- Letter
- Open Access
From orbital to paramagnetic pair breaking in layered superconductor
Phys. Rev. Research 6, L042006 – Published 7 October, 2024
DOI: https://doi.org/10.1103/PhysRevResearch.6.L042006
Abstract
The superconducting transition-metal dichalcogenides and are intensively studied on account of their unique electronic properties such as Ising superconductivity, found in multi- and monolayers, with upper critical fields beyond the Pauli limit. Even in bulk crystals, there are reports of multiband superconductivity and exotic states, such as the Fulde-Ferrell-Larkin-Ovchinnikov phase. In this work, we investigate the superconducting properties of through a detailed high-field mapping of the phase diagram by means of magnetotransport and magnetostriction experiments. We compare the phase diagram between bulk crystals and a 6-nm-thick flake of and find a drastically enhanced Maki parameter in the flake, signifying a change of the relevant pair-breaking mechanism from orbital to paramagnetic pair breaking, which we attribute to an effect of enhanced spin-orbit coupling.
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References (59)
- B. T. Zhou, N. F. Q. Yuan, H. L. Jiang, and K. T. Law, Ising superconductivity and Majorana fermions in transition-metal dichalcogenides, Phys. Rev. B 93, 180501(R) (2016).
- S. C. de la Barrera, M. R. Sinko, D. P. Gopalan,N. Sivadas, K. L. Seyler, K. Watanabe, T. Taniguchi, A. W. Tsen, X. Xu, D. Xiao, and B. M. Hunt, Tuning Ising superconductivity with layer and spin-orbit coupling in two-dimensional transition-metal dichalcogenides, Nat. Commun. 9, 1427 (2018).
- Y. Xing, K. Zhao, P. Shan, F. Zheng, Y. Zhang, H. Fu, Y. Liu, M. Tian, C. Xi, H. Liu, J. J. Feng, X. X. Lin, S. Ji, X. Chen, Q. K. Xue, and J. Wang, Ising superconductivity and quantum phase transition in macro-size monolayer , Nano Lett. 17, 6802 (2017).
- D. Lin, S. Li, J. Wen, H. Berger, L. Forró, H. Zhou, S. Jia, T. Taniguchi, K. Watanabe, X. Xi, and M. S. Bahramy, Patterns and driving forces of dimensionality-dependent charge density waves in 2H-type transition metal dichalcogenides, Nat. Commun. 11, 2406 (2020).
- M. Leroux, M. Le Tacon, M. Calandra, L. Cario, M.-A. Méasson, P. Diener, E. Borrissenko, A. Bosak, and P. Rodière, Anharmonic suppression of charge density waves in , Phys. Rev. B 86, 155125 (2012).
- M. Leroux, L. Cario, A. Bosak, and P. Rodière, Traces of charge density waves in , Phys. Rev. B 97, 195140 (2018).
- R. Bianco, I. Errea, L. Monacelli, M. Calandra, and F. Mauri, Quantum enhancement of charge density wave in in the two-dimensional limit, Nano Lett. 19, 3098 (2019).
- C. Wen, Y. Xie, Y. Wu, S. Shen, P. Kong, H. Lian, J. Li, H. Xing, and S. Yan, Impurity-pinned incommensurate charge density wave and local phonon excitations in , Phys. Rev. B 101, 241404(R), (2020).
- A. Majumdar, D. Vangennep, J. Brisbois, D. Chareev, A. V. Sadakov, A. S. Usoltsev, M. Mito, A. V. Silhanek, T. Sarkar, A. Hassan, O. Karis, R. Ahuja, and M. Abdel-Hafiez, Interplay of charge density wave and multiband superconductivity in layered quasi-two-dimensional materials: The case of and , Phys. Rev. Mater. 4, 084005 (2020).
- V. G. Tissen, M. R. Osorio, J. P. Brison, N. M. Nemes, M. García-Hernández, L. Cario, P. Rodière, S. Vieira, and H. Suderow, Pressure dependence of superconducting critical temperature and upper critical field of , Phys. Rev. B 87, 134502 (2013).
