Increased Performance of Matsubara space calculations: A case study within Eliashberg theory

Abstract

We present a method to considerably improve the numerical performance for solving Eliashberg-type coupled equations on the imaginary axis. Instead of the standard practice of introducing a hard numerical cutoff for treating the infinite summations involved, our scheme allows for the efficient calculation of such sums extended formally up to infinity. The method is first benchmarked with isotropic Migdal-Eliashberg theory calculations and subsequently applied to the solution of the full-bandwidth, multiband and anisotropic equations focusing on the FeSe/SrTiO${}_3$ interface as a case study. Compared to the standard procedure, we reach similarly well converged results with less than one fifth of the number of frequencies for the anisotropic case, while for the isotropic set of equations we spare approximately ninety percent of the complexity. Since our proposed approximations are very general, our numerical scheme opens the possibility of studying the superconducting properties of a wide range of materials at ultra-low temperatures.

References in corpus (8)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Monolayer FeSe on SrTiO${}_3$
• Ubiquitous strong electron phonon coupling at the interface of FeSe/SrTiO3
• Conventional Superconductivity in Type II Dirac Semimetal PdTe${}_2$
• Temperature-filling phase diagram of the two-dimensional Holstein model in the thermodynamic limit by self-consistent Migdal approximation
• Advanced first-principles theory of superconductivity including both lattice vibrations and spin fluctuations: The case of FeB${}_4$
• Anisotropic type-I superconductivity and anomalous superfluid density in OsB 2
• Self-consistent temperature dependence of quasiparticle bands in monolayer FeSe on SrTiO${}_3$

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• Efficient fluctuation exchange approach to low-temperature spin fluctuations and superconductivity: from the Hubbard model to Na${}_x$CoO${}_2\cdot y$H${}_2$O
• Eliashberg theory for spin-fluctuations mediated superconductivity -- Application to bulk and monolayer FeSe
• Phonon-mode specific contributions to room-temperature superconductivity in atomic hydrogen at high pressures
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• Prominent Cooper Pairing Away From the Fermi Level and its Spectroscopic Signature in Twisted Bilayer Graphene
• Influence of phonon renormalization in Eliashberg theory for superconductivity in 2D and 3D systems
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• Prediction of an unusual trigonal phase of superconducting LaH${}_{10}$ stable from 250 to 425 GPa pressure
• Cascade of replica bands in flat band systems: predictions for twisted bilayer graphene
• Exploring multichannel superconductivity in ThFeAsN
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