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arXiv:1908.02757 · Physical Review Research

Intrinsic superconducting instabilities of a solvable model for an incoherent metal

Debanjan Chowdhury, Erez Berg

Published Mar 12, 2020• 36 citations
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Abstract

This paper reveals the unconventional nature of pairing instabilities out of a non-Fermi liquid metal at strong coupling in a family of exactly solvable Sachdev-Ye-Kitaev models that goes beyond the conventional BCS framework, but that still shows surprising similarities with the BCS-Eliashber theory theory.
DOI
10.1103/physrevresearch.2.013301

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We construct a family of translationally invariant lattice models with a large number (N) of orbitals at every site coupled together via single-electron tunneling. By tuning the relative strength of the electronic bandwidth and on-site interactions, which have a modified Sachdev-Ye-Kitaev form, we demonstrate a number of unusual features at strong coupling and in the large-N limit. We find examples of (i) an intrinsic non-BCS superconducting instability arising out of an incoherent non-Fermi-liquid metal, and (ii) an instability of an incipient heavy Fermi-liquid metal to superconductivity with transition temperatures comparable to its renormalized bandwidth. At strong coupling, these solvable models display pairing instabilities that are not driven by any special “nesting” properties associated with an underlying Fermi surface.
The interplay of non-Fermi liquid and superconductivity born out of strong dynamical interactions is at the heart of the physics of unconventional superconductivity. As a solvable platform of the strongly correlated superconductors, we study the pairing instabilities of the Yukawa-Sachdev-Ye-Kitaev (Yukawa-SYK) model, which describes spin-1/2 fermions coupled to bosons by the random, all-to-all, spin-independent and dependent Yukawa interactions. In contrast to the previously studied models, the random Yukawa couplings are sampled from a collection of Gaussian ensembles whose variances follow a continuous distribution rather than being fixed to a constant. By tuning the analytic behaviour of the distribution, we could control the fermion incoherence to systematically examine various normal states ranging from the Fermi liquid to non-Fermi liquids that are different from the conformal solution of the SYK model with a constant variance. Using the linearised Eliashberg theory, we show that the onset of the unconventional spin-triplet pairing is preferred with the spin-dependent interactions while all pairing channels show instabilities with the spin-independent interactions. Although the interactions shorten the lifetime of the fermions in the non-Fermi liquid, the same interactions also dress the bosons to strengthen the tendency to pair the incoherent fermions. As a consequence, the onset temperature T_c T c of the pairing is enhanced in the non-Fermi liquid compared to the case of the Fermi liquid.
We provide a quantitative and controlled analysis of the phase diagram of the Yukawa-Sachdev-Ye-Kitaev model on a lattice, in the normal and superconducting states. We analyze the entire crossover from Bardeen-Cooper-Schrieffer (BCS)/weak coupling to Eliashberg/strong coupling superconductivity, as a function of fermion-boson interaction strength and hopping parameter. Cooper pairs of sharp Fermi-liquid quasiparticles at weak coupling evolve into pairing of fully incoherent fermions in the non-Fermi liquid regime. The crossovers leave observable traces in the critical temperature, the zero-temperature and zero-energy gap, the entropy, and the phase stiffness.
A mysterious incoherent metallic (IM) normal state with T-linear resistivity is ubiquitous among strongly correlated superconductors. Recent progress with microscopic models exhibiting IM transport has presented the opportunity for us to study new models that exhibit direct transitions into a superconducting state out of IM states within the framework of connected Sachdev-Ye-Kitaev "quantum dots." Here, local Sachdev-Ye-Kitaev interactions within a dot produce IM transport in the normal state, while local attractive interactions drive superconductivity. Through explicit calculations, we find two features of superconductivity arising from an IM normal state. First, despite the absence of quasiparticles in the normal state, the superconducting state still exhibits coherent superfluid transport. Second, the nonquasiparticle nature of the IM Green's functions produces a large enhancement in the ratio of the zero-temperature superconducting gap Δ and transition temperature T_{SC}, 2Δ/T_{SC}, with respect to its BCS value of 3.53.
Characterizing the interplay between non-Fermi-liquid physics and superconductivity is an important open problem in condensed matter physics. From a theoretical standpoint, the challenge stems from the difficulty in identifying controlled models where these phenomena can be simultaneously treated on equal footing. Here, the authors propose a new model of strongly interacting electrons and phonons, in close analogy with the well-known Sachdev-Ye-Kitaev model, and, via exact solution, explore how superconductivity can emerge from quantum critical and highly incoherent non-Fermi-liquid normal states. Many of the results are in qualitative agreement with observations made in iron-based, heavy-fermion, and cuprate superconductors.
Models for strongly interacting fermions in disordered clusters forming an array, with electron hopping between sites, reproduce the linear dependence on temperature of the resistivity, typical of the strange metal phase of high temperature superconducting materials [extended Sachdev-Ye-Kitaev (SYK) models]. We identify the low energy collective excitations as neutral energy excitations, diffusing in the lattice of the thermalized non-Fermi liquid phase. However, the diffusion is heavily hindered by coupling to the pseudo-Goldstone modes of the conformal broken symmetry SYK phase, which are local in space. The imaginary time evolution of the extended model in the strong interaction and 1/N1/N1/N expansion limit is presented in the incoherent nonchaotic regime. On the other hand, a Fermi electronic liquid at low energy becomes marginal when perturbed by the SYK dots. A critical temperature for superconductivity is derived, which is not BCS-like, in case the collective excitations are assumed to mediate an attractive Cooper pairing.