Implicit renormalization approach to the problem of Cooper instability

Abstract

In the vast majority of cases, superconducting transition takes place at exponentially low temperature $T_c$ out of the Fermi liquid regime. We discuss the problem of determining $T_c$ from known system properties at temperatures $T\gg T_c$, and stress that this cannot be done reliably by following the standard protocol of solving for the largest eigenvalue of the original gap-function equation. However, within the implicit renormalization approach, the gap-function equation can be used to formulate an alternative eigenvalue problem, solving which leads to an accurate prediction for both $T_c$ and the gap function immediately below $T_c$. With the diagrammatic Monte Carlo techniques, this eigenvalue problem can be solved without invoking the matrix inversion or even explicitly calculating the four-point vertex function.

arXiv comment12 pages, 6 figures

References in corpus (34)

• Unconventional sign-reversing superconductivity in LaFeAsO_(1-x)F_x
• Unconventional pairing originating from disconnected Fermi surfaces in superconducting LaFeAsO${}_{1-x}$F${}_x$}
• Electron-phonon interactions from first principles
• A Common Thread: the pairing interaction for the unconventional superconductors
• Magnetism, superconductivity, and pairing symmetry in Fe-based superconductors
• Nematic Fermi Fluids in Condensed Matter Physics
• Enhancement of superconductivity near a nematic quantum critical point
• Topological $R$PdBi half-Heusler semimetals: a new family of non-centrosymmetric magnetic superconductors
• Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point
• Quantum critical origin of the superconducting dome in SrTiO${}_3$
• Experimental evidence for bulk superconductivity in pure Bismuth single crystal at ambient pressure
• Critical doping for the onset of a two-band superconducting ground state in SrTiO${}_{3-\delta }$
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• Superconductivity at very low density: the case of strontium titanate
• Enhanced superconductivity due to forward scattering in FeSe thin films on SrTiO3 substrates
• Superconductivity in three-dimensional spin-orbit coupled semimetals
• Monte Carlo Studies of Quantum Critical Metals
• Superconductivity at low density near a ferroelectric quantum critical point: doped SrTiO
• Unconventional multi-band superconductivity in bulk SrTiO${}_3$ and LaAlO${}_3$/SrTiO${}_3$ interfaces
• Charge transfer and electron-phonon coupling in monolayer FeSe on Nb doped SrTiO${}_3$
• Quantum-critical pairing in electron-doped cuprates
• Notes on calculating temperature of the superconducting transition: interacting fermi gas and phonon mechanisms in non-adiabatic regime
• Multiband full-bandwidth anisotropic Eliashberg theory of interfacial electron-phonon coupling and high-T${}_c$ superconductivity in FeSe/SrTiO${}_3$
• Superconductivity near a nematic quantum critical point -- the interplay between hot and lukewarm regions
• Critical temperature and giant isotope effect in presence of paramagnons
• Dipolar phonons and electronic screening in monolayer FeSe on SrTiO${}_3$
• Phonon mediated superconductivity in low carrier-density systems
• Pairing from dynamically screened Coulomb repulsion in bismuth
• Modulation of the superconducting critical temperature due to quantum confinement at the LaAlO${}_3$/SrTiO${}_3$ interface
• Eliashberg Theory in the Weak Coupling Limit
• Self-consistent temperature dependence of quasiparticle bands in monolayer FeSe on SrTiO${}_3$
• Superconductivity in the vicinity of a ferroelectric quantum phase transition
• Electron - phonon coupling in Eliashberg - McMillan theory beyond adiabatic approximation
• Antiadiabatic phonons, Coulomb pseudopotential and superconductivity in Eliashberg - McMillan theory

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