- Letter
- Open Access
Superconductivity-induced improper orders in nonsymmorphic systems
Phys. Rev. B 110, L180503 – Published 18 November, 2024
DOI: https://doi.org/10.1103/PhysRevB.110.L180503
Abstract
In this work, we highlight an overlooked mechanism that couples superconducting order parameters to orders in the charge and spin sectors such that the latter emerge as improper orders. At the core of this mechanism are nonsymmorphic symmetries and new families of modulated order parameters with two components of opposite parity. While nonsymmorphic systems have been extensively discussed in the context of topological band theory, our work demonstrates the profound effects of such symmetries on the interplay of ordered phases of matter. As a working example, we focus on the space group P4/nmm and provide a real-space perspective on the classification of order parameters. Our findings can account for the unusual phenomenology of , a recently discovered heavy fermion superconductor, and open the door for the exploration of nonsymmorphic symmetries in the broader context of improper orders with potential applications to functional topological materials.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (51)
- E. Fradkin, S. A. Kivelson, and J. M. Tranquada, Colloquium: Theory of intertwined orders in high temperature superconductors, Rev. Mod. Phys. 87, 457 (2015).
- R. M. Fernandes, P. P. Orth, and J. Schmalian, Intertwined vestigial order in quantum materials: Nematicity and beyond, Annu. Rev. Condens. Matter Phys. 10, 133 (2019).
- B. V. Svistunov, N. Prokof'ev, and E. Babaev, Superfluid States of Matter (CRC Press, Boca Raton, FL, 2015).
- D. F. Agterberg, J. S. Davis, S. D. Edkins, E. Fradkin, D. J. Van Harlingen, S. A. Kivelson, P. A. Lee, L. Radzihovsky, J. M. Tranquada, and Y. Wang, The physics of pair-density waves: Cuprate superconductors and beyond, Annu. Rev. Condens. Matter Phys. 11, 231 (2020).
- A. P. Levanyuk and D. G. Sannikov, Improper ferroelectrics, Sov. Phys. Uspekhi 17, 199 (1974).
- V. Dvořák, Improper ferroelectrics, Ferroelectrics 7, 1 (1974).
- Y. Tokura, S. Seki, and N. Nagaosa, Multiferroics of spin origin, Rep. Prog. Phys. 77, 076501 (2014).
- N. A. Benedek and M. A. Hayward, Hybrid improper ferroelectricity: A theoretical, computational, and synthetic perspective, Annu. Rev. Mater. Res. 52, 331 (2022).
- R. S. K. Mong, A. M. Essin, and J. E. Moore, Antiferromagnetic topological insulators, Phys. Rev. B 81, 245209 (2010).
- C.-X. Liu, R.-X. Zhang, and B. K. VanLeeuwen, Topological nonsymmorphic crystalline insulators, Phys. Rev. B 90, 085304 (2014).
- Y. X. Zhao and A. P. Schnyder, Nonsymmorphic symmetry-required band crossings in topological semimetals, Phys. Rev. B 94, 195109 (2016).
- Y. Chen, H.-S. Kim, and H.-Y. Kee, Topological crystalline semimetals in nonsymmorphic lattices, Phys. Rev. B 93, 155140 (2016).
- B. Bradlyn, J. Cano, Z. Wang, M. G. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals, Science 353, aaf5037 (2016).
- Q.-Z. Wang and C.-X. Liu, Topological nonsymmorphic crystalline superconductors, Phys. Rev. B 93, 020505(R) (2016).
- K. Shiozaki, M. Sato, and K. Gomi, Topology of nonsymmorphic crystalline insulators and superconductors, Phys. Rev. B 93, 195413 (2016).
- S. Kobayashi, Y. Yanase, and M. Sato, Topologically stable gapless phases in nonsymmorphic superconductors, Phys. Rev. B 94, 134512 (2016).
- T. Micklitz and M. R. Norman, Odd parity and line nodes in nonsymmorphic superconductors, Phys. Rev. B 80, 100506(R) (2009).
- T. Micklitz and M. R. Norman, Symmetry-enforced line nodes in unconventional superconductors, Phys. Rev. Lett. 118, 207001 (2017).
- S. Sumita and Y. Yanase, Unconventional superconducting gap structure protected by space group symmetry, Phys. Rev. B 97, 134512 (2018).
- C. Bradley and A. Cracknell, The Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space Groups, EBSCO ebook academic collection (Oxford University Press, Oxford, 2010).
- V. Cvetkovic and O. Vafek, Space group symmetry, spin-orbit coupling, and the low-energy effective Hamiltonian for iron-based superconductors, Phys. Rev. B 88, 134510 (2013).
- J. W. F. Venderbos, Symmetry analysis of translational symmetry broken density waves: Application to hexagonal lattices in two dimensions, Phys. Rev. B 93, 115107 (2016).
- J. M. Perez-Mato, S. V. Gallego, L. Elcoro, E. Tasci, and M. I. Aroyo, Symmetry conditions for type II multiferroicity in commensurate magnetic structures, J. Phys.: Condens. Matter 28, 286001 (2016).
- S. Khim, J. Landaeta, J. Banda, N. Bannor, M. Brando, P. Brydon, D. Hafner, R. Küchler, R. Cardoso-Gil, U. Stockert et al., Field-induced transition within the superconducting state of , Science 373, 1012 (2021).
- S. Ogata, S. Kitagawa, K. Kinjo, K. Ishida, M. Brando, E. Hassinger, C. Geibel, and S. Khim, Parity transition of spin-singlet superconductivity using sublattice degrees of freedom, Phys. Rev. Lett. 130, 166001 (2023).