- J. Kačmarčík, Z. Pribulová, C. Marcenat, T. Klein, P. Rodière, L. Cario, and P. Samuely, Specific heat measurements of a superconducting single crystal in an external magnetic field: Energy gap structure, Phys. Rev. B 82, 014518 (2010).
- H. Lian, Y. Wu, H. Xing, S. Wang, and Y. Liu, Effect of stoichiometry on the superconducting transition temperature in single crystalline , Physica C 538, 27 (2017).
- I. Guillamón, H. Suderow, S. Vieira, L. Cario, P. Diener, and P. Rodière, Superconducting density of states and vortex cores of , Phys. Rev. Lett. 101, 166407 (2008).
- J. Kačmarčík, Z. Pribulová, C. Marcenat, T. Klein, P. Rodière, L. Cario, and P. Samuely, Studies on two-gap superconductivity in , Physica C 470, S719 (2010).
- X. Bi, Z. Li, J. Huang, F. Qin, C. Zhang, Z. Xu, L. Zhou, M. Tang, C. Qiu, P. Tang, T. Ideue, T. Nojima, Y. Iwasa, and H. Yuan, Orbital-selective two-dimensional superconductivity in , Phys. Rev. Res. 4, 013188 (2022).
- C. Cho, J. Lyu, C. Y. Ng, J. Jun He, K. To 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).
- R. Küchler, A. Wörl, P. Gegenwart, M. Berben, B. Bryant, and S. Wiedmann, The world's smallest capacitive dilatometer, for high-resolution thermal expansion and magnetostriction in high magnetic fields, Rev. Sci. Instrum. 88, 083903 (2017).
- D. Huang, H. Nakamura, K. Küster, U. Wedig, N. B. M. Schröter, V. N. Strocov, U. Starke, and H. Takagi, Probing the interlayer coupling in via soft-x-ray angle-resolved photoemission spectroscopy, Phys. Rev. B 105, 245145 (2022).
- R. Yan, G. Khalsa, B. T. Schaefer, A. Jarjour, S. Rouvimov, K. C. Nowack, H. G. Xing, and D. Jena, Thickness dependence of superconductivity in ultrathin , Appl. Phys. Express 12, 023008 (2019).
- E. Martino, C. Putzke, M. König, P. J. W. Moll, H. Berger, D. LeBoeuf, M. Leroux, C. Proust, A. Akrap, H. Kirmse, C. Koch, S. N. Zhang, Q. S. Wu, O. V. Yazyev, L. Forró, and K. Semeniuk, Unidirectional Kondo scattering in layered , npj 2D Mater. Appl. 5, 86 (2021).
- B. Bag, D. J. Sivananda, P. Mandal, S. S. Banerjee, A. K. Sood, and A. K. Grover, Vortex depinning as a nonequilibrium phase transition phenomenon: Scaling of current-voltage curves near the low and the high critical-current states in single crystals, Phys. Rev. B 97, 134510 (2018).
- K. Onabe, M. Naito, and S. Tanaka, Anisotropy of the upper critical field in superconducting , J. Phys. Soc. Jpn. 45, 50 (1978).
- J. Singleton, N. Harrison, C. H. Mielke, J. A. Schlueter, and A. M. Kini, A statistical model for the intrinsically broad superconducting-to-normal transition in quasi-two-dimensional crystalline organic metals, J. Phys.: Condens. Matter 13, L899 (2001).
- 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).
- P. Szabó, P. Samuely, J. Kačmarčik, A. G. M. Jansen, A. Briggs, A. Lafond, and A. Meerschaut, Interlayer transport in the highly anisotropic misfit-layer superconductor (LaSe)1.14(), Phys. Rev. Lett. 86, 5990 (2001).
