- Letter
- Open Access
Unconventional superconductivity mediated solely by isotropic electron-phonon interaction
Phys. Rev. B 104, L140506 – Published 28 October, 2021
DOI: https://doi.org/10.1103/PhysRevB.104.L140506
Abstract
Unconventional superconductivity is commonly linked to electronic pairing mechanisms, since it is believed that the conventional electron-phonon interaction (EPI) cannot cause sign-changing superconducting gap symmetries. Here, we show that this common understanding needs to be revised when one considers a more elaborate theory of electron-phonon superconductivity beyond standard approximations. We self-consistently solve the full-bandwidth, anisotropic Eliashberg equations including vertex corrections beyond Migdal's approximation assuming the usual isotropic EPI for cuprate, Fe-based, and heavy-fermion superconductors with nested Fermi surfaces. In the case of the high- cuprates we find a -wave order parameter, as well as a nematic state upon increased doping. For Fe-based superconductors, we obtain gap symmetry, while for heavy-fermion we find unconventional -wave pairing. These results provide a proof of concept that EPI cannot be excluded as a mediator of unconventional and of high- superconductivity.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (44)
- M. Sigrist and K. Ueda, Rev. Mod. Phys. 63, 239 (1991).
- X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
- 100 Years of Superconductivity, edited by H. Rogalla and P. H. Kes (CRC Press, Boca Raton, FL, 2011).
- B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Zaanen, Nature (London) 518, 179 (2015).
- C. C. Tsuei and J. R. Kirtley, Rev. Mod. Phys. 72, 969 (2000).
- G. R. Stewart, Rev. Mod. Phys. 83, 1589 (2011).
- Y. J. Uemura, L. P. Le, G. M. Luke, B. J. Sternlieb, W. D. Wu, J. H. Brewer, T. M. Riseman, C. L. Seaman, M. B. Maple, M. Ishikawa, D. G. Hinks, J. D. Jorgensen, G. Saito, and H. Yamochi, Phys. Rev. Lett. 66, 2665 (1991).
- P. Dai, Rev. Mod. Phys. 87, 855 (2015).
- D. J. Scalapino, Rev. Mod. Phys. 84, 1383 (2012).
- G.-H. Gweon, T. Sasagawa, S. Y. Zhou, J. Graf, H. Takagi, D.-H. Lee, and A. Lanzara, Nature (London) 430, 187 (2004).
- H. Iwasawa, J. F. Douglas, K. Sato, T. Masui, Y. Yoshida, Z. Sun, H. Eisaki, H. Bando, A. Ino, M. Arita, K. Shimada, H. Namatame, M. Taniguchi, S. Tajima, S. Uchida, T. Saitoh, D. S. Dessau, and Y. Aiura, Phys. Rev. Lett. 101, 157005 (2008).
- R. H. Liu, T. Wu, G. Wu, H. Chen, X. F. Wang, Y. L. Xie, J. J. Ying, Y. J. Yan, Q. J. Li, B. C. Shi, W. S. Chu, Z. Y. Wu, and X. H. Chen, Nature (London) 459, 64 (2009).
- R. Khasanov, M. Bendele, A. Bussmann-Holder, and H. Keller, Phys. Rev. B 82, 212505 (2010).
- A. Lanzara, P. V. Bogdanov, X. J. Zhou, S. A. Kellar, D. L. Feng, E. D. Lu, T. Yoshida, H. Eisaki, A. Fujimori, K. Kishio, J.-I. Shimoyama, T. Noda, S. Uchida, Z. Hussain, and Z.-X. Shen, Nature (London) 412, 510 (2001).
- D. J. Scalapino, E. Loh, and J. E. Hirsch, Phys. Rev. B 34, 8190 (1986).
- J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957).
- G. M. Eliashberg, Sov. Phys. JETP 11, 696 (1960).
- G. Varelogiannis, Phys. Rev. B 57, 13743 (1998).
- A. Aperis, P. Kotetes, G. Varelogiannis, and P. M. Oppeneer, Phys. Rev. B 83, 092505 (2011).
- J. J. Lee, F. T. Schmitt, R. G. Moore, S. Johnston, Y.-T. Cui, W. Li, M. Yi, Z. K. Liu, M. Hashimoto, Y. Zhang, D. H. Lu, T. P. Devereaux, D.-H. Lee, and Z.-X. Shen, Nature (London) 515, 245 (2014).
