BCS Superconductivity in Quantum Critical Metals

Abstract

Departing from the assumption that pairing is induced by an retarded external 'bosonic glue', we reformulate the Bardeen-Cooper-Schrieffer theory of superconductivity as a scaling theory. Conventional superconductors correspond with the asymptotically free case but the theory can be effortlessly generalized to handle quantum critical metals. We find that superconducting Tc's are strongly enhanced in the latter when retardation is strong while the coupling is weak. It appears that this simple scaling theory does account quite well for superconducting properties near quantum critical points.

20 pages, 12 figures, much extended version, added several new sections including one on transition temperature, more references added

References in corpus (17)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Quantum Criticality in Heavy Fermion Metals
• Quantum criticality
• String Theory, Quantum Phase Transitions and the Emergent Fermi-Liquid
• Interplay of electron-lattice interactions and superconductivity in Bi2Sr2CaCu2O8+d
• Critical fermi surfaces and non-fermi liquid metals
• Specific heat jump at the superconducting transition temperature in Ba(Fe(1-x)Cox)2As2 and Ba(Fe(1-x)Nix)2As2 single crystals
• Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs
• Optical determination of the relation between the electron-boson coupling function and the critical temperature in high T${}_c$ cuprates
• Competition between spin density wave order and superconductivity in the underdoped cuprates
• Divergence of the Magnetic Grüneisen Ratio at the Field-Induced Quantum Critical Point in YbRh${}_2$Si${}_2$
• Gap anisotropy and universal pairing scale in a spin fluctuation model for cuprates
• Colossal enhancement of upper critical fields in noncentrosymmetric heavy fermion superconductors near quantum criticality: CeRhSi${}_3$ and CeIrSi${}_3$
• Paired electron pockets in the hole-doped cuprates
• Theory of non-Fermi liquid and pairing in electron-doped cuprates
• Fermionic quantum criticality and the fractal nodal surface
• Spin-liquid model of the sharp resistivity drop in $L{a}_{1.85}B{a}_{0.125}Cu{O}_4$

Cited by in corpus (8)

• Inhomogeneity of charge density wave order and quenched disorder in a high Tc superconductor
• Cooper pairing of incoherent electrons: an electron-phonon version of the Sachdev-Ye-Kitaev model
• Proximity of Iron Pnictide Superconductors to a Quantum Tricritical Point
• Cooper pairing near charged black holes
• Towards a Holographic Realization of Homes' Law
• Superconductivity from Luttinger surfaces: Emergent $\infty$-body SYK physics
• Thermal effects in non-Fermi liquid superconductivity
• Determination of Gap Solution and Critical Temperature in Doped Graphene Superconductivity