Abstract—
We consider experimental data on the order parameter structure in superconductors with a layered perovskite structure: La2CuO4 and Sr2RuO4. Experimental data are analyzed using the space group approach to two-electron states in crystals. From the crystalline symmetry of Sr2RuO4, we derive two-electron functions with Eu symmetry, having nodal planes consistent with experimental data. In the case of La2CuO4 and high-Tc materials, the order parameter corresponds to the irreducible representation B1g with hidden symmetry D4h. It is also shown that the charge density waves found in pseudogap states of high-Tc materials can be thought of as two-electron states of equivalent electrons with a nonzero momentum.
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REFERENCES
Bednorz, J.G. and Müller, K.A., Possible high T c superconductivity in the Ba–La–Cu–O systems, Z. Phys. B, 1986, vol. 64, no. 2, pp. 189–193.
Maeno, Y., Hashimoto, H., Yoshida, K., Nishizaki, S., Fujita, T., Bednorz, J.G., and Lichtenberg, F., Superconductivity in layered perovskite without copper, Nature, 1994, vol. 372, pp. 532–534.
Bardeen, J.L., Cooper, N., and Schriffer, J.R., Theory of superconductivity, Phys. Rev., 1957, vol. 108, no. 5, pp. 1175–1204.
Zhang, Y., Liu, W., Zhu, X., Zhao, H., Hu, Z., He, C., and Wen, H.-H., Unprecedented high irreversibility line in the nontoxic cuprate superconductor (Cu,C)Ba2Ca3Cu4O11 + δ, Sci. Adv., 2018, vol. 4, paper 0192.
Shaplygin, I.S., Kakhan, B.G., and Lazarev, V.B., Preparation and properties of Ln2CuO4 (Ln = La, Pr, Nd, Sm, Eu, Gd) solid solutions, Zh. Neorg. Khim., 1979, vol. 24, no. 6, pp. 1478–1485.
Steglich, F., Aarts, J., Bredl, C.D., Lieke, W., Meschede, D., Franz, W., and Schafer, H., Superconductivity in the presence of strong Pauli paramagnetism: CeCu2Si2, Phys. Rev. Lett., 1979, vol. 43, pp. 1892–1895.
Bishop, D.J., Varma, C.M., Batlogg, B., Bucher, E., Fisk, Z., and Smith, J.L., Ultrasonic attenuation in UPt3, Phys. Rev. Lett., 1984, vol. 53, no. 10, pp. 1009–1011.
Ott, H.R., Rudiger, H., Rice, T.M., Ueda, K., Fisk, Z., and Smith, J.L., p-Wave superconductivity in UBe13, Phys. Rev. Lett., 1984, vol. 52, no. 21, pp. 1915–1918.
Yarzhemsky, V.G. and Murav’ev, E.N., Space group approach to the wavefunction of a Cooper pair, J. Phys.: Condens. Matter, 1992, vol. 4, pp. 3525–3532.
Yarzhemsky, V.G., Space-group approach to the nodal structure of superconducting order parameter in UPt3, Phys. Status Solidi B, 1998, vol. 209, pp. 101–107.
Yarzhemsky, V.G. and Nefedov, V.I., Symmetry of two-electron states in unconventional superconductors, Inorg. Mater., 2005, vol. 41, no. 12, pp. 1247–1255.
Yarzhemsky, V.G., Nodal quantum numbers for two-electron states in solids, Few-Body Systems, 2012, vol. 53, no. 3, pp. 499–504.
Yarzhemsky, V.G., Wavefunction of a Cooper pair in crystals of \(D_{{2{\text{h}}}}^{1}\) and \(D_{{4{\text{h}}}}^{{17}}\) symmetry, Z. Phys. B: Condens. Matter, 1995, vol. 99, no. 1, pp. 19–23.
Yarzhemsky, V.G., Group theoretical lines of nodes in triplet chiral superconductor Sr2RuO4, J. Phys. Soc. Jpn., 2018, vol. 87, paper 114 711.
Tsuei, C.C. and Kirtley, J.R., Pairing symmetry in cuprate superconductors, Rev. Mod. Phys., 2000, vol. 72, pp. 969–1017.
Yarzhemsky, V.G. and Nefedov, V.I., Crystal symmetry and the structure of two-electron states in high-temperature superconductors, Dokl. Phys., 2005, vol. 50, no. 10. pp. 494–498.
