Superconductivity of non-Fermi liquids described by Sachdev-Ye-Kitaev models

Abstract

We investigate models of electrons in the Sachdev-Ye-Kitaev class with random and all-to-all electron hopping, electron spin exchange, and Cooper-pair hopping. An attractive on-site interaction between electrons leads to superconductivity at low temperatures. Depending on the relative strengths of the hopping and spin exchange, the normal state at the critical temperature is either a Fermi-liquid or a non-Fermi liquid. We present a large-$M$ (where spin symmetry is enlarged to SU$(M)$) study of the normal state to superconductor phase transition. We describe the transition temperature, the superconducting order parameter, and the electron spectral functions. We contrast between Fermi liquid and non-Fermi liquid normal states: we find that for weaker attractive on-site interaction there is a relative enhancement of $T_c$ when the normal state is a non-Fermi liquid, and correspondingly a strong deviation from BCS limit. Also, the phase transition in this case becomes a first-order transition for strong non-Fermi liquids. On the other hand, for stronger on-site interaction, there is no appreciable difference in $T_c$ between whether the superconductivity emerges from a Fermi liquid or a non-Fermi liquid. Notable features of superconductivity emerging from a non-Fermi liquid are that the superconducting electron spectral function is different from the Fermi-liquid case, with additional peaks at higher energies, and there is no Hebel-Slichter peak in the NMR relaxation rate in the non-Fermi liquid case.

arXiv comment26 pages, 13 figures; (v2) Added new results, figures, and references, modified abstract, and expanded discussion

References in corpus (25)

• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Are non-Fermi-liquids stable to Cooper pairing?
• A strongly correlated metal built from Sachdev-Ye-Kitaev models
• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• Non-Fermi liquid regime of a doped Mott insulator
• Finite Temperature Properties of Quantum Antiferromagnets in a Uniform Magnetic Field in One and Two Dimensions
• Overscreened multi-channel SU(N) Kondo model : large-N solution and Conformal Field Theory
• Possible Multiple Gap Superconductivity with Line Nodes in Heavily Hole-Doped Superconductor KFe2As2 Studied by 75As-NQR and Specific Heat
• Cooper pairing of incoherent electrons: an electron-phonon version of the Sachdev-Ye-Kitaev model
• Large $N$ theory of critical Fermi surfaces
• Solvable Strong-coupling Quantum Dot Model with a Non-Fermi-liquid Pairing Transition
• Strong Coupling Expansion for the Pairing Hamiltonian
• Coherent superconductivity with large gap ratio from incoherent metals
• Finite Size Corrections for the Pairing Hamiltonian
• Superconducting instability in non-Fermi liquids
• Traversable wormhole and Hawking-Page transition in coupled complex SYK models
• Intrinsic superconducting instabilities of a solvable model for an incoherent metal
• Superconducting instabilities in a spinful Sachdev-Ye-Kitaev model
• Spontaneous Breaking of $U(1)$ Symmetry in Coupled Complex SYK Models
• SYK Superconductivity: Quantum Kuramoto and Generalized Richardson Models
• Spin liquid to spin glass crossover in the random quantum Heisenberg magnet
• Hierarchy of energy scales in an O(3) symmetric antiferromagnetic quantum critical metal: a Monte Carlo study
• Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. VI. The $\gamma$ model and its phase diagram at $2<\gamma <3$
• Twists and turns of superconductivity from a repulsive dynamical interaction
• Critical anomalous metals near superconductivity in models with random interactions

Cited by in corpus (1)

• Enhancement of Superconductivity in a Dirty Marginal Fermi Liquid