Superconductivity in the cuprates: Deduction of mechanism for d-wave pairing through analysis of ARPES

Abstract

In the Eliashberg integral equations for d-wave superconductivity, two different functions (α²F)_n(ω, θ) and (α²F)_p,d(ω) determine, respectively, the “normal” self-energy and the “pairing” self-energy. ω is the frequency of fluctuations scattering the fermions whose momentum is near the Fermi-surface and makes an angle θ to a chosen axis. We present a quantitative analysis of the high-resolution laser based Angle Resolved Photoemission Spectroscopy (ARPES) data on a slightly under doped cuprate compound Bi2212 and use the Eliashberg equations to deduce the ω and θ dependence of (α²F)_n(ω, θ) for T just above T_c and below T_c. Besides its detailed ω dependence, we find the remarkable result that this function is nearly independent of θ between the (π; π)-direction and 25 degrees from it, except for the dependence of the cut-off energy on θ. Assuming that the same fluctuations determine both the normal and the pairing self-energy, we ask what theories give the function (α²F)_p,d(ω) required for the d-wave pairing instability at high temperatures as well as the deduced (α²F)_n(θ, ω). We show that the deduced (α²F)_n(θ, ω) can only be obtained from antiferromagnetic (AFM) fluctuations if their correlation length is smaller than a lattice constant. Using (α²F)_p,d(ω) consistent with such a correlation length and the symmetry of matrix-elements scattering fermions by AFM fluctuations, we calculate T_c and show that AFM fluctuations are excluded as the pairing mechanism for d-wave superconductivity in cuprates. We also consider the quantumcritical fluctuations derived microscopically as the fluctuations of the observed loop–current order discovered in the under-doped cuprates, and which lead to the marginal Fermi–liquid properties in the normal state. We show that their frequency dependence and the momentum dependence of their matrix-elements to scatter fermions are consistent with the θ and ω dependence of the deduced (α²F)_n(ω, θ). The pairing kernel (α²F)_p,d(ω) calculated using the experimental values in the Eliashberg equation gives d-wave instability at T_c comparable to the experiments.

Keywords

high temperature superconductivity / mechanisms of superconductivity

References

[1] G. M. Eliashberg, Zh. Eksp. Teor. Fiz., 1960, 38: 966

[2] L. P. Gorkov, Sov. Phys. JETP, 1960, 7: 505

[3] W. McMillan and J. R. Rowell, Phys. Rev. Lett., 1965, 14(4): 108

[4] J. R. Schrieffer, D. J. Scalapino, and J. W. Wilkins, Phys. Rev. Lett., 1963, 10(8): 336

[5] I. Vekhter and C. M. Varma, Phys. Rev. Lett., 2003, 90(23): 237003

[6] K. Miyake, S. Schmitt-Rink, and C. M. Varma, Phys. Rev. B, 1986, 34(9): 6554

[7] C. M. Varma, arXiv: 1001.3618, 2010

[8] J. M. Bok, J. H. Yun, H. Y. Choi, and C. M. Varma, Phys. Rev. B, 2010, 81(17): 174516

[9] J. H. Yun, J. M. Bok, H. Y. Choi, W. Zhang, X. J. Zhou, and C. M. Varma, Phys. Rev. B, 2011, 814(10): 104521

[10] W. Zhang, J. M. Bok, J. H. Yun, G. Liu, L. Zhao, H. Liu, J. Meng, X. Dong, J. Zhang, W. Lu, H. Y. Choi, and X. Zhou, Phys. Rev. B, to be published

[11] E. Schachinger and J. P. Carbotte, Phys. Rev. B, 2008, 77(9): 094525

[12] J. Hwang, T. Timusk, E. Schachinger, and J. P. Carbotte, Phys. Rev. B, 2007, 75(14): 144508

[13] E. van Hemmen, E. Muhlethaler, A. B. Kuzmenko, H. Eisaki, W. Meevasana, M. Greven, and D. van der Marel, Phys. Rev. B, 2009, 79(18): 184512

[14] L. Zhu, V. Aji, A. Shekhter, and C. M. Varma, Phys. Rev. Lett., 2008, 100(5): 057001

