A bound on superconducting $T_c$'s

I. Esterlis; S. A. Kivelson; D. J. Scalapino

doi:10.1038/s41535-018-0133-0

paper

A bound on superconducting $T_{c}$ 's

arXiv:1806.00488 · doi:10.1038/s41535-018-0133-0

Abstract

It is notoriously difficult to make quantitative theoretical predictions of the superconducting $T_{c}$ , 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 1 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 $ℏ ω ˉ ≪ E_{F}$ where $ω ˉ$ is an appropriate characteristic phonon frequency and $E_{F}$ is the Fermi energy. Specifically, drawing on both empirical results (shown in Figure 2 below) and recent results[1] of determinant quantum Monte Carlo (DQMC) studies of the paradigmatic Holstein model, we propose that \begin{equation} k_B T_c \leq A_{max} \ \hbar \bar ω\end{equation} where $A_{ma x}$ is a dimensionless number of order one that we estimate to be \begin{equation} A_{max} \approx 1/10. \end{equation}

arXiv comment7 pages, 2 figures

A bound on superconducting $T_{c}$ 's

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A bound on superconducting Tc​'s

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A bound on superconducting $T_{c}$ 's