- J. L. Vicent, S. J. Hillenius, and R. V. Coleman, Critical-field enhancement and reduced dimensionality in superconducting layer compounds, Phys. Rev. Lett. 44, 892 (1980).
- P. Baidya, D. Sahani, H. Kumar Kundu, S. Kaur, P. Tiwari, V. Bagwe, J. Jesudasan, A. Narayan, P. Raychaudhuri, and A. Bid, Transition from three- to two-dimensional Ising superconductivity in few-layer by proximity effect from van der Waals heterostacking, Phys. Rev. B 104, 174510 (2021).
- F. Jellinek, G. Brauer and H. Müller, Molybdenum and niobium sulphides, Nature (London) 185, 376 (1960).
- K. Momma, and F. Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr. 44, 1272 (2011).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L042006 for the models and calculations used for this work, as well as figures showing additional data.
- M. Tinkham, Effect of fluxoid quantization on transition of superconducting films, Phys. Rev. 129, 2413 (1963).
- M. Tinkham, Introduction to Superconductivity, 2nd ed. (McGraw-Hill, New York, 1996).
- V. V. Eremenko, V. A. Sirenko, H. Szymczak, and A. Nabialek, Magnetostriction of superconductors (a review), Low Temp. Phys. 25, 225 (1999).
- C. H. Sharma, A. P. Surendran, S. S. Varma, and M. Thalakulam, 2D superconductivity and vortex dynamics in , Commun. Phys. 1, 90 (2018).
- J. M. Lu, O. Zheliuk, I. Leermakers, N. F. Q. Yuan, U. Zeitler, K. T. Law, and J. T. Ye, Evidence for two-dimensional Ising superconductivity in gated , Science 350, 1353 (2015).
- J. Zeng, E. Liu, Y. Fu, Z. Chen, C. Pan, C. Wang, M. Wang, Y. Wang, K. Xu, S. Cai, X. Yan, Y. Wang, X. Liu, P. Wang, S. J. Liang, Y. Cui, H. Y. Hwang, H. Yuan, and F. Miao, Gate-induced interfacial superconductivity in , Nano Lett. 18, 1410 (2018).
- X. Xing, W. Zhou, J. Wang, Z. Zhu, Y. Zhang, N. Zhou, B. Qian, X. Xu, and Z. Shi, Two-band and Pauli-limiting effects on the upper critical field of 112-type iron pnictide superconductors, Sci. Rep. 7, 45943 (2017).
- N. R. Werthamer, E. Helfand, and P. C. Hohenberg, Temperature and purity dependence of the superconducting critical field, . III. Electron spin and spin-orbit effects, Phys. Rev. 147, 295 (1966).
- J. Wosnitza, FFLO states in layered organic superconductors, Ann. Phys. 530, 1700282 (2018).
- L. W. Gruenberg and L. Gunther, Fulde-Ferrell effect in type-II superconductors, Phys. Rev. Lett. 16, 996 (1966).
- W. M. J. van Weerdenburg, A. Kamlapure, E. H. Fyhn, X. Huang, N. P. E. van Mullekom, M. Steinbrecher, P. Krogstrup, J. Linder, and A. A. Khajetoorians, Extreme enhancement of superconductivity in epitaxial aluminum near the monolayer limit, Sci. Adv. 9, eadf5500 (2023).
- H. Nam, H. Chen, P. W. Adams, S.-Y. Guan, T.-M. Chuang, C.-S. Chang, A. H. MacDonald, and C.-K. Shih, Geometric quenching of orbital pair breaking in a single crystalline superconducting nanomesh network, Nat. Commun. 9, 5431 (2018).
- Y. Matsuda and H. Shimahara, Fulde-Ferrell-Larkin-Ovchinnikov state in heavy fermion superconductors, J. Phys. Soc. Jpn. 76, 051005 (2007).
- L. S. Farrar, M. Bristow, A. A. Haghighirad, A. McCollam, S. J. Bending, and A. I. Coldea, Suppression of superconductivity and enhanced critical field anisotropy in thin flakes of FeSe, npj Quantum Mater. 5, 29 (2020).
