Abstract

Strange-metal phases, found in, e.g., heavy fermions, pnictides, and cuprates, defy
conventional theoretical descriptions based on Fermi-liquid (FL) theory [1,2]. Some
anomalous properties of such phases include: linear-in-temperature (T-linear) DC
resistivity [3-6], universal w/T scalings of the optical conductivity as a function of
frequency w [7], B/T scalings of the magnetoresistivity as a function of applied
magnetic field B [4,5,8], T2 behaviour of the Hall angle cotangent [9,10], and
interaction-dependent renormalizations of the cyclotron frequency [11]. In addition,
strange metals host partially coherent superconducting states, born out of incoherent,
non-Fermi liquid (NFL) normal-state spectra [12-14].

Constructing minimal exactly solvable models for NFL states might shed new light on
the electrodynamics and superconducting instabilities of strange metals. In this context,
the Sachdev-Ye-Kitaev (SYK) approach [1,15,16], based on all-to-all interactions
among N fermion species ("flavors") in 0-dimensional dots, is a promising route. A
superconducting instability emerges by coupling fermions to M bosonic flavors (the
Yukawa-SYK model), at once responsible for Cooper pairing and for normal-state
incoherence [17,18]. 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
[19,20]. 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 [21].

We then generalize the theory to 2D dispersive fermions and bosons, coupled through
random interactions which are contact-like in real space. This model realizes a marginal
Fermi liquid (MFL) in the normal state [22-24], with T-linear DC resistivity down to
zero temperature, when the system is tuned to criticality by softening of the bosons.
Moreover, the optical scattering rate and effective mass of fermionic carriers, extracted
from the normal-state optical conductivity, display w/T scaling [25], in striking analogy
with recent optical experiments on the La2–xSrxCuO4 cuprate [7].
The phase diagram also includes a low-temperature superconducting phase, where swave pairing is mediated by the spatially random fermion-boson interactions [25]. We
find that this superconductor has finite phase stiffness [25], which in the low-T limit
increases with increasing detuning from the quantum critical point, thus anticorrelating
with Tc [19,25].
We apply this model to DC and AC strange-metal magnetotransport. Focusing on the
effects of orbital magnetism, