Reconsidering the electron-phonon problem and bounds on Tc

ITS Seminar with Steve Kivelson (Stanford University)

Please contact Vadim Oganesyan at vadim.oganesyan@gmail.com to join via Zoom.

We exploit the fact that the Holstein model of the electron-phonon problem can be treated without approximation using fermion-minus-sign-free determinent quantum Monte Carlo methods to establish results that can be compared quantitatively and unambiguously with approximate methods based on Migdal-Eliashberg (ME) theory. In the relevant limit in which the phonon frequencies are small compared to the Fermi energy (strong retardation), we find that ME theory is extremely accurate up to moderate values of the dimensionless electron-phonon coupling λ, and then breaks down relatively suddenly beyond a characteristic value, λ*~1, beyond which polaron physics is significant. One consequence of this is that – in contrast with earlier beliefs based on ME theory – the superconducting Tc(λ) has its maximum value at λ ≈λ*. This implies that there is an upper bound on Tc from the electron phonon mechanism Tc ≤ A wmax, where wmax is the maximum phonon energy and we estimate that A ≈ 1/10.

References
[1]. I. Esterlis, B.Nosarzewski, E.W.Huang, B. Moritz, T. P. Devereaux, D. J. Scalapino, and S. A. Kivelson, “Breakdown of Migdal-Eliashberg theory; a determinant quantum Monte Carlo study,” Phys. Rev. B 97, 140501 (2018).
[2] I.Esterlis, S.A.Kivelson, and D.J.Scalapino, “A bound on the superconducting transition temperature,” npj Quantum Materials 3, 59 (2018).
[3] I. Esterlis, S. A. Kivelson, and D. J. Scalapino, “Pseudogap crossover in the
electron-phonon system,” Phys. Rev. B 99, 174516 (2019).
[4]  A. V. Chubukov, A. Abanov, I. Esterlis, and S. A. Kivelson, “Eliashberg theory of phonon-mediated superconductivity – when it is valid and how it breaks down,” arXiv:2004.01281.