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Temperature-induced superconductivity enhancement under large exchange fields
Phys. Rev. Research 8, 043079 – Published 20 October, 2026
DOI: https://doi.org/10.1103/6q41-1cxp
Abstract
Through a comprehensive free energy analysis, we demonstrate that finite temperature can simultaneously weaken superconductivity and mitigate Zeeman-effect-induced depairing, leading to potential nonmonotonic temperature-dependent behaviors in superconductors subjected to large exchange fields. Remarkably, superconductivity can be counterintuitively enhanced by temperature when the Zeeman energy exceeds the superconducting order parameter, owing to the competition between thermal and magnetic effects. We propose that multiband effect offers one possible microscopic route for this temperature-induced enhancement and demonstrate it explicitly within a two-band superconducting model. A detailed parameter analysis identifies the conditions under which this phenomenon emerges, suggesting that temperature-enhanced superconductivity may be observable in materials such as and through transport and tunneling measurements.
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References (61)
- A. M. Clogston, Upper limit for the critical field in hard superconductors, Phys. Rev. Lett. 9, 266 (1962).
- B. Chandrasekhar, A note on the maximum critical field of high-field superconductors, Appl. Phys. Lett. 1, 7 (1962).
- G. Sarma, On the influence of a uniform exchange field acting on the spins of the conduction electrons in a superconductor, J. Phys. Chem. Solids 24, 1029 (1963).
- K. Maki, Effect of Pauli paramagnetism on magnetic properties of high-field superconductors, Phys. Rev. 148, 362 (1966).
- P. Fulde, High field superconductivity in thin films, Adv. Phys. 22, 667 (1973).
- P. Fulde and R. A. Ferrell, Superconductivity in a strong spin-exchange field, Phys. Rev. 135, A550 (1964).
- A. Larkin and Y. N. Ovchinnikov, Nonuniform state of superconductors, Sov. Phys. JETP 20, 762 (1965).
- P. Tedrow, R. Meservey, and B. Schwartz, Experimental evidence for a first-order magnetic transition in thin superconducting aluminum films, Phys. Rev. Lett. 24, 1004 (1970).
- R. Meservey, P. Tedrow, and P. Fulde, Magnetic field splitting of the quasiparticle states in superconducting aluminum films, Phys. Rev. Lett. 25, 1270 (1970).
- R. Meservey, P. Tedrow, and R. C. Bruno, Tunneling measurements on spin-paired superconductors with spin-orbit scattering, Phys. Rev. B 11, 4224 (1975).
- P. M. Tedrow and R. Meservey, Supercooling magnetic field and thermodynamic fluctuations in very thin superconducting aluminum films, Phys. Rev. B 16, 4825 (1977).
- P. Tedrow and R. Meservey, Measurement of the supercooling curve of a paramagnetically limited superconductor, Phys. Lett. A 63, 398 (1977).
- S. Kasahara, Y. Sato, S. Licciardello, M. Čulo, S. Arsenijević, T. Ottenbros, T. Tominaga, J. Böker, I. Eremin, T. Shibauchi, J. Wosnitza, N. E. Hussey, and Y. Matsuda, Evidence for an Fulde-Ferrell-Larkin-Ovchinnikov state with segmented vortices in the BCS-BEC-crossover superconductor FeSe, Phys. Rev. Lett. 124, 107001 (2020).
- C. Cho, J. Lyu, C. Y. Ng, J. J. He, K. T. Lo, D. Chareev, T. A. Abdel-Baset, M. Abdel-Hafiez, and R. Lortz, Evidence for the Fulde-Ferrell-Larkin-Ovchinnikov state in bulk , Nat. Commun. 12, 3676 (2021).
- P. Wan, O. Zheliuk, N. F. Q. Yuan, X. Peng, L. Zhang, M. Liang, U. Zeitler, S. Wiedmann, N. E. Hussey, T. T. M. Palstra, and J. Ye, Orbital Fulde-Ferrell-Larkin-Ovchinnikov state in an Ising superconductor, Nature (London) 619, 46 (2023).
- P. G. de Gennes and G. Sarma, Some properties of high field superconductors with magnetic impurities, Solid State Commun. 4, 449 (1966).
- K. Bennemann, Anomalous dependence of the superconducting transition temperature on paramagnetic impurities, Phys. Rev. Lett. 17, 438 (1966).
- J. Crow and R. Parks, The transition temperature of superconductors with paramagnetic impurities, Phys. Lett. 21, 378 (1966).
- J. E. Crow, R. Guertin, and R. Parks, Superconductivity in the presence of magnetic exchange fields, Phys. Rev. Lett. 19, 77 (1967).
- K. Bennemann, J. Garland, and F. Mueller, Nature of the magnetic order in superconducting dilute rare-earth alloys, Phys. Rev. Lett. 23, 169 (1969).
