- Letter
- Open Access
Time-reversal symmetry breaking superconductivity in three-dimensional Dirac semimetallic silicides
Phys. Rev. Research 4, L012031 – Published 15 March, 2022
DOI: https://doi.org/10.1103/PhysRevResearch.4.L012031
Abstract
Superconductors with broken time-reversal symmetry represent arguably one of the most promising venues for realizing highly sought-after topological superconductivity that is vital to fault-tolerant quantum computation. Here, by using extensive muon-spin relaxation and rotation measurements, we report that the isostructural silicide superconductors (Ta, Nb)OsSi spontaneously break time-reversal symmetry at the superconducting transition while surprisingly showing a fully gapped superconductivity characteristic of conventional superconductors. The first-principles calculations show that (Ta, Nb)OsSi are three-dimensional Dirac semimetals protected by nonsymmorphic symmetries. Taking advantage of the exceptional low symmetry crystal structure of these materials, we have performed detailed theoretical calculations to establish that the superconducting ground state for both (Ta, Nb)OsSi is most likely a nonunitary triplet state.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (36)
- N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018).
- B. Q. Lv, T. Qian, and H. Ding, Experimental perspective on three-dimensional topological semimetals, Rev. Mod. Phys. 93, 025002 (2021).
- S. K. Ghosh, M. Smidman, T. Shang, J. F. Annett, A. D. Hillier, J. Quintanilla, and H. Yuan, Recent progress on superconductors with time-reversal symmetry breaking, J. Phys.: Condens. Matter 33, 033001 (2020).
- M. Sato and Y. Ando, Topological superconductors: A review, Rep. Prog. Phys. 80, 076501 (2017).
- J. F. Annett, Symmetry of the order parameter for high-temperature superconductivity, Adv. Phys. 39, 83 (1990).
- M. Sigrist and K. Ueda, Phenomenological theory of unconventional superconductivity, Rev. Mod. Phys. 63, 239 (1991).
- A. D. Hillier, J. Quintanilla, and R. Cywinski, Evidence for Time-Reversal Symmetry Breaking in the Noncentrosymmetric Superconductor , Phys. Rev. Lett. 102, 117007 (2009).
- J. Chen, L. Jiao, J. Zhang, Y. Chen, L. Yang, M. Nicklas, F. Steglich, and H. Yuan, Evidence for two-gap superconductivity in the non-centrosymmetric compound , New J. Phys. 15, 053005 (2013).
- A. D. Hillier, J. Quintanilla, B. Mazidian, J. F. Annett, and R. Cywinski, Nonunitary Triplet Pairing in the Centrosymmetric Superconductor , Phys. Rev. Lett. 109, 097001 (2012).
- Z. F. Weng, J. L. Zhang, M. Smidman, T. Shang, J. Quintanilla, J. F. Annett, M. Nicklas, G. M. Pang, L. Jiao, W. B. Jiang, Y. Chen, F. Steglich, and H. Q. Yuan, Two-Gap Superconductivity in with Nonunitary Triplet Pairing and Even Parity Gap Symmetry, Phys. Rev. Lett. 117, 027001 (2016).
- S. K. Ghosh, G. Csire, P. Whittlesea, J. F. Annett, M. Gradhand, B. Újfalussy, and J. Quintanilla, Quantitative theory of triplet pairing in the unconventional superconductor , Phys. Rev. B 101, 100506(R) (2020).
- J. R. Badger, Y. Quan, M. C. Staab, S. Sumita, A. Rossi, K. P. Devlin, K. Neubauer, D. S. Shulman, J. C. Fettinger, P. Klavins et al., Dirac lines and loop at the fermi level in the time-reversal symmetry breaking superconductor , Commun. Phys. 5, 22 (2022).
- S. Ran, C. Eckberg, Q.-P. Ding, Y. Furukawa, T. Metz, S. R. Saha, I.-L. Liu, M. Zic, H. Kim, J. Paglione et al., Nearly ferromagnetic spin-triplet superconductivity, Science 365, 684 (2019).
- T. Metz, S. Bae, S. Ran, I.-L. Liu, Y. S. Eo, W. T. Fuhrman, D. F. Agterberg, S. M. Anlage, N. P. Butch, and J. Paglione, Point-node gap structure of the spin-triplet superconductor , Phys. Rev. B 100, 220504(R) (2019).
- C. Benndorf, L. Heletta, G. Heymann, H. Huppertz, H. Eckert, and R. Pöttgen, NbOsSi and TaOsSi—two new superconducting ternary osmium silicides, Solid State Sci. 68, 32 (2017).
