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arXiv:2012.12491 · Physical review. B./Physical review. B

Superconducting instabilities in a spinful Sachdev-Ye-Kitaev model

Étienne Lantagne-Hurtubise, Vedangi Pathak, Sharmistha Sahoo, Marcel Franz

Published Jul 23, 2021• 30 citations
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Abstract

We introduce a spinful variant of the Sachdev-Ye-Kitaev model with an effective time-reversal symmetry, which can be solved exactly in the limit of a large number $N$ of degrees of freedom. At low temperature, its phase diagram includes a compressible non-Fermi liquid and a strongly correlated spin singlet superconductor that shows a tunable enhancement of the gap ratio predicted by BCS theory. These two phases are separated by a first-order transition, in the vicinity of which a gapless superconducting phase, characterized by a nonzero magnetization, is stabilized upon applying a Zeeman field. We study equilibrium transport properties of such superconductors using a lattice construction and propose a physical platform based on topological insulator flakes where they may arise from repulsive electronic interactions.

DOI
10.1103/physrevb.104.l020509

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We introduce a spinful variant of the Sachdev-Ye-Kitaev model with an effective time-reversal symmetry, which can be solved exactly in the limit of a large number NNN of degrees of freedom. At low temperature, its phase diagram includes a compressible non-Fermi liquid and a strongly correlated spin singlet superconductor that shows a tunable enhancement of the gap ratio predicted by BCS theory. These two phases are separated by a first-order transition, in the vicinity of which a gapless superconducting phase, characterized by a nonzero magnetization, is stabilized upon applying a Zeeman field. We study equilibrium transport properties of such superconductors using a lattice construction and propose a physical platform based on topological insulator flakes where they may arise from repulsive electronic interactions.
We introduce a spinful variant of the complex Sachdev-Ye-Kitaev model with time reversal symmetry, which can be solved exactly in the limit of a large number NNN of degrees of freedom. At low temperature, the phase diagram of the model includes a compressible non-Fermi liquid and a strongly-correlated spin singlet superconductor that shows a tunable enhancement of the gap ratio predicted by BCS theory. The two phases are separated by a first-order phase transition, in the vicinity of which a gapless superconducting phase is stabilized. We also discuss time-reversal breaking perturbations that introduce a finite magnetization coexisting with superconductivity.
We analyze the phase diagram of the spin-12\frac{1}{2}21​ Yukawa--Sachdev-Ye-Kitaev model, which describes complex spin-12\frac{1}{2}21​ fermions randomly interacting with real bosons via a Yukawa coupling, at finite temperatures and varying fermion density. A recent work [Wang and Chubukov, Phys. Rev. Res. 2, 033084 (2020).] showed that, upon varying the filling or chemical potential, a first-order quantum phase transition exists between a non-Fermi-liquid (NFL) phase and an insulating phase. Here we show that in such a model with time-reversal symmetry this quantum phase transition is preempted by a pairing phase that develops as a low-temperature instability. As a remnant of the would-be NFL-insulator transition, the superconducting critical temperature rapidly decreases beyond a certain chemical potential. On the other hand, depending on the parameters, the first-order quantum phase transition extends to finite temperatures and terminates at a thermal critical point, beyond which the NFL and the insulator become the same phase, similar to that of the liquid-gas and metal-insulator transition in real materials. We determine the pairing phase boundary and the location of the thermal critical point via combined analytic and quantum Monte Carlo numeric efforts. Our results provide a model realization of the transition of NFLs towards superconductivity and insulating states and therefore offer a controlled platform for future investigations of the generic phase diagram that hosts a NFL, insulator, and superconductor and their phase transitions.
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.
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-MMM [where spin symmetry is enlarged to SU(M)]\mathrm{SU}(M)]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 Tc{T}_{c}Tc​ 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 Tc{T}_{c}Tc​ 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.
A charge-4e4e4e superconductor forms due to the condensation of quartets of electrons. While in previous works, the mechanism for the formation of charge-4e4e4e superconductivity has been analyzed in terms of the binding of Cooper pairs in unconventional superconductors, its properties in the fermionic sector have not been studied systematically due to its inherently interacting nature even at the mean-field level. Here we propose a solvable model for a charge-4e4e4e superconductor---a spinful version of the Sachdev-Ye-Kitaev model with an anomalous quartic term. We show that the ground state is gapless and resembles a heavy Fermi liquid. We analytically solve for the superfluid density and show that it is perturbative in the strength of the charge-4e4e4e order parameter, in sharp contrast with a regular (charge-2e2e2e) superconductor. Upon lowering the temperature, we show that the correlation between charge-4e4e4e order and regular interaction terms can drive a first-order phase transition to a charge-2e2e2e superconducting state.
In this Rapid Communication, we construct a large-NNN exactly solvable model to study the interplay between interaction and topology, by connecting the Sachdev-Ye-Kitaev (SYK) model with constant hopping. The hopping forms a band structure that can exhibit both topologically trivial and nontrivial phases. Starting from a topologically trivial insulator with zero Hall conductance, we show that the interaction can drive a phase transition to a topologically nontrivial insulator with quantized nonzero Hall conductance, and a single gapless Dirac fermion emerges when the interaction is fine tuned to the critical point. The finite temperature effect is also considered, and we show that the topological phase with a stronger interaction is less stable against temperature. Our model provides a concrete example to illustrate the interacting topological phases and phase transitions, and can shed light on similar problems in physical systems.