- A. B. Migdal, Sov. Phys. JETP 34, 996 (1958).
- P. Benedetti, C. Grimaldi, L. Pietronero, and G. Varelogiannis, Europhys. Lett. 28, 351 (1994).
- F. Schrodi, P. M. Oppeneer, and A. Aperis, Phys. Rev. B 102, 024503 (2020).
- C. Grimaldi, L. Pietronero, and S. Strässler, Phys. Rev. Lett. 75, 1158 (1995).
- M. Botti, E. Cappelluti, C. Grimaldi, and L. Pietronero, Phys. Rev. B 66, 054532 (2002).
- P. Miller, J. K. Freericks, and E. J. Nicol, Phys. Rev. B 58, 14498 (1998).
- J. P. Hague, J. Phys.: Condens. Matter 15, 2535 (2003).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.104.L140506 for the complete formalism of vertex-corrected Eliashberg theory, details on the tight-binding models used for the cuprate, Fe-based, and heavy-fermion superconductors, and explicit convergence studies for the momentum and Matsubara frequency grids. Furthermore, additional results are presented for the superconducting gaps varying the EPI interaction strength, phonon frequencies, and temperatures, as well as full calculations of the temperature dependence of the cuprate superconducting gap. Also, the calculated renormalized charge susceptibilities and results for the electron-phonon coupling constant are given.
- The Uppsala Superconductivity (UppSC) code provides a package to self-consistently solve the anisotropic, multiband, and full-bandwidth Eliashberg equations for frequency-even and frequency-odd superconductivity mediated by phonons, and charge or spin fluctuations on the basis of ab initio calculated input.
- A. A. Kordyuk, V. B. Zabolotnyy, D. V. Evtushinsky, T. K. Kim, I. V. Morozov, M. L. Kulić, R. Follath, G. Behr, B. Büchner, and S. V. Borisenko, Phys. Rev. B 83, 134513 (2011).
- M. Zbiri, H. Schober, M. R. Johnson, S. Rols, R. Mittal, Y. Su, M. Rotter, and D. Johrendt, Phys. Rev. B 79, 064511 (2009).
- L. Boeri, O. V. Dolgov, and A. A. Golubov, Phys. C: Superconductivity 469, 628 (2009).
- J. S. Van Dyke, F. Massee, M. P. Allan, J. C. S. Davis, C. Petrovic, and D. K. Morr, Proc. Natl. Acad. Sci. USA 111, 11663 (2014).
- H. Martinho, P. G. Pagliuso, V. Fritsch, N. O. Moreno, J. L. Sarrao, and C. Rettori, Phys. Rev. B 75, 045108 (2007).
- J. P. Hague, Phys. Rev. B 73, 060503(R) (2006).
- Y. Fasano, P. Szabó, J. Kacmarcik, Z. Pribulova, P. Pedrazzini, P. Samuely, and V. F. Correa, Phys. B: Condens. Matter 536, 798 (2018).
- F. Schrodi, A. Aperis, and P. M. Oppeneer, Phys. Rev. B 102, 014502 (2020).
- H. Yamase and T. Agatsuma, Phys. Rev. B 102, 060504(R) (2020).
- F. Schrodi, A. Aperis, and P. M. Oppeneer, Phys. Rev. B 102, 180501(R) (2020).
- E. Fradkin, S. A. Kivelson, M. J. Lawler, J. P. Eisenstein, and A. P. Mackenzie, Annu. Rev. Condens. Matter Phys. 1, 153 (2010).
- Using a larger leads to a higher , therefore allowing us to work at higher temperatures that demand fewer Matsubara frequencies and are thus less computationally demanding. For meV and the same parameter set as used in Fig. 1 we find the same -wave symmetry but with a larger gap value and K.
- G. Livanas, A. Aperis, P. Kotetes, and G. Varelogiannis, Phys. Rev. B 91, 104502 (2015).
- F. Giustino, M. L. Cohen, and S. G. Louie, Nature (London) 452, 975 (2008).
- A. Aperis and P. M. Oppeneer, Phys. Rev. B 97, 060501(R) (2018).