Alloul, H., Ohno, T., and Mendels, P., 89Y NMR evidence for a Fermi-liquid behavior in YBa2Cu3O6 + x, Phys. Rev. Lett., 1989, vol. 63, pp. 1700–1703.
Kaminski, A., Rosenkranz, S., Fretwell, H.M., Campuzano, J.C., Li, Z., Raffy, H., Cullen, W.G., You, H.C., Olson, G., Varma, C.M., and Höchst, H., Spontaneous breaking of time-reversal symmetry in the pseudogap state of a high-T c superconductor, Nature, 2002, vol. 416, pp. 610–612.
Borisenko, S.V., Kordyuk, A.A., Koitzsch, A., Kim, T.K., Nenkov, K.A., Knupfer, M., Fink, J., Grazioli, C., Turchini, S., and Berger, H., Circular dichroism in angle-resolved photoemission spectra of under- and overdoped Pb-Bi2212, Phys. Rev. Lett., 2004, vol. 92, paper 207 001.
He, J., Mion, T.R., Gao, S., Myers, G.T., Arita, M., Shimada, K., Gu, G.D., and He, R.H., Angle-resolved photoemission with circularly polarized light in the nodal mirror plane of underdoped Bi2Sr2CaCu2O8 + δ superconductor, Appl. Phys. Lett., 2016, vol. 109, paper 182 601.
Fauqué, B., Sidis, Y., Hinkov, V., Pailhes, S., Lin, C.T., Chaud, X., and Bourges, P., Magnetic order in the pseudogap phase of high-T c superconductors, Phys. Rev. Lett., 2006, vol. 96, paper 197 010.
Li, Y., Baledent, V., Yu, G., Barisic, N., Hradil, K., Mole, R.A., Sidis, Y., Steffens, P., Zhao, X., Bourges, P., and Greven, M., Hidden magnetic excitation in the pseudogap phase of a high-T c superconductor, Nat. Lett., 2010, vol. 468, pp. 283–285.
Xia, J., Schemm, E., Deutscher, G., Kivelson, S.A., Bonn, D.A., Hardy, W.N., Liang, R., Siemons, W., Koster, G., Fejer, M.M., and Kapitulnik, A., Polar Kerr effect of the high-temperature superconductor YBa2Cu3O6 + x: evidence of broken symmetry near the pseudogap temperature, Phys. Rev. Lett., 2008, vol. 100, paper 127 002.
Daou, R., Chang, J., Le Boeuf, D., Cyr-Choiniere, O., Laliberte, F., Doiron-Leyraud, N., Ramshaw, B.J., Liang, R., Bonn, D.A., Hardy, W.N., and Taillefer, L., Broken rotational symmetry in the pseudogap phase of a high-T c superconductor, Nature, 2010, vol. 463, pp. 519–522.
Hinkov, V., Haug, D., Fauqué, B., Bourges, P., Sidis, Y., Ivanov, A., Bernhard, C., Lin, C.T., and Keimer, B., Electronic liquid crystal state in the high-temperature superconductor YBa2Cu3O6.45, Science, 2008, vol. 319, pp. 597–600.
Van Harlingen, D.J., Phase-sensitive tests of the symmetry of the pairing state in the high-temperature superconductors—evidence for \({{d}_{{{{x}^{{\text{2}}}} - {{y}^{{\text{2}}}}}}} \) symmetry, Rev. Mod. Phys., 1995, vol. 67, no. 2, pp. 515–535.
Hashimoto, M.M., Vishik, I.M., He, R.H., Devereaux, T.P., and Shen, Z., Energy gaps in high-transition-temperature cuprate superconductors, Nat. Phys., 2014, vol. 10, pp. 483–495.
Chang, J., Blackburn, E., Holmes, A.T., Christensen, N.B., Larsen, J., Mesot, J., Ruixing, Liang, R., Bonn, D.A., Hardy, W.N., Watenphul, A., Zimmermann, M.V., Forgan, E.M., and Hayden, S.M., Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3Oy , Nat. Phys., 2012, vol. 8, pp. 871–876.
Montiel, X., Kloss, T., and Pépin, C., Effective SU(2) theory for the pseudogap state, Phys. Rev. B: Condens. Matter Mater. Phys., 2017, vol. 95, paper 104 510.
Montiel, X., Kloss, T., and Pépin, C., Local particle–hole pair excitations by SU(2) symmetry fluctuations, Sci. Rep., 2017, vol. 7, paper 3477.
