Efficient ab initio Migdal-Eliashberg calculation considering the retardation effect in phonon-mediated superconductors

Abstract

We formulate an efficient scheme to perform Migdal-Eliashberg calculation considering the retardation effect from first principles. While the conventional approach requires a huge number of Matsubara frequencies, we show that the intermediate representation of the Green's function [H. Shinaoka et al., Phys. Rev. B 96, 035147 (2017)] dramatically reduces the numerical cost to solve the linearized gap equation. Without introducing any empirical parameter, we demonstrate that we can successfully reproduce the experimental superconducting transition temperature of elemental Nb ($\sim 10$ K) very accurately. The present result indicates that our approach has a superior performance for many superconductors for which $T_{\mathrm{c}}$ is lower than $\mathcal{O}(10)$ K

8 pages, 4 figures

References in corpus (4)

• Advanced capabilities for materials modelling with Quantum ESPRESSO
• First-principles study of the pressure and crystal-structure dependences of the superconducting transition temperature in compressed sulfur hydrides
• Superconducting pairing mediated by spin-fluctuations from first principles
• Sparse Modeling in Quantum Many-Body Problems

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