Fermi-liquid to non-Fermi liquid crossovers, superconductivity, and magnetotransport in Yukawa-Sachdev-Ye-Kitaev models for strange metals

Strange-metal phases, found in, e.g., heavy fermions, pnictides, and cuprates, host partially coherent superconducting states, born out of incoherent, non-Fermi liquid (NFL) normal-state spectra [1-4]. The Sachdev-Ye-Kitaev (SYK) approach [5-7], based on all-to-all interactions among N fermion species ("flavors") in 0-dimensional dots, is a promising route for building toy models of NFL physics. A superconducting instability emerges by coupling fermions to M bosonic flavors (the Yukawa-SYK model), responsible for Cooper pairing and for normal-state incoherence [8,9].
In this work, we generalize the Yukawa-SYK model to a lattice with random hopping parameters. We exactly solve the model in the spin-singlet large-N limit, at N=M and at particle-hole symmetry, we construct the phase diagram, and we characterize the FL to NFL crossovers in the normal and superconducting states [10,11].
Hopping exponentially decreases the critical temperature in FL regime, which is maximal in the single-dot NFL limit at given coupling. However, the phase stiffness and the condensation energy are maximal precisely at the NFL/FL crossover. Such correlation is reminiscent of an analogous experimental evidence found in superconducting cuprates [12].
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We then generalize the theory to 2D dispersive fermions and bosons, which realizes a marginal Fermi liquid (MFL) in the normal state [13-15]. We apply this model to DC and AC strange-metal magnetotransport [16]. The cyclotron resonance frequency in the conductivity shifts linearly with applied magnetic field and is renormalized by disordered interactions [17]. The latter also affect the DC longitudinal and Hall resistivities, which we analyze as a function of temperature and field.
References
1. N. D. Mathur et al., Nature 394, 39 (1998)
2. N. Doiron-Leyraud et al., Phys. Rev. B 80, 214531 (2009)