Morice, C., Chakraborty, D., and Pépin, C., Collective mode in the SU(2) theory of cuprates, Phys. Rev. B: Condens. Matter Mater. Phys., 2018, vol. 98, paper 224 514.
Ishida, K., Mukuda, H., Kitaoka, Y., Asayama, K., Mao, Z.Q., Mori, Y., and Maeno, Y., Spin-triplet superconductivity in Sr2RuO4 identified by 17O Knight shift, Nature, 1998, vol. 96, pp. 658–660.
Nelson, K.D., Mao, Z.Q., Maeno, Y., and Liu, Y., Odd-parity superconductivity in Sr2RuO4, Science, 2004, vol. 306, no. 5699, pp. 1151–1154.
Luke, G.M., Fudamoto, Y., Kojima, K.M., Larkin, M.I., Merrin, J., Nachumi, B., Uemura, Y.J., Maeno, Y., Mao, Z.Q., Mori, Y., Nakamura, H., and Sigrist, M., Time-reversal symmetry-breaking superconductivity in Sr2RuO4, Nature, 1998, vol. 394, pp. 558–561.
Bonalde, I., Yanoff, B.D., Salamon, M.B., Van Harlingen, D.J., Chia, E.M.E., Mao, Z.Q., and Maeno, Y., Temperature dependence of the penetration depth in Sr2RuO4: evidence for nodes in the gap function, Phys. Rev. Lett., 2000, vol. 85, pp. 4775–4778.
Rice, T.M. and Sigrist, M., Sr2RuO4: an electronic analogue of 3He, J. Phys. Condens. Matter, 1995, vol. 7, pp. L643–L648.
Lupien, C., MacFarlane, W.A., Proust, C., Taillefer, L., Mao, Z.Q., and Maeno, Y., Ultrasound attenuation in Sr2RuO4: an angle-resolved study of the superconducting gap function, Phys. Rev. Lett., 2001, vol. 86, pp. 5986–5986.
Deguchi, K., Mao, Z.Q., and Maeno, Y.J., Determination of the superconducting gap structure in all bands of the spin-triplet superconductor Sr2RuO4, J. Phys. Soc. Jpn., 2004, vol. 73, pp. 1313–1321.
Hassinger, E., Bourgeois-Hope, P., Taniguchi, H., René de Cotret, S., Grissonnanche, G., Anwar, M.S., Maeno, Y., Doiron-Leyraud, N., and Taillefer, L., Vertical line nodes in the superconducting gap structure of Sr2RuO4, Phys. Rev. X, 2017, vol. 7, paper 011 032.
Blount, E.I., Symmetry properties of triplet superconductors, Phys. Rev. B: Condens. Matter Mater. Phys., 1985, vol. 32, pp. 2935–2944.
Xia, J., Maeno, Y., Beyersdorf, P.T., Fejer, M.M., and Kapitulnik, A., High resolution polar Kerr effect measurements of Sr2RuO4: evidence for broken time reversal symmetry in the superconducting state, Phys. Rev. Lett., 2006, vol. 97, paper 167 002.
Maeno, Y., Kittaka, S., Nomura, T., Yonezava, S., and Ishida, K., Evaluation of spin-triplet superconductivity in Sr2RuO4, J. Phys. Soc. Jpn., 2012, vol. 81, paper 011 009.
Kovalev, O.V., Neprivodimye i indutsirovannye predstavleniya grupp (Irreducible and Induced Representations of Groups), Moscow: Nauka, 1985.
Bradley, C.J. and Davies, B.L., Kronecker products and symmetrized squares of irreducible representations of space groups, J. Math. Phys., 1970, vol. 11, pp. 1536–1552.
Yarzhemsky, V.G., Izotov, A.D., and Izotova, V.O., Structure of the order parameter in iron pnictide-based superconducting materials, Inorg. Mater., 2017, vol. 53, no. 9, pp. 923–929. https://doi.org/10.1134/S0020168517090163
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This work was supported by the Russian Federation Ministry of Education and Science (state research target for the Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, in the field of basic research).
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Yarzhemsky, V.G., Izotov, A.D. Structure of the Order Parameter of Topological Superconductors Based on 3d and 4d Transition Metal Oxides. Inorg Mater 55, 944–951 (2019). https://doi.org/10.1134/S002016851909019X
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DOI: https://doi.org/10.1134/S002016851909019X