skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A bound on the superconducting transition temperature

Abstract

It is notoriously difficult to make quantitative theoretical predictions of the superconducting transition temperature, T c, either from first-principles or even from a knowledge of normal state properties. Ultimately, this reflects the fact that the energy scales involved in the superconducting state are extremely small in natural units, and that T c depends exponentially on a subtle interplay between different interactions so that small uncertainties in microscopic processes can lead to order one effects on T c. However, in some circumstances, it may be possible to determine (approximate) bounds on T c. Here we propose such a bound for the conventional phonon-mediated mechanism of pairing with strongly retarded interactions, i.e. in the case in which ℏ$$\bar{ω}$$«EF, where $$\bar{ω}$$ is an appropriate characteristic phonon frequency and EF is the Fermi energy. Specifically, drawing on both empirical results (shown in Fig. 2 below) and recent results of determinant quantum Monte Carlo (DQMC) studies of the paradigmatic Holstein model, we propose that k BT c≤A maxℏ$$\bar{ω}$$, where A max is a dimensionless number of order one that we estimate to be A max ≈ 1/10.

Authors:
 [1];  [1];  [2]
  1. Stanford Univ., CA (United States)
  2. Univ. of California, Santa Barbara, CA (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1490570
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
npj Quantum Materials
Additional Journal Information:
Journal Volume: 3; Journal Issue: 1; Journal ID: ISSN 2397-4648
Publisher:
Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Esterlis, I., Kivelson, S. A., and Scalapino, D. J. A bound on the superconducting transition temperature. United States: N. p., 2018. Web. doi:10.1038/s41535-018-0133-0.
Esterlis, I., Kivelson, S. A., & Scalapino, D. J. A bound on the superconducting transition temperature. United States. doi:10.1038/s41535-018-0133-0.
Esterlis, I., Kivelson, S. A., and Scalapino, D. J. Mon . "A bound on the superconducting transition temperature". United States. doi:10.1038/s41535-018-0133-0. https://www.osti.gov/servlets/purl/1490570.
@article{osti_1490570,
title = {A bound on the superconducting transition temperature},
author = {Esterlis, I. and Kivelson, S. A. and Scalapino, D. J.},
abstractNote = {It is notoriously difficult to make quantitative theoretical predictions of the superconducting transition temperature, Tc, either from first-principles or even from a knowledge of normal state properties. Ultimately, this reflects the fact that the energy scales involved in the superconducting state are extremely small in natural units, and that Tc depends exponentially on a subtle interplay between different interactions so that small uncertainties in microscopic processes can lead to order one effects on Tc. However, in some circumstances, it may be possible to determine (approximate) bounds on Tc. Here we propose such a bound for the conventional phonon-mediated mechanism of pairing with strongly retarded interactions, i.e. in the case in which ℏ$\bar{ω}$«EF, where $\bar{ω}$ is an appropriate characteristic phonon frequency and EF is the Fermi energy. Specifically, drawing on both empirical results (shown in Fig. 2 below) and recent results of determinant quantum Monte Carlo (DQMC) studies of the paradigmatic Holstein model, we propose that kBTc≤Amaxℏ$\bar{ω}$, where Amax is a dimensionless number of order one that we estimate to be Amax ≈ 1/10.},
doi = {10.1038/s41535-018-0133-0},
journal = {npj Quantum Materials},
number = 1,
volume = 3,
place = {United States},
year = {2018},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Figures / Tables:

Fig. 1 Fig. 1: Occupancy of the $\overrightarrow{k}$ = $\overrightarrow{0}$ (band bottom) single-particle state as a function of the bare dimensionless electron-phonon coupling λ0 (lower scale) and the renormalized coupling, λ (upper scale). (The definitions are as given in ref. 1). Solid dots are from DQMC simulations described in ref. 1 withmore » ℏω0/EF= 0.1, and the data shown are at a temperature T ≈ EF/30, at which n$\overrightarrow{0}$ has reached its asymptotic low T-value. The dashed line is the same quantity computed within ME theory. The inset shows the difference between the DQMC and ME results. The scale on the vertical axis has been chosen such that 0 is the value for non-interacting electrons and 1 is the value in the polaronic limit. (ρ = 0.8 is the average electron density per site.)« less

Save / Share:

Works referenced in this record:

Two bounds on the maximum phonon-mediated superconducting transition temperature
journal, September 2006


Transition temperature of strong-coupled superconductors reanalyzed
journal, August 1975


Specific heat of polycrystalline Ba 0.6 K 0.4 BiO 3 from 0.5 to 20 K
journal, September 1990


Superconductivity in Bad Metals
journal, April 1995


Breakdown of the Migdal-Eliashberg theory: A determinant quantum Monte Carlo study
journal, April 2018


Properties of boson-exchange superconductors
journal, October 1990


Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime
journal, October 2001


Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system
journal, August 2015

  • Drozdov, A. P.; Eremets, M. I.; Troyan, I. A.
  • Nature, Vol. 525, Issue 7567
  • DOI: 10.1038/nature14964

Superconductivity in the A15 structure
journal, July 2015


Superconductivity in the elements, alloys and simple compounds
journal, July 2015

  • Webb, G. W.; Marsiglio, F.; Hirsch, J. E.
  • Physica C: Superconductivity and its Applications, Vol. 514
  • DOI: 10.1016/j.physc.2015.02.037

Review of the superconducting properties of MgB 2
journal, November 2001


Specific heat of the cubic high-Tc superconductor Ba0·6K0·4BiO3
journal, June 1989


Critical temperature for the two-dimensional attractive Hubbard model
journal, May 2004


High-Pressure Hydrogen Sulfide from First Principles: A Strongly Anharmonic Phonon-Mediated Superconductor
journal, April 2015


A least upper bound on the superconducting transition temperature
journal, December 1975


Barium potassium bismuth oxide: A review
journal, February 1995


Design for a Room-Temperature Superconductor
journal, December 2006


Specific Heatof the Filled Skutterudite Superconductor LaOs 4 As 12
journal, August 2016


Anisotropic superconductivity in bulk Ca C 6
journal, August 2007


    Figures / Tables found in this record:

      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.