A bound on the superconducting transition temperature. Issue 1 (December 2018) - Esterlis, I.; Kivelson, S.; Scalapino, D.
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 thatT c depends exponentially on a subtle interplay between different interactions so that small uncertainties in microscopic processes can lead to order one effects onT c . However, in some circumstances, it may be possible to determine (approximate) bounds onT 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 ω E_F ℏ ω ¯ ≪ E F, where ω ω ¯ is an appropriate characteristic phonon frequency andE F is the Fermi energy. Specifically, drawing on both empirical results (shown in Fig. 2 below) and recent results1 of determinant quantum Monte Carlo (DQMC) studies of the paradigmatic Holstein model, we propose that k_BT_c A_ω k B T c ≤ A max ℏ ω ¯, whereA max is a dimensionless number of order one that we estimate to beA max ≈ 1/10. Superconductivity: A bound forT c in conventional superconductors A bound for the superconducting transition temperature (Tc ) is proposed for conventional superconductors with phonon-mediated pairing mechanism. I. Esterlis and S.A. Kivelson from Stanford University, and D. J. Scalapino from University of California at Santa Barbara, perform analysis on the Holstein model and propose a bound forT c of superconductors where electron-phonon coupling (λ) plays a dominant role. They re-evaluate the Migdal-Eliashberg theory with the assumption of monotonicλ dependence ofT c and point out where the theory applies and where it doesn't due to non-monotonicλ dependence. With this knowledge, they estimate a key dimensionless parameter, with which a bound forT c is related. Experimentally, T c is further related to Debye temperature, θ D and a bound is proposed to beθ D /10. This result adds insights into the enigmatic problem of predictingT c .