Pairing Instabilities of the Yukawa-SYK Models with Controlled Fermion Incoherence

Submission summary

 As Contributors: Wonjune Choi Preprint link: scipost_202110_00021v2 Date accepted: 2022-04-21 Date submitted: 2022-03-18 19:01 Submitted by: Choi, Wonjune Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Approach: Theoretical

Abstract

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 $T_c$ of the pairing is enhanced in the non-Fermi liquid compared to the case of the Fermi liquid.

Published as SciPost Phys. 12, 151 (2022)

Dear Editor,

Thank you for arranging the review of our article. We are grateful to all referees for carefully reading our paper.
We largely expanded Section 4 about the normal state properties of the Yukawa-SYK models following the suggestion of one of the reviewers, Prof. Yuxuan Wang. Also, we wrote another appendix to explain why the Bose-Einstein condensation can occur in class I systems despite strong quantum fluctuations due to low dimensionality. We further highlighted how our work is distinguished from the previous works; we investigated a one-parameter family of states, whose fermion incoherence can be systematically controlled rather than being fixed.

Sincerely,

Wonjune Choi
Omid Tavakol
Yong Baek Kim

List of changes

1. Major revision on Section 4 with detailed discussions about the normal state properties of the Yukawa-SYK models
2. New appendix about the Bose-Einstein condensation in class I systems.
3. Include more discussions to compare and contrast our work from previous research works on the SYK model and its variants.