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Eliashberg theory of phonon-mediated superconductivity — When it is valid and how it breaks down

Journal Article · · Annals of Physics
 [1];  [2];  [3];  [4]
  1. University of Minnesota, Minneapolis, MN (United States); University of Minnesota
  2. Texas A&M University, College Station, TX (United States)
  3. Harvard University, Cambridge, MA (United States)
  4. Stanford University, CA (United States)

We analyze the validity of Eliashberg theory of phonon-mediated superconductivity in 2D systems in light of recent extensive Monte-Carlo studies of the Holstein model. Conventional wisdom says that Eliashberg theory is applicable as long as vertex corrections remain small. For small ratio of the phonon energy Ω0 and the Fermi energy EF, this condition is supposed to hold even when the dimensionless electron–phonon coupling λ is larger than one, i.e., in the strong coupling regime. A comparison between various quantities computed in the Migdal approximation and those computed by Quantum Monte Carlo prove that this belief is wrong, and we identify analytically some of the ways in which this breakdown occurs for various ‘‘normal state’’ properties at λ = λcr, where λcr = O(1). Here, the breakdown occurs at temperatures high enough that neither superconducting nor charge–density wave correlations extend over any significant range of distances, so it cannot be associated with the onset of an instability toward any of the relevant ordered ground-states — rather it is associated with the local physics of classical bipolaron formation. Still, we show that certain properties, including the superconducting Tc and the superconducting gap structure below Tc, can be accurately inferred from the strong-coupling limit of Eliashberg theory at λ ≤ λcr.

Research Organization:
University of Minnesota, Minneapolis, MN (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES); NSF
Grant/Contract Number:
SC0014402
OSTI ID:
1660772
Alternate ID(s):
OSTI ID: 1691823
Journal Information:
Annals of Physics, Journal Name: Annals of Physics Vol. 417; ISSN 0003-4916
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (3)

Double-valued strong-coupling corrections to Bardeen–Cooper–Schrieffer ratios journal November 2020
Direct evidence for Cooper pairing without a spectral gap in a disordered superconductor above T c journal October 2021
Quantum critical Eliashberg theory, the SYK superconductor and their holographic duals text January 2021

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