomenon without including interband transitions. The theory is corroborated by numerical simulations, which incorporate interband effects and allow us to clarify the signatures of the collective modes in the long-time dynamics of the superconductor.
Physics Subject Headings (PhySH)
Article Text
References (43)
- L. P. Gor'kov and E. I. Rashba, Superconducting 2D system with lifted spin degeneracy: Mixed singlet-triplet state, Phys. Rev. Lett. 87, 037004 (2001).
- E. Bauer and M. Sigrist, Non-centrosymmetric superconductors: introduction and overview (Springer Science & Business Media, 2012), Vol. 847.
- P. A. Frigeri, D. F. Agterberg, and M. Sigrist, Spin susceptibility in superconductors without inversion symmetry, New J. Phys. 6, 115 (2004).
- P. A. Frigeri, D. F. Agterberg, A. Koga, and M. Sigrist, Superconductivity without inversion symmetry: MnSi versus , Phys. Rev. Lett. 92, 097001 (2004).
- P. A. Frigeri, D. F. Agterberg, A. Koga, and M. Sigrist, Erratum: Superconductivity without inversion symmetry: MnSi versus [Phys. Rev. Lett. 92, 097001(E) (2004)], Phys. Rev. Lett. 93, 099903(E) (2004).
- P. Frigeri, D. Agterberg, I. Milat, and M. Sigrist, Phenomenological theory of the s-wave state in superconductors without an inversion center, Eur. Phys. J. B 54, 435 (2006).
- K. V. Samokhin and V. P. Mineev, Gap structure in noncentrosymmetric superconductors, Phys. Rev. B 77, 104520 (2008).
- A. B. Vorontsov, I. Vekhter, and M. Eschrig, Surface bound states and spin currents in noncentrosymmetric superconductors, Phys. Rev. Lett. 101, 127003 (2008).
- L. Klam, D. Einzel, and D. Manske, Electronic Raman scattering in noncentrosymmetric superconductors, Phys. Rev. Lett. 102, 027004 (2009).
- N. Bittner, D. Einzel, L. Klam, and D. Manske, Leggett modes and the Anderson-Higgs mechanism in superconductors without inversion symmetry, Phys. Rev. Lett. 115, 227002 (2015).
- 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).
- 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).
- P. Badica, T. Kondo, and K. Togano, Superconductivity in a new pseudo-binary boride system, J. Phys. Soc. Jpn. 74, 1014 (2005).
- R. Matsunaga, Y. I. Hamada, K. Makise, Y. Uzawa, H. Terai, Z. Wang, and R. Shimano, Higgs amplitude mode in the BCS superconductors induced by terahertz pulse excitation, Phys. Rev. Lett. 111, 057002 (2013).
- F. Giorgianni, T. Cea, C. Vicario, C. P. Hauri, W. K. Withanage, X. Xi, and L. Benfatto, Leggett mode controlled by light pulses, Nat. Phys. 15, 341 (2019).
- H. Chu, M.-J. Kim, K. Katsumi, S. Kovalev, R. D. Dawson, L. Schwarz, N. Yoshikawa, G. Kim, D. Putzky, Z. Z. Li, et al., Phase-resolved Higgs response in superconducting cuprates, Nat. Commun. 11, 1793 (2020).
- N. Tsuji and H. Aoki, Theory of Anderson pseudospin resonance with Higgs mode in superconductors, Phys. Rev. B 92, 064508 (2015).
- Y. Murotani, N. Tsuji, and H. Aoki, Theory of light-induced resonances with collective Higgs and leggett modes in multiband superconductors, Phys. Rev. B 95, 104503 (2017).
- M. A. Müller, P. Shen, M. Dzero, and I. Eremin, Short-time dynamics in -wave superconductor with incipient bands, Phys. Rev. B 98, 024522 (2018).
- L. Schwarz and D. Manske, Theory of driven Higgs oscillations and third-harmonic generation in unconventional superconductors, Phys. Rev. B 101, 184519 (2020).
- M. A. Müller, P. A. Volkov, I. Paul, and I. M. Eremin, Interplay between nematicity and bardasis-Schrieffer modes in the short-time dynamics of unconventional superconductors, Phys. Rev. B 103, 024519 (2021).
