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arXiv:1809.01846 · Communications in Theoretical Physics

Superconducting gap ratio from strange metal phase in the absence of quasiparticles

Wenhe Cai, Xian-Hui Ge

Published Jan 15, 2021• 4 citations
arXivHTMLPDF

Abstract

Abstract A lattice model for strongly interacting electrons motivated by a rank-3 tensor model provides a tool for understanding the pairing mechanism of high-temperature superconductivity. This Sachdev–Ye–Kitaev-like model describes the strange metal phase in the cuprate high temperature superconductors. Our calculation indicates that the superconducting gap ratio in this model is higher than the ratio in the BCS theory due to the coupling term and the spin operator. Under certain conditions, the ratio also agrees with the BCS theory. Our results relate to the case of strong coupling, so it may pave the way to gaining insight into the cuprate high temperature superconductors.

DOI
10.1088/1572-9494/abd0e9

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•Jan 14, 2021•0 citations
Abstract A lattice model for strongly interacting electrons motivated by a rank-3 tensor model provides a tool for understanding the pairing mechanism of high-temperature superconductivity. This Sachdev–Ye–Kitaev-like model describes the strange metal phase in the cuprate high temperature superconductors. Our calculation indicates that the superconducting gap ratio in this model is higher than the ratio in the BCS theory due to the coupling term and the spin operator. Under certain conditions, the ratio also agrees with the BCS theory. Our results relate to the case of strong coupling, so it may pave the way to gaining insight into the cuprate high temperature superconductors.
We propose a lattice model for strongly interacting electrons with the potential to explain the main phenomenology of the strange metal phase in the cuprate high-temperature superconductors. Our model is motivated by the recently developed ``tetrahedron'' rank-3 tensor model that mimics much of the physics of the better-known Sachdev-Ye-Kitaev (SYK) model. Our electron model has the following advantageous properties: (1) it needs only one orbital per site on the square lattice. (2) It does not require any quenched random interaction. (3) It has local interactions and respects all the symmetries of the system. (4) The soluble limit of this model has a longitudinal dc resistivity that scales linearly with temperature within a finite temperature window. (5) Again, the soluble limit of this model has a fermion pairing instability in the infrared, which can lead to either superconductivity or a ``pseudogap'' phase. The linear-TTT longitudinal resistivity and the pairing instability originate from the generic scaling feature of the SYK model and the tetrahedron tensor model.
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.
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.
Correlated Electrons In many materials, charge carriers are well described as noninteracting quasiparticles. However, in materials with strong correlations, this approximation can break down, leading to anomalous transport properties at high temperatures. Huang et al. used quantum Monte Carlo calculations to look for this so-called strange metal phase in the simplest two-dimensional model of interacting electrons, the Hubbard model. They found that the calculated resistivity had a linear temperature dependence when hole doping was introduced, as expected in the strange metal phase. This observation provides confidence that simplified models can be used to describe and understand the behavior of real materials, such as cuprate high-temperature superconductors. Science , this issue p. [987][1] [1]: /lookup/doi/10.1126/science.aau7063
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.
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). Our hydrodynamical approach to the marginal Fermi liquid emerging out of the interaction, identifies the low energy collective excitations of the system in its coherent phase. These neutral excitations diffuse in the lattice, but the diffusion is heavily hindered by coupling to the pseudo Goldstone modes of the conformal broken symmetry SYK phase, which are local in space. A critical temperature for superconductivity arises in the electron liquid,in case these excitations are assumed to mediate an attractive Cooper-pairing, in the electron liquid, which is not BCS-like.