- Open Access
Anisotropic fully gapped superconductivity in quasi-one-dimensional
Phys. Rev. B 113, 094524 – Published 24 March, 2026
DOI: https://doi.org/10.1103/y4fj-8c2m
Abstract
Superconductivity in quasi-one-dimensional emerges from an exotic, nonmetallic normal state that exhibits signatures of Tomonaga-Luttinger liquid behavior, emergent symmetry, and excitonic order. The high upper critical field, , in suggests that that the favored pairing state is spin-triplet in nature. Here, we report measurements of the magnetic penetration depth down to () and the specific heat down to (), and show that they are consistent with a moderately coupled, fully gapped superconducting state with marked gap anisotropy and a minimum () occurring over a very narrow region in space. Combined with knowledge of , these measurements support the presence of a nodeless and possibly odd-parity spin-triplet superconducting order parameter in .
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (52)
- M. Dressel, Ordering phenomena in quasi-one-dimensional organic conductors, Naturwissenschaften 94, 527 (2007).
- T. Giamarchi, Quantum Physics in One-Dimension (Oxford University Press, Oxford, 2003).
- W. Zhang and C. A. R. Sá De Melo, Triplet versus singlet superconductivity in quasi-one-dimensional conductor, Adv. Phys. 56, 545 (2007).
- M. Kociak, A. Y. Kasumov, S. Guéron, S. Reulet, I. I. Khodos, Y. U. Gorbatov, V. T. Volkov, L. Vaccarini, and H. Bouchiat, Superconductivity in ropes of single-walled carbon nanotubes, Phys. Rev. Lett. 86, 2416 (2001).
- D. Jérome, A. Mazaud, M. Ribault, and K. Bechgaard, Superconductivity in a synthetic organic conductor (TMTSF), J. Phyique Lett. 41, 95 (1980).
- G. M. Pang, M. Smidman, W. B. Jiang, J. K. Bao, Z. F. Weng, Y. F. Wang, L. Jiao, J. L. Zhang, G. H. Cao, and H. Q. Yuan, Evidence for nodal superconductivity in quasi-one-dimensional , Phys. Rev. B 91, 220502(R) (2015).
- J. Yang, J. Luo, C. Yi, Y. Shi, Y. Zhou, and G.-Z. Zheng, Spin-triplet superconductivity in , Sci. Adv. 7, eabl4432 (2021).
- M. D. Watson, Y. Feng, C. W. Nicholson, C. Monney, J. M. Riley, H. Iwasawa, K. Refson, V. Sacksteder, D. T. Adroja, J. Zhao, and M. Hoesch, Multiband one-dimensional electronic structure and spectroscopic signature of Tomonaga-Luttinger liquid behavior in , Phys. Rev. Lett. 118, 097002 (2017).
- J. K. Bao, J. Y. Liu, C. W. Ma, Z. H. Meng, Z. T. Tang, Y. L. Sun, H. F. Zhai, H. Jiang, H. Bai, C. M. Feng, Z. A. Xu, and G. H. Cao, Superconductivity in quasi-one-dimensional with significant electron correlations, Phys. Rev. X 5, 011013 (2015).
- F. F. Balakirev, T. Kong, M. Jaime, R. D. McDonald, C. H. Mielke, A. Gurevich, P. C. Canfield, and S. L. Bud'ko, Anisotropy reversal of the upper critical field at low temperatures and spin-locked superconductivity in , Phys. Rev. B 91, 220505 (2015).
- Z. S. Popović and S. Satpathy, Density-functional study of the Luttinger liquid behavior of the lithium molybdenum purple bronze , Phys. Rev. B 74, 045117 (2006).
- P. Chudzinski, Multi-orbital physics in lithium-molybdenum purple-bronze: Going beyond paradigm, Eur. Phys. J. B 90, 148 (2017).
- T. Podlich, M. Klinke, B. Nansseu, M. Waelsch, R. Bienert, J. He, R. Jin, D. Mandrus, and R. Matzdorf, Luttinger liquid behavior of studied by scanning tunneling microscopy, J. Phys.: Condens. Matter 25, 014008 (2013).
- J. D. Denlinger, G.-H. Gweon, J. W. Allen, C. G. Olson, J. Marcus, C. Schlenker, and L.-S. Hsu, Non-Fermi-liquid single particle line shape of the quasi-one-dimensional non-CDW metal : Comparison to the Luttinger liquid, Phys. Rev. Lett. 82, 2540 (1999).