- E. Haque and M. A. Hossain, Elastic, electronic, thermodynamic and transport properties of XOsSi (X= Nb, Ta) superconductors: First-principles calculations, J. Alloys Compd. 739, 737 (2018).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L012031 for details of the measurements of the crystal structure, heat capacity, and critical field, as well as for the data analysis, DFT calculation, symmetry analysis, and toy-model calculations.
- R. Kubo, A stochastic theory of spin relaxation, Hyperfine Interact. 8, 731 (1981).
- J. E. Sonier, J. H. Brewer, and R. F. Kiefl, studies of the vortex state in type-II superconductors, Rev. Mod. Phys. 72, 769 (2000).
- E. H. Brandt, Properties of the ideal Ginzburg-Landau vortex lattice, Phys. Rev. B 68, 054506 (2003).
- R. Prozorov and R. W. Giannetta, Magnetic penetration depth in unconventional superconductors, Supercond. Sci. Technol. 19, R41 (2006).
- A. Carrington and F. Manzano, Magnetic penetration depth of , Physica C 385, 205 (2003).
- C. Q. Xu, B. Li, J. J. Feng, W. H. Jiao, Y. K. Li, S. W. Liu, Y. X. Zhou, R. Sankar, N. D. Zhigadlo, H. B. Wang, Z. D. Han, B. Qian, W. Ye, W. Zhou, T. Shiroka, P. K. Biswas, X. Xu, and Z. X. Shi, Two-gap superconductivity and topological surface states in TaOsSi, Phys. Rev. B 100, 134503 (2019).
- The nonsymmorphic symmetries present in (Ta, Nb)OsSi, in general, can give rise to superconducting order parameters with additional symmetry required nodes along the high symmetry directions in the Brillouin zone boundaries but cannot give rise to a multicomponent order parameter to facilitate TRS breaking [12, 34, 35].
- J. E. Han, Spin-triplet -wave local pairing induced by hund's rule coupling, Phys. Rev. B 70, 054513 (2004).
- K. Araki, T. Kohei, H. Tanaka, S. Nakamura, T. Nojima, A. Ochiai, and K. Katoh, Magnetic and transport properties of YbNiGe with a TiNiSi-type structure, J. Phys. Soc. Jpn. 88, 114709 (2019).
- D. Aoki, K. Ishida, and J. Flouquet, Review of u-based ferromagnetic superconductors: Comparison between UGe2, URhGe, and UCoGe, J. Phys. Soc. Jpn. 88, 022001 (2019).
- S.-L. Wu, K. Sumida, K. Miyamoto, K. Taguchi, T. Yoshikawa, A. Kimura, Y. Ueda, M. Arita, M. Nagao, S. Watauchi et al., Direct evidence of hidden local spin polarization in a centrosymmetric superconductor , Nat. Commun. 8, 1919 (2017).
- X. Zhang, Q. Liu, J.-W. Luo, A. J. Freeman, and A. Zunger, Hidden spin polarization in inversion-symmetric bulk crystals, Nat. Phys. 10, 387 (2014).
- Although the experimental specific heat data for TaOsSi was shown to be fitted well by a two-gap model having more fitting parameters [23], we note from Fig. 4 that the two-band toy model in the INT ground state giving rise to a single full gap provides a very good fitting as well.
- I. Hayes, D. Wei, T. Metz, J. Zhang, Y. Eo, S. Ran, S. Saha, J. Collini, N. Butch, D. Agterberg et al., Multicomponent superconducting order parameter in , Science 373, 797 (2021).
- W. X. Zhong, B. Chevalier, J. Etourneau, and P. Hagenmuller, Relationships between occurrence of superconductivity and crystal structure in new equiatomic ternary silicides MTSi (M = Ti, Zr, Hf and T = Ru, Os, Rh), Solid State Commun. 59, 839 (1986).
- B. M. Huddart, I. J. Onuorah, M. M. Isah, P. Bonfà, S. J. Blundell, S. J. Clark, R. De Renzi, and T. Lancaster, Intrinsic Nature of Spontaneous Magnetic Fields in Superconductors with Time-Reversal Symmetry Breaking, Phys. Rev. Lett. 127, 237002 (2021).
- S. Sumita and Y. Yanase, Unconventional superconducting gap structure protected by space group symmetry, Phys. Rev. B 97, 134512 (2018).
- S. Sumita, T. Nomoto, K. Shiozaki, and Y. Yanase, Classification of topological crystalline superconducting nodes on high-symmetry lines: Point nodes, line nodes, and Bogoliubov Fermi surfaces, Phys. Rev. B 99, 134513 (2019).
- P. K. Biswas et al., (2020): STFC ISIS Neutron and Muon Source, https://doi.org/10.5286/ISIS.E.RB1920724.