- J. Fiore, M. Udina, M. Marciani, G. Seibold, and L. Benfatto, Contribution of collective excitations to third harmonic generation in two-band superconductors: The case of , Phys. Rev. B 106, 094515 (2022).
- S. Klein and D. Manske, Role of Higgs and leggett modes for the third harmonic response in noncentrosymmetric superconductors, Phys. Rev. B 110, 014510 (2024).
- H. Krull, N. Bittner, G. Uhrig, D. Manske, and A. Schnyder, Coupling of Higgs and leggett modes in non-equilibrium superconductors, Nat. Commun. 7, 11921 (2016).
- M. A. Silaev, R. Ojajärvi, and T. T. Heikkilä, Spin and charge currents driven by the Higgs mode in high-field superconductors, Phys. Rev. Res. 2, 033416 (2020).
- M. Smidman, M. Salamon, H. Yuan, and D. Agterberg, Superconductivity and spin–orbit coupling in non-centrosymmetric materials: A review, Rep. Prog. Phys. 80, 036501 (2017).
- I. E. Dzyaloshinskii, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics, J. Phys. Chem. Solids 4, 241 (1958).
- T. Moriya, Anisotropic superexchange interaction and weak ferromagnetism, Phys. Rev. 120, 91 (1960).
- M. Schüler, J. A. Marks, Y. Murakami, C. Jia, and T. P. Devereaux, Gauge invariance of light-matter interactions in first-principle tight-binding models, Phys. Rev. B 103, 155409 (2021).
- K.-C. Weng and C. Hu, The -wave superconductivity in the presence of Rashba interaction in 2DEG, Sci. Rep. 6, 29919 (2016).
- D. Bercioux and P. Lucignano, Quantum transport in Rashba spin–orbit materials: A review, Rep. Prog. Phys. 78, 106001 (2015).
- K. Hamamoto, M. Ezawa, K. W. Kim, T. Morimoto, and N. Nagaosa, Nonlinear spin current generation in noncentrosymmetric spin-orbit coupled systems, Phys. Rev. B 95, 224430 (2017).
- E. I. Rashba, Spin–orbit coupling and spin transport, Phys. E (Amsterdam, Neth.) 34, 31 (2006).
- E. I. Rashba, Spin currents in thermodynamic equilibrium: The challenge of discerning transport currents, Phys. Rev. B 68, 241315(R) (2003).
- S. Maekawa, H. Adachi, K.-i. Uchida, J. Ieda, and E. Saitoh, Spin current: Experimental and theoretical aspects, J. Phys. Soc. Jpn. 82, 102002 (2013).
- T. Cea, C. Castellani, and L. Benfatto, Nonlinear optical effects and third-harmonic generation in superconductors: Cooper pairs versus Higgs mode contribution, Phys. Rev. B 93, 180507(R) (2016).
- A. Alvermann and H. Fehske, High-order commutator-free exponential time-propagation of driven quantum systems, J. Comput. Phys. 230, 5930 (2011).
- J. Li, D. Golez, G. Mazza, A. J. Millis, A. Georges, and M. Eckstein, Electromagnetic coupling in tight-binding models for strongly correlated light and matter, Phys. Rev. B 101, 205140 (2020).
- R. Matsunaga, N. Tsuji, H. Fujita, A. Sugioka, K. Makise, Y. Uzawa, H. Terai, Z. Wang, H. Aoki, and R. Shimano, Light-induced collective pseudospin precession resonating with Higgs mode in a superconductor, Science 345, 1145 (2014).
- N. Tsuji, Y. Murakami, and H. Aoki, Nonlinear light–Higgs coupling in superconductors beyond BCS: Effects of the retarded phonon-mediated interaction, Phys. Rev. B 94, 224519 (2016).
- S. Maekawa, T. Kikkawa, H. Chudo, J. Ieda, and E. Saitoh, Spin and spin current—from fundamentals to recent progress, J. Appl. Phys. 133, 020902 (2023).
- S. Wolf and S. Rachel, Spin-orbit coupled superconductivity: Rashba-Hubbard model on the square lattice, Phys. Rev. B 102, 174512 (2020).
- M. Tohyama, Applications of time-dependent density-matrix approach, Front. Phys. 8, 67 (2020).