- M. Kibune, S. Kitagawa, K. Kinjo, S. Ogata, M. Manago, T. Taniguchi, K. Ishida, M. Brando, E. Hassinger, H. Rosner et al., Observation of antiferromagnetic order as odd-parity multipoles inside the superconducting phase in , Phys. Rev. Lett. 128, 057002 (2022).
- K. Semeniuk, D. Hafner, P. Khanenko, T. Lühmann, J. Banda, J. F. Landaeta, C. Geibel, S. Khim, E. Hassinger, and M. Brando, Decoupling multiphase superconductivity from normal state ordering in , Phys. Rev. B 107, L220504 (2023).
- M. Pfeiffer, K. Semeniuk, J. F. Landaeta, R. Borth, C. Geibel, M. Nicklas, M. Brando, S. Khim, and E. Hassinger, Pressure-tuned quantum criticality in the locally non-centrosymmetric superconductor , Phys. Rev. Lett. 133, 126506 (2024).
- X. Ma, G. Wang, R. Liu, T. Yu, Y. Peng, P. Zheng, and Z. Yin, Correlation-corrected band topology and topological surface states in iron-based superconductors, Phys. Rev. B 106, 115114 (2022).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.110.L180503 for the details of the Landau free energy analysis, the real-space group extension leading to Table 1 in the main text, and the classification of order parameters from the perspective of the extended unit cell, which includes Refs. [45, 46, 47, 48, 49, 50, 51].
- C. Herring, Character tables for two space groups, J. Franklin Inst. 233, 525 (1942).
- S. Khim, O. Stockert, M. Brando, C. Geibel, C. Baines, T. J. Hicken, H. Luetkens, D. Das, T. Shiroka, Z. Guguchia, and R. Scheuermann, Coexistence of local magnetism and superconductivity in the heavy-fermion revealed by studies, arXiv:2406.16575.
- G. Chajewski and D. Kaczorowski, Discovery of magnetic phase transitions in heavy-fermion superconductor , Phys. Rev. Lett. 132, 076504 (2024).
- 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 (2021).
- T. Shang, M. Smidman, S. K. Ghosh, C. Baines, L. J. Chang, D. J. Gawryluk, J. A. T. Barker, R. P. Singh, D. M. Paul, G. Balakrishnan, E. Pomjakushina, M. Shi, M. Medarde, A. D. Hillier, H. Q. Yuan, J. Quintanilla, J. Mesot, and T. Shiroka, Time-reversal symmetry breaking in re-based superconductors, Phys. Rev. Lett. 121, 257002 (2018).
- G. Csire, J. F. Annett, J. Quintanilla, and B. Újfalussy, Magnetically textured superconductivity in elemental rhenium, Phys. Rev. B 106, L020501 (2022).
- H.-H. Lai, S. E. Grefe, S. Paschen, and Q. Si, Weyl–Kondo semimetal in heavy-fermion systems, Proc. Natl. Acad. Sci. USA 115, 93 (2018).
- S. E. Grefe, H.-H. Lai, S. Paschen, and Q. Si, Weyl-Kondo semimetals in nonsymmorphic systems, Phys. Rev. B 101, 075138 (2020).
- T. Kamatani, S. Kitamura, N. Tsuji, R. Shimano, and T. Morimoto, Optical response of the Leggett mode in multiband superconductors in the linear response regime, Phys. Rev. B 105, 094520 (2022).
- R. Nagashima, S. Tian, R. Haenel, N. Tsuji, and D. Manske, Classification of Lifshitz invariant in multiband superconductors: An application to Leggett modes in the linear response regime in kagome lattice models, Phys. Rev. Res. 6, 013120 (2024).
- C. N. Yang, pairing and off-diagonal long-range order in a Hubbard model, Phys. Rev. Lett. 63, 2144 (1989).
- T. Liu, C. Repellin, B. Douçot, N. Regnault, and K. Le Hur, Triplet FFLO superconductivity in the doped Kitaev-Heisenberg honeycomb model, Phys. Rev. B 94, 180506(R) (2016).
- F. Chen, F. D. M. Haldane, and D. N. Sheng, D-wave and pair-density-wave superconductivity in the square-lattice t-j model, arXiv:2311.15092.
- J. Li, D. Golez, P. Werner, and M. Eckstein, -paired superconducting hidden phase in photodoped Mott insulators, Phys. Rev. B 102, 165136 (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).
- L. Elcoro, B. Bradlyn, Z. Wang, M. G. Vergniory, J. Cano, C. Felser, B. A. Bernevig, D. Orobengoa, G. de la Flor, and M. I. Aroyo, Double crystallographic groups and their representations on the Bilbao Crystallographic Server, J. Appl. Crystallog. 50, 1457 (2017).
- R. M. Fernandes, A. I. Coldea, H. Ding, I. R. Fisher, P. J. Hirschfeld, and G. Kotliar, Iron pnictides and chalcogenides: A new paradigm for superconductivity, Nature (London) 601, 35 (2022).
- A. Kataria, J. A. T. Verezhak, O. Prakash, R. K. Kushwaha, A. Thamizhavel, S. Ramakrishnan, M. S. Scheurer, A. D. Hillier, and R. P. Singh, Time-reversal symmetry breaking in the superconducting low carrier density quasiskutterudite , Phys. Rev. B 107, L100506 (2023).
- A. Kataria, J. A. T. Verezhak, O. Prakash, R. K. Kushwaha, A. Thamizhavel, S. Ramakrishnan, M. S. Scheurer, A. D. Hillier, and R. P. Singh, Broken time-reversal symmetry in the cubic skutterudite-like superconductor , Phys. Rev. B 108, 214512 (2023).
- 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).
- R. Joynt and L. Taillefer, The superconducting phases of , Rev. Mod. Phys. 74, 235 (2002).