- M. Ishikawa and Ø. Fischer, Destruction of superconductivity by magnetic ordering in , Solid State Commun. 23, 37 (1977).
- W. A. Fertig, D. C. Johnston, L. E. DeLong, R. W. McCallum, M. B. Maple, and B. T. Matthias, Destruction of superconductivity at the onset of long-range magnetic order in the compound , Phys. Rev. Lett. 38, 987 (1977).
- L. Woolf, D. Johnston, H. MacKay, R. McCallum, and M. Maple, Superconducting and normal state properties of and , J. Low Temp. Phys. 35, 651 (1979).
- H. Eisaki, H. Takagi, R. J. Cava, B. Batlogg, J. J. Krajewski, W. F. Peck, Jr., K. Mizuhashi, J. O. Lee, and S. Uchida, Competition between magnetism and superconductivity in rare-earth nickel boride carbides, Phys. Rev. B 50, 647 (1994).
- V. Crespo, J. G. Rodrigo, H. Suderow, S. Vieira, D. G. Hinks, and I. K. Schuller, Evolution of the local superconducting density of states in close to the ferromagnetic transition, Phys. Rev. Lett. 102, 237002 (2009).
- U. Paramanik, D. Das, R. Prasad, and Z. Hossain, Reentrant superconductivity in , J. Phys.: Condens. Matter 25, 265701 (2013).
- L. M. Tran, A. J. Zaleski, and Z. Bukowski, Reentrant resistivity due to the interplay of superconductivity and magnetism in (), Phys. Rev. B 109, 014509 (2024).
- X. Wang, L. He, and S. Ji, Unified description for reentrance and enhancement in ferromagnetic superconductors, arXiv:2509.06889.
- V. Barzykin and L. P. Gor'kov, Gapless Fermi surfaces of anisotropic multiband superconductors in a magnetic field, Phys. Rev. Lett. 98, 087004 (2007).
- V. Barzykin, Magnetic-field-induced gapless state in multiband superconductors, Phys. Rev. B 79, 134517 (2009).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/6q41-1cxp for details of the free energy derivation for the two-band model; discussion of the validity and limitations of the weak-coupling approximation; distinction between the supercooling field and the physical critical field; detailed free energy analysis of two-band systems; discussion of highly anisotropic systems; analysis of the order of the phase transition in two-band systems; results for two-band -wave superconductors; additional examples of temperature-induced nonmonotonic superconducting behavior; and discussion of realistic two-band superconducting systems, which includes Refs. [56, 57, 58, 59, 60, 61].
- L. He and P. Zhuang, Stable Sarma state in two-band Fermi systems, Phys. Rev. B 79, 024511 (2009).
- T. Salamone, H. G. Hugdal, S. H. Jacobsen, and M. Amundsen, High magnetic field superconductivity in a two-band superconductor, Phys. Rev. B 107, 174516 (2023).
- K. Maki and T. Tsuneto, Pauli paramagnetism and superconducting state, Prog. Theor. Phys. 31, 945 (1964).
- X. Wang, G. Tang, and S.-H. Ji, First-order transitions in weak Ising spin-orbit-coupled superconductors, Phys. Rev. B 114, 144513 (2026).
- Y.-M. Xie, B. T. Zhou, and K. T. Law, Spin-orbit-parity-coupled superconductivity in topological monolayer , Phys. Rev. Lett. 125, 107001 (2020).
- M. Zehetmayer, A review of two-band superconductivity: Materials and effects on the thermodynamic and reversible mixed-state properties, Supercond. Sci. Technol. 26, 043001 (2013).
- A. Y. Liu, I. I. Mazin, and J. Kortus, Beyond Eliashberg superconductivity in : Anharmonicity, two-phonon scattering, and multiple gaps, Phys. Rev. Lett. 87, 087005 (2001).
- P. Szabó, P. Samuely, J. Kačmarčík, T. Klein, J. Marcus, D. Fruchart, S. Miraglia, C. Marcenat, and A. G. M. Jansen, Evidence for two superconducting energy gaps in by point-contact spectroscopy, Phys. Rev. Lett. 87, 137005 (2001).
- M. Iavarone, G. Karapetrov, A. E. Koshelev, W. K. Kwok, G. W. Crabtree, D. G. Hinks, W. N. Kang, E.-M. Choi, H. J. Kim, H.-J. Kim, and S. I. Lee, Two-band superconductivity in , Phys. Rev. Lett. 89, 187002 (2002).
- T. Yokoya, T. Kiss, A. Chainani, S. Shin, M. Nohara, and H. Takagi, Fermi surface sheet-dependent superconductivity in 2H-, Science 294, 2518 (2001).
- T. Kiss, T. Yokoya, A. Chainani, S. Shin, T. Hanaguri, M. Nohara, and H. Takagi, Charge-order-maximized momentum-dependent superconductivity, Nat. Phys. 3, 720 (2007).