[15] D. J. Scalapino, E. Loh, and J. E. Hirsch, Phys. Rev. B, 1986, 34(11): 8190

[16] D. J. Scalapino, Phys. Rep., 1995, 250(6): 329

[17] H. Monien, A. J. Millis, and D. Pines, Phys. Rev. B, 1990, 42: 167

[18] D. Pines, A. V. Chubukov, and J. Schmalian, The Physics of Superconductors, Vol. 2, Berlin: Springer, 2003

[19] H. A. Mook, M. Yethiraj, G. Aeppli, T. Mason, and T. Armstrong, Phys. Rev. Lett., 1993, 70(22): 3490

[20] A. V. Balatasky and P. Bourges, Phys. Rev. Lett., 1990, 82: 5337

[21] V. Aji and C. M. Varma, Phys. Rev. Lett., 2007, 99(6): 067003

[22] V. Aji and C. M. Varma, Phys. Rev. B, 2009, 79(18): 184501

[23] V. Aji and C. M. Varma, Phys. Rev. B, 2010, 82(17): 174501

[24] M. E. Simon and C. M. Varma, Phys. Rev. Lett., 2001, 86(9): 1781

[25] C. M. Varma, Phys. Rev. B, 2006, 73(15): 155113

[26] B. Fauque, Y. Sidis, V. Hinkov, S. Pailhès, C. T. Lin, X. Chaud, and P. Bourges, Phys. Rev. Lett., 2006, 96(19): 197001

[27] H. Mook, Y. Sidis, B. Fauqué, V. Balédent, and P. Bourges, Phys. Rev. B, 2008, 78(2): 020506

[28] Y. Li, V. Balédent, N. BarišićY. Cho, B. Fauqué, Y. Sidis, G. Yu, X. Zhao, P. Bourges, and M. Greven, Nature, 2008, 455(7211): 372

[29] A. Kaminski, S. Rosenkranz, H. M. Fretwell, J. C. Campuzano, Z. Li, H. Raffy, W. G. Cullen, H. You, C. G. Olson, C. M. Varma, and H. Höchst, Nature, 2002, 416(6881): 610

[30] A. Shekhter, V. Aji, and C. M. Varma, Phys. Rev. B, 2010, 81: 064515

[31] C. M. Varma, P. B. Littlewood, and S. Schmitt-Rink, Phys. Rev. Lett., 1989, 63(18): 1996

[32] Y. He and C. M. Varma, Phys. Rev. Lett., 2011, 106(14): 147001

[33] Y. Li, V. Balédent, G. Yu, N. BarišićK. Hradil, R. A. Mole, Y. Sidis, P. Steffens, X. Zhao, P. Bourges, and M. Greven, Nature, 2010, 468(7321): 283

[34] S. Johnston, F. Vernay, B. Moritz, Z.X. Shen, N. Nagaosa, J. Zaanen, and T. Devereaux, Phys. Rev. B, 2010, 82(6): 064513

[35] C. M. Varma, Phys. Rev. B, 1997, 55(21): 14554

[36] Y. Li, V. Baledent, N. Barisic, Y. C. Cho, Y. Sidis, G. Yu, X. Zhao, P. Bourges, and M. Greven, Phys. Rev. B, to the published

[37] J. L. Tallon and J. W. Loram, Physica C, 2000, 349(1-2): 53

[38] B. Fauque, Y. Sidis, V. Hinkov, S. Pailhès, C. T. Lin, X. Chaud, and P. Bourges, Phys. Rev. Lett., 2006, 96(19): 197001

[39] V. Baledent, B. Fauqué, Y. Sidis, N. Christensen, S. Pailhès, K. Conder, E. Pomjakushina, J. Mesot, and P. Bourges, Phys. Rev. Lett., 2010, 105(2): 0207004

[40] P. Bourges, Private communication, to be published, 2010

[41] A. Kaminski, S. Rosenkranz, H. M. Fretwell, J. C. Campuzano, Z. Li, H. Raffy, W. G. Cullen, H. You, C. G. Olson, C. M. Varma, and H. Höchst, Nature, 2002, 416(6881): 610

[42] P. Bourges and Y. Sidis, Comptes Rendus Physique, 2011, 12(5-6): 461

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