- J. Hager, R. Matzdorf, J. He, R. Jin, D. Mandrus, M. A. Cazalilla, and E. W. Plummer, Non-Fermi-liquid behavior in quasi-one-dimensional , Phys. Rev. Lett. 95, 186402 (2005).
- F. Wang, J. V. Alvarez, S.-K. Mo, J. W. Allen, G.-H. Gweon, J. He, R. Jin, D. Mandrus, and H. Höchst, New Luttinger-liquid physics from photoemission on , Phys. Rev. Lett. 96, 196403 (2006).
- L. Dudy, J. D. Denlinger, J. W. Allen, F. Wang, J. He, D. Hitchcock, A. Sekiyama, and S. Suga, Photoemission spectroscopy and the unusually robust one-dimensional physics of lithium purple bronze, J. Phys.: Condens. Matter 25, 014007 (2013).
- N. Wakeham, A. F. Bangura, X. Xu, J.-F. Mercure, M. Greenblatt, and N. E. Hussey, Gross violation of the Wiedemann–Franz law in a quasi-one-dimensional conductor, Nat. Commun. 2, 396 (2011).
- J. L. Cohn, B. D. White, C. A. M. dos Santos, and J. J. Neumeier, Giant Nernst effect and bipolarity in the quasi-one-dimensional metal , Phys. Rev. Lett. 108, 056604 (2012).
- M. Onoda, K. Toriumi, Y. Matsuda, and M. Sato, Crystal structure of lithium molybdenum purple bronze , J. Solid State Chem. 66, 163 (1987).
- J.-F. Mercure, A. F. Bangura, X. Xu, N. Wakeham, A. Carrington, P. Walmsley, M. Greenblatt, and N. E. Hussey, Upper critical magnetic field far above the paramagnetic pair-breaking limit of superconducting one-dimensional single crystals, Phys. Rev. Lett. 108, 187003 (2012).
- J. Ke, C. Dong, H. Zhu, W. Liu, M. Shi, Y. Du, J. Wang, and M. Yang, Synthesis and physical properties of the theoretically predicted spin-triplet superconductor , Ceram. Int. 47, 25229 (2021).
- X. Xu, A. F. Bangura, J. G. Analytis, J. D. Fletcher, M. M. J. French, N. Shannon, J. He, S. Zhang, D. Mandrus, R. Jin, and N. E. Hussey, Directional field-induced metallization of quasi-one-dimensional , Phys. Rev. Lett. 102, 206602 (2009).
- Y. Matsuda, M. Sato, M. Onoda, and K. Nakao, On the anomalous transport properties of , J. Phys. C: Solid State Phys. 19, 6039 (1986).
- J. Chakhalian, Z. Salman, J. Brewer, A. Froese, J. He, D. Mandrus, and R. Jin, Magnetism in purple bronze , Physica B 359, 1333 (2005).
- J. Choi, J. L. Musfeldt, J. He, R. Jin, J. R. Thompson, D. Mandrus, X. N. Lin, V. A. Bondarenko, and J. W. Brill, Probing localization effects in purple bronze: An optical-properties investigation, Phys. Rev. B 69, 085120 (2004).
- G. Wu, X.-s. Ye, X. Zeng, B. Wu, and W. Clark, Direct observation of charge state in the quasi-one-dimensional conductor , Sci. Rep. 6, 20721 (2016).
- J. Lu, X. Xu, M. Greenblatt, R. Jin, P. Tinnemans, S. Licciardello, M. R. van Delft, J. Buhot, P. Chudzinski, and N. E. Hussey, Emergence of a real-space symmetry axis in the magnetoresistance of the one-dimensional conductor , Sci. Adv. 5, eaar8027 (2019).
- P. Chudzinski, M. Berben, X. Xu, N. Wakeham, B. Bernáth, C. Duffy, R. Hinlopen, Y.-T. Hsu, S. Wiedmann, P. Tinnemans, et al., Emergent symmetry in a low-dimensional superconductor on the edge of Mottness, Science 382, 792 (2023).
- O. Sepper and A. G. Lebed, Nodeless versus nodal scenarios of possible triplet superconductivity in the quasi-one-dimensional layered conductor , Phys. Rev. B 88, 094520 (2013).
- W. Cho, C. Platt, R. H. McKenzie, and S. Raghu, Spin-triplet superconductivity in a weak-coupling Hubbard model for the quasi-one-dimensional compound , Phys. Rev. B 92, 134514 (2015).