- Y. Noat, J. A. Silva-Guillén, T. Cren, V. Cherkez, C. Brun, S. Pons, F. Debontridder, D. Roditchev, W. Sacks, L. Cario, P. Ordejón, A. García, and E. Canadell, Quasiparticle spectra of 2H-: Two-band superconductivity and the role of tunneling selectivity, Phys. Rev. B 92, 134510 (2015).
- T. Dvir, F. Massee, L. Attias, M. Khodas, M. Aprili, C. H. Quay, and H. Steinberg, Spectroscopy of bulk and few-layer superconducting with van der Waals tunnel junctions, Nat. Commun. 9, 598 (2018).
- C. Petrovic, P. Pagliuso, M. F. Hundley, R. Movshovich, J. L. Sarrao, J. D. Thompson, Z. Fisk, and P. Monthoux, Heavy-fermion superconductivity in at 2.3 K, J. Phys.: Condens. Matter 13, L337 (2001).
- P. M. C. Rourke, M. A. Tanatar, C. S. Turel, J. Berdeklis, C. Petrovic, and J. Y. T. Wei, Spectroscopic evidence for multiple order parameter components in the heavy fermion superconductor , Phys. Rev. Lett. 94, 107005 (2005).
- G. Seyfarth, J. P. Brison, G. Knebel, D. Aoki, G. Lapertot, and J. Flouquet, Multigap superconductivity in the heavy-fermion system , Phys. Rev. Lett. 101, 046401 (2008).
- M. P. Allan, F. Massee, D. Morr, J. Van Dyke, A. W. Rost, A. Mackenzie, C. Petrovic, and J. C. Davis, Imaging Cooper pairing of heavy fermions in , Nat. Phys. 9, 468 (2013).
- R. Khasanov, M. Bendele, A. Amato, K. Conder, H. Keller, H.-H. Klauss, H. Luetkens, and E. Pomjakushina, Evolution of two-gap behavior of the superconductor , Phys. Rev. Lett. 104, 087004 (2010).
- P. Bourgeois-Hope, S. Chi, D. Bonn, R. Liang, W. N. Hardy, T. Wolf, C. Meingast, N. Doiron-Leyraud, and L. Taillefer, Thermal conductivity of the iron-based superconductor FeSe: Nodeless gap with a strong two-band character, Phys. Rev. Lett. 117, 097003 (2016).
- Y. Sun, S. Kittaka, S. Nakamura, T. Sakakibara, K. Irie, T. Nomoto, K. Machida, J. Chen, and T. Tamegai, Gap structure of FeSe determined by angle-resolved specific heat measurements in applied rotating magnetic field, Phys. Rev. B 96, 220505(R) (2017).
- P. O. Sprau, A. Kostin, A. Kreisel, A. E. Böhmer, V. Taufour, P. C. Canfield, S. Mukherjee, P. J. Hirschfeld, B. M. Andersen, and J. S. Davis, Discovery of orbital-selective Cooper pairing in FeSe, Science 357, 75 (2017).
- H. Lin, W. Huang, G. Rai, Y. Yin, L. He, Q.-K. Xue, S. Haas, S. Kettemann, X. Chen, and S.-H. Ji, Real-space BCS-BEC crossover in FeSe monolayers, Phys. Rev. B 107, 104517 (2023).
- W. Huang, Y. Yin, H. Lin, W. Chen, Y. Liu, L. Ji, Z. Zhang, X. Zhou, X. Wang, X. Hu, et al., Experimental discovery of Sarma state in atomically thick superconducting FeSe films under high magnetic fields, arXiv:2412.15850.
- F. Giubileo, D. Roditchev, W. Sacks, R. Lamy, D. X. Thanh, J. Klein, S. Miraglia, D. Fruchart, J. Marcus, and P. Monod, Two-gap state density in : A true bulk property or a proximity effect? Phys. Rev. Lett. 87, 177008 (2001).
- Y. Sun and K. Maki, Impurity effects in -wave superconductors, Phys. Rev. B 51, 6059 (1995).
- R. C. Dynes, V. Narayanamurti, and J. P. Garno, Direct measurement of quasiparticle-lifetime broadening in a strong-coupled superconductor, Phys. Rev. Lett. 41, 1509 (1978).
- J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957).
- D. Liu, C. Li, J. Huang, B. Lei, L. Wang, X. Wu, B. Shen, Q. Gao, Y. Zhang, X. Liu, et al., Orbital origin of extremely anisotropic superconducting gap in nematic phase of FeSe superconductor, Phys. Rev. X 8, 031033 (2018).
- A. A. Vargas-Paredes, A. A. Shanenko, A. Vagov, M. V. Milošević, and A. Perali, Crossband versus intraband pairing in superconductors: Signatures and consequences of the interplay, Phys. Rev. B 101, 094516 (2020).
- N. Schopohl and K. Scharnberg, Tunneling density of states for the two-band model of superconductivity, Solid State Commun. 22, 371 (1977).