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Title: Non-Fermi-liquid superconductivity: Eliashberg approach versus the renormalization group

Here, we address the problem of superconductivity for non-Fermi liquids using two commonly adopted, yet apparently distinct, methods: (1) the renormalization group (RG) and (2) Eliashberg theory. The extent to which both methods yield consistent solutions for the low-energy behavior of quantum metals has remained unclear. We show that the perturbative RG beta function for the 4-Fermi coupling can be explicitly derived from the linearized Eliashberg equations, under the assumption that quantum corrections are approximately local across energy scales. We apply our analysis to the test case of phonon-mediated superconductivity and show the consistency of both the Eliashberg and RG treatments. We next study superconductivity near a class of quantum critical points and find a transition between superconductivity and a “naked” metallic quantum critical point with finite, critical BCS couplings. We speculate on the applications of our theory to the phenomenology of unconventional metals.
Authors:
 [1] ;  [2] ;  [3]
  1. Univ. of Illinois, Urbana, IL (United States)
  2. Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
  3. Centro Atomico Bariloche adn CONICET, Rio Negro (Argentina)
Publication Date:
Grant/Contract Number:
AC02-76SF00515; 11220110100752; D15AP00108
Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 95; Journal Issue: 16; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Research Org:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
OSTI Identifier:
1361073
Alternate Identifier(s):
OSTI ID: 1352975

Wang, Huajia, Raghu, Srinivas, and Torroba, Gonzalo. Non-Fermi-liquid superconductivity: Eliashberg approach versus the renormalization group. United States: N. p., Web. doi:10.1103/PhysRevB.95.165137.
Wang, Huajia, Raghu, Srinivas, & Torroba, Gonzalo. Non-Fermi-liquid superconductivity: Eliashberg approach versus the renormalization group. United States. doi:10.1103/PhysRevB.95.165137.
Wang, Huajia, Raghu, Srinivas, and Torroba, Gonzalo. 2017. "Non-Fermi-liquid superconductivity: Eliashberg approach versus the renormalization group". United States. doi:10.1103/PhysRevB.95.165137. https://www.osti.gov/servlets/purl/1361073.
@article{osti_1361073,
title = {Non-Fermi-liquid superconductivity: Eliashberg approach versus the renormalization group},
author = {Wang, Huajia and Raghu, Srinivas and Torroba, Gonzalo},
abstractNote = {Here, we address the problem of superconductivity for non-Fermi liquids using two commonly adopted, yet apparently distinct, methods: (1) the renormalization group (RG) and (2) Eliashberg theory. The extent to which both methods yield consistent solutions for the low-energy behavior of quantum metals has remained unclear. We show that the perturbative RG beta function for the 4-Fermi coupling can be explicitly derived from the linearized Eliashberg equations, under the assumption that quantum corrections are approximately local across energy scales. We apply our analysis to the test case of phonon-mediated superconductivity and show the consistency of both the Eliashberg and RG treatments. We next study superconductivity near a class of quantum critical points and find a transition between superconductivity and a “naked” metallic quantum critical point with finite, critical BCS couplings. We speculate on the applications of our theory to the phenomenology of unconventional metals.},
doi = {10.1103/PhysRevB.95.165137},
journal = {Physical Review B},
number = 16,
volume = 95,
place = {United States},
year = {2017},
month = {4}
}