- N. Lera and J. V. Alvarez, Triplet superconductivity in a model of , Phys. Rev. B 92, 174523 (2015).
- C. Platt, W. Cho, R. H. McKenzie, R. Thomale, and S. Raghu, Spin-orbit coupling and odd-parity superconductivity in the quasi-one-dimensional compound , Phys. Rev. B 93, 214515 (2016).
- W. McCarroll and M. Greenblatt, Preparation of lithium molybdenum oxide bronzes by a temperature gradient flux growth technique, J. Solid State Chem. 54, 282 (1984).
- C. Schlenker, H. Schwenk, C. Escribe-Filippini, and J. Marcus, Superconducting properties of the low dimensional purple bronze , Physica B+C 135, 511 (1985).
- M. Boujida, C. Escribe-Filippini, J. Marcus, and C. Schlenker, Superconducting properties of the low dimensional lithium molybdenum purple bronze , Physica C 153-155, 465 (1988).
- J. L. Cohn, P. Boynton, J. Triviño, J. Trastoy, B. D. White, C. A.M. dos Santos, and J. J. Neumeier, Stoichiometry, structure, and transport in the quasi-one-dimensional metal , Phys. Rev. B 86, 195143 (2012).
- C. T. van Degrift, Tunnel diode oscillator for 0.001 ppm measurements at low temperatures, Rev. Sci. Instrum. 46, 599 (1975).
- R. Giannetta, A. Carrington, and R. Prozorov, London penetration depth measurements using tunnel diode resonators, J. Low Temp. Phys. 208, 119 (2022).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/y4fj-8c2m for additional details of the analysis procedures presented.
- R. Prozorov, Meissner-London susceptibility of superconducting right circular cylinders in an axial magnetic field, Phys. Rev. Appl. 16, 024014 (2021).
- O. J. Taylor, A. Carrington, and J. A. Schlueter, Specific-heat measurements of the gap structure of the organic superconductors and , Phys. Rev. Lett. 99, 057001 (2007).
- M. Tinkham, Introduction to Superconductivity, 2nd ed. (Dover, Garden City, 2004).
- M. J. Grant, Y. Liu, G.-H. Cao, J. A. Wilcox, Y. Guo, X. Xu, and A. Carrington, Superconducting energy gap structure of from magnetic penetration depth measurements, J. Phys.: Condens. Matter 37, 065601 (2025).
- K. Cho, M. Kończykowski, S. Teknowijoyo, M. A. Tanatar, Y. Liu, T. A. Lograsso, W. E. Straszheim, V. Mishra, S. Maiti, P. J. Hirschfeld, et al., Energy gap evolution across the superconductivity dome in single crystals of (), Sci. Adv. 2, e1600807 (2016).
- H. Kim, M. A. Tanatar, R. Flint, C. Petrovic, R. Hu, B. D. White, I. K. Lum, M. B. Maple, and R. Prozorov, Nodal to nodeless superconducting energy-gap structure change concomitant with Fermi-surface reconstruction in the heavy-fermion compound , Phys. Rev. Lett. 114, 027003 (2015).
- J. Merino and R. H. McKenzie, Effective Hamiltonian for the electronic properties of the quasi-one-dimensional material , Phys. Rev. B 85, 235128 (2012).
- M. Nuss and M. Aichhorn, Effective model for the electronic properties of quasi-one-dimensional purple bronze based on ab initio calculations, Phys. Rev. B 89, 045125 (2014).
- B. S. Chandrasekhar and D. Einzel, The superconducting penetration depth from the semiclassical model, Ann. Phys. (N.Y.) 505, 535 (1993).
- M. Li, N. R. Lee-Hone, S. Chi, R. Liang, W. N. Hardy, D. A. Bonn, E. Girt, and D. M. Broun, Superfluid density and microwave conductivity of FeSe superconductor: ultra-long-lived quasiparticles and extended -wave energy gap, New J. Phys. 18, 082001 (2016).
- L. Jiao, C.-L. Huang, S. Rößler, C. Koz, U. K. Rößler, U. Schwarz, and S. Wirth, Superconducting gap structure of FeSe, Sci. Rep. 7, 44024 (2017).
- A. Carrington and M. Grant, Anisotropic fully-gapped superconductivity in quasi-one-dimensional (2026), https://doi.org/10.5523/bris.4v30c1zoc8n72o46lpipdp4b9.