Pairing instability on a Luttinger surface: A non-Fermi liquid to superconductor transition and its Sachdev-Ye-Kitaev dual

Abstract

Superconductivity results from an instability of the Fermi surface -- contour of \textit{poles} of the single particle propagator -- to an infinitesimally small attraction between electrons. Here, we instead discuss the analogous problem on a model \textit{Luttinger} surface, or contour of \textit{zeros} of the Green function. At zero temperature ($\beta \to \infty$) and a critical interaction strength ($u_{c\infty }$) characterized by the residue of self-energy pole, we find that the pair susceptibility diverges leading to a superconducting instability. We evaluate the pair fluctuation partition function and find that the spectral density in the normal state has an interaction-driven, power-law $\frac{1}{\sqrt{\omega }}$ type, van-Hove singularity (vHS) indicating non-Fermi liquid (NFL) physics. Crucially, in the strong coupling limit ($\beta u\gg 1$), the leading order fluctuation free energy terms in the normal state of this NFL-SC transition resemble the equivalent $\left(O(1)\right)$ terms of the Sachdev-Ye-Kitaev (SYK) model. This free energy contribution takes a simple form $-\beta F=\beta u_{c\infty }-\gamma \text{ln}\left(\beta u_{c\infty }\right)$ where $\gamma$ is a constant equal to $\frac{1}{2}$. Weak impurity scattering ($\tau \gg {\beta }^{-1}$) leaves the low-energy spectral density unaffected, but leads to an interaction-driven enhancement of superconductivity. Our results shed light on the role played by order-parameter fluctuations in providing the key missing link between Mott physics and strongly coupled toy-models exhibiting gravity duals.

16 pages, 6 figures including Appendices

References in corpus (35)

• Comments on the Sachdev-Ye-Kitaev model
• Black Holes and Random Matrices
• Fractionalized Fermi liquids
• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Holographic metals and the fractionalized Fermi liquid
• A Phenomenological Theory of The Pseudogap State
• Doping Evolution of the Underlying Fermi Surface in La2-xSrxCuO4
• Evolution of electronic structure of doped Mott insulators - reconstruction of poles and zeros of Green's function
• Fermi arcs and the hidden zeros of the Green's function in the pseudogap state
• Modeling the Fermi arc in underdoped cuprates
• On the Reconstructed Fermi Surface in the Underdoped Cuprates
• ARPES studies of cuprate Fermiology: superconductivity, pseudogap, and quasiparticle dynamics
• Cooper pairing of incoherent electrons: an electron-phonon version of the Sachdev-Ye-Kitaev model
• Weakly coupled one-dimensional Mott insulators
• Topological order in the pseudogap metal
• Dynamically Generated Gap from Holography: Mottness from a Black Hole
• Doped Spin Liquid: Luttinger Sum Rule and Low Temperature Order
• Dynamical Gap and Cuprate-like Physics from Holography
• Much Ado about Zeros: The Luttinger Surface and Mottness
• Absence of Luttinger's Theorem due to Zeros in the Single-Particle Green Function
• Phenomenological description of the two energy scales in underdoped superconducting cuprates
• Spin glass versus superconductivity
• Luttinger-volume violating Fermi liquid in the pseudogap phase of the cuprate superconductors
• Breakdown of Luttinger's theorem in two-orbital Mott insulators
• Breakup of the Fermi surface near the Mott transition in low-dimensional systems
• Topological interpretation of Luttinger theorem
• Fermi surface reconstruction in hole-doped t-J models without long-range antiferromagnetic order
• Key issues in theories of high temperature superconductors
• Emergent gauge fields and the high temperature superconductors
• Self-energy and Fermi surface of the 2-dimensional Hubbard model
• Theory of fluctuations in a two-band superconductor
• Doping dependence of the $(\pi ,\pi )$ shadow band in La-based cuprates studied by angle-resolved photoemission spectroscopy
• Glass-induced enhancement of superconducting $T_c$: Pairing via dissipative mediators
• Evolution of Holographic Fermi Arcs from a Mott Insulator
• Towards the Standard Model of Fermi Arcs from a Wilsonian Reduction of the Hubbard Model

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• Phase diagram of the spin-1/2 Yukawa-SYK model: Non-Fermi liquid, insulator, and superconductor
• Electronic properties, correlated topology and Green's function zeros
• Exactly solvable model of Fermi arcs and pseudogap
• Solvable Periodic Anderson Model with Infinite-Range Hatsugai-Kohmoto Interaction: Ground-states and beyond
• Symmetry constraints and spectral crossing in a Mott insulator with Green's function zeros
• Two-stage superconductivity in the Hatsugai-Kohmoto-BCS model
• Anharmonic theory of superconductivity and its applications to emerging quantum materials
• Superconductivity from Luttinger surfaces: Emergent $\infty$-body SYK physics
• Friedel oscillation in non-Fermi liquid: Lesson from exactly solvable Hatsugai-Kohmoto model
• Notes on Quantum oscillation for Hatsugai-Kohmoto model
• Strong pair-density-wave fluctuations in an exactly solvable doped Mott insulator
• Dilute magnetic moments in an exactly solvable interacting host
• Enhanced Superconducting Diode Effect in the Asymmetric Hatsugai-Kohmoto Model