A bound on the superconducting transition temperature

Journal Article · 19 November 2018 · npj Quantum Materials

DOI: https://doi.org/10.1038/s41535-018-0133-0 · OSTI ID:1490570

Esterlis, I. ^[1]; Kivelson, S. A. ^[1]; Scalapino, D. J. ^[2]

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1. Stanford Univ., CA (United States)
2. Univ. of California, Santa Barbara, CA (United States)

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.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 1490570
• Journal Information: npj Quantum Materials, Vol. 3, Issue 1; ISSN 2397-4648
• Publisher: Nature Publishing GroupCopyright Statement
• Country of Publication: United States
• Language: English