- S. Khim, J. W. Kim, E. S. Choi, Y. Bang, M. Nohara, H. Takagi, and K. H. Kim, Evidence for dominant Pauli paramagnetic effect in the upper critical field of single-crystalline , Phys. Rev. B 81, 184511 (2010).
- G. Fuchs, S. L. Drechsler, N. Kozlova, M. Bartkowiak, G. Behr, K. Nenkov, H. H. Klauss, J. Freudenberger, M. Knupfer, F. Hammerath, G. Lang, H. J. Grafe, B. Büchner, and L. Schultz, Evidence for Pauli-limiting behaviour at high fields and enhanced upper critical fields near in several disordered FeAs based superconductors, Physica C 470, S288 (2010).
- S. Ilić, J. S. Meyer, and M. Houzet, Enhancement of the upper critical field in disordered transition metal dichalcogenide monolayers, Phys. Rev. Lett. 119, 117001 (2017).
- C. Heil, M. Schlipf, and F. Giustino, Quasiparticle GW band structures and Fermi surfaces of bulk and monolayer , Phys. Rev. B 98, 075120 (2018).
- C. Heil, S. Poncé, H. Lambert, M. Schlipf, E. R. Margine, and F. Giustino, Origin of superconductivity and latent charge density wave in , Phys. Rev. Lett. 119, 087003 (2017).
- D. Wickramaratne, S. Khmelevskyi, D. F. Agterberg, and I. I. Mazin, Ising superconductivity and magnetism in , Phys. Rev. X 10, 041003, (2020).
- M. Kuzmanović, T. Dvir, D. Leboeuf, S. Ilić, M. Haim, D. Möckli, S. Kramer, M. Khodas, M. Houzet, J. S. Meyer, M. Aprili, H. Steinberg, and C. H. L. Quay, Tunneling spectroscopy of few-monolayer in high magnetic fields: Triplet superconductivity and Ising protection, Phys. Rev. B 106, 184514 (2022).
- S. Khim, B. Lee, J. W. Kim, E. S. Choi, G. R. Stewart, and K. H. Kim, Pauli-limiting effects in the upper critical fields of a clean LiFeAs single crystal, Phys. Rev. B 84, 104502 (2011).
- A. Gurevich, Enhancement of the upper critical field by nonmagnetic impurities in dirty two-gap superconductors, Phys. Rev. B 67, 184515 (2003).
- P. Diener, M. Leroux, L. Cario, T. Klein, and P. Rodière, In-plane magnetic penetration depth in , Phys. Rev. B 84, 054531 (2011).
- X. Xi, Z. Wang, W. Zhao, J. H. Park, K. T. Law, H. Berger, L. Forró, J. Shan, and K. F. Mak, Ising pairing in superconducting atomic layers, Nat. Phys. 12, 139 (2016).
- P. Wan, O. Zheliuk, N. F. Q. Yuan, X. Peng, L. Z., M. Liang, U. Zeitler, S. Wiedmann, N. Hussey, T. T. M. Palstra, and J. Ye, Orbital Fulde–Ferrell–Larkin–Ovchinnikov state in an Ising superconductor, Nature (London) 619, 46 (2023).
- R. A. Cooper, Y. Wang, B. Vignolle, O. J. Lipscombe, S. M. Hayden, Y. Tanabe, T. Adachi, Y. Koike, M. Nohara, H. Takagi, C. Proust, and N. E. Hussey, Anomalous criticality in the electrical resistivity of , Science 323, 603 (2009).
- J. Molenda, T. Bak, and J. Marzec, Electrical and electrochemical properties of niobium disulphide, Phys. Status Solidi A 156, 159 (1996).
- M. Naito and S. Tanaka, Electrical transport properties in , -, - and -, J. Phys. Soc. Jpn. 51, 219 (1982).