Superconductivity out of a non-Fermi liquid. Free energy analysis

Abstract

In this paper, we present in-depth analysis of the condensation energy $E_c$ for a superconductor in a situation when superconductivity emerges out of a non-Fermi liquid due to pairing mediated by a massless boson. This is the case for electronic-mediated pairing near a quantum-critical point in a metal, for pairing in SYK-type models, and for phonon-mediated pairing in the properly defined limit, when the dressed Debye frequency vanishes. We consider a subset of these quantum-critical models, in which the pairing in a channel with a proper spatial symmetry is described by an effective $0+1$ dimensional model with the effective dynamical interaction $V({\Omega }_m)={\bar{g}}^{\gamma }/|{\Omega }_m{|}^{\gamma }$, where $\gamma$ is model-specific (the $\gamma$-model). In previous papers, we argued that the pairing in the $\gamma$ model is qualitatively different from that in a Fermi liquid, and the gap equation at $T=0$ has an infinite number of topologically distinct solutions, ${\Delta }_n({\omega }_m)$, where an integer $n$, running between $0$ and infinity, is the number of zeros of ${\Delta }_n({\omega }_m)$ on the positive Matsubara axis. This gives rise to the set of extrema of $E_c$ at $E_{c,n}$, of which $E_{c,0}$ is the global minimum. The spectrum $E_{c,n}$ is discrete for a generic $\gamma <2$, but becomes continuous at $\gamma =2-0$. Here, we discuss in more detail the profile of the condensation energy near each $E_{c,n}$ and the transformation from a discrete to a continuous spectrum at $\gamma \to 2$. We also discuss the free energy and the specific heat of the $\gamma$-model in the normal state.

arXiv comment64 pages, 13 figures

References in corpus (51)

• Singular quasiparticle scattering in the proximity of charge instabilities
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order
• On the low energy properies of fermions with singular interactions
• Enhancement of superconductivity near a nematic quantum critical point
• Pseudogap state from quantum criticality
• Non-Fermi Liquid Fixed Point in 2+1 Dimensions
• Odd-frequency superconductivity
• A relation between the resonance neutron peak and ARPES data in cuprates
• Gauge-invariant response functions of fermions coupled to a gauge field
• Charge order, superconductivity, and a global phase diagram of doped antiferromagnets
• Perturbative non-Fermi liquids from dimensional regularization
• d-wave superconductivity near charge instabilities
• Crossover and scaling in a nearly antiferromagnetic Fermi liquid in two dimensions
• Coherent vs incoherent pairing in 2D systems near magnetic instability
• Gauge Fields and Pairing in Double-Layer Composite Fermion Metals
• Cooper pairing of incoherent electrons: an electron-phonon version of the Sachdev-Ye-Kitaev model
• Anomalous isotopic effect near the charge-ordering quantum criticality
• Quantum critical effects on transition temperature of magnetically mediated p-wave superconductivity
• Competition between spin density wave order and superconductivity in the underdoped cuprates
• Fluctuating spin density waves in metals
• Eliashberg theory of phonon-mediated superconductivity -- when it is valid and how it breaks down
• Solvable Strong-coupling Quantum Dot Model with a Non-Fermi-liquid Pairing Transition
• Cascade of phase transitions in the vicinity of a quantum critical point
• Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics
• First order superconducting transition near a ferromagnetic quantum critical point
• Density-wave instabilities of fractionalized Fermi liquids
• Gap anisotropy and universal pairing scale in a spin fluctuation model for cuprates
• Superconductivity near Itinerant Ferromagnetic Quantum Criticality
• Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. I: The $\gamma$-model and its phase diagram at $T=0$. The case $0<\gamma <1$
• Eliashberg equations for an electron-phonon version of the Sachdev-Ye-Kitaev model: Pair Breaking in non-Fermi liquid superconductors
• Interplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal. II. The $\gamma$-model at a finite $T$ for $0<\gamma <1$
• Superconductivity at the onset of spin-density-wave order in a metal
• Normal state properties of quantum critical metals at finite temperature
• Enhancement of superconductivity at the onset of charge-density-wave order in a metal
• Breakdown of the Migdal-Eliashberg theory and a theory of lattice-fermionic superfluidity
• Intrinsic superconducting instabilities of a solvable model for an incoherent metal
• Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal: V. The $\gamma$ model and its phase diagram. The case $\gamma =2$
• On the spin density wave transition in a two dimensional spin liquid
• The ladder physics in the Spin Fermion model
• Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. IV: The $\gamma$ model and its phase diagram at $1<\gamma <2$
• Superconductivity of incoherent electrons in Yukawa-SYK model
• Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. III: The $\gamma$ model and its phase diagram across $\gamma =1$
• Superconductivity near a quantum critical point in the extreme retardation regime
• Luttinger-Ward functional approach in the Eliashberg framework : A systematic derivation of scaling for thermodynamics near a quantum critical point
• Quantum criticality in two dimensions and Marginal Fermi Liquid
• Specific Heat of a Quantum Critical Metal
• Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. VI. The $\gamma$ model and its phase diagram at $2<\gamma <3$
• Real space Eliashberg approach to charge order of electrons coupled to dynamic antiferromagnetic fluctuations
• Odd frequency pairing in a quantum critical metal
• Phonon-mediated superconductivity in strongly correlated electron systems: a Luttinger-Ward functional approach

Cited by in corpus (6)

• Free energy and specific heat near a quantum critical point of a metal
• Multiband strong-coupling superconductors with spontaneously broken time-reversal symmetry
• Constrained weak-coupling superconductivity in multiband superconductors
• The field theory of a superconductor with repulsion
• Exceeding the Chandrasekhar-Clogston limit in flat-band superconductors: A multiband strong-coupling approach
• Universal scaling relations in electron-phonon superconductors