ITS/GC E-seminar S. Kivelson Tue 4/14 2:30pm "Reconsidering the electron-phonon problem and bounds on Tc"
Vadim Oganesyan
Reconsidering the electron-phonon problem and bounds on Tc
Steven
Kivelson
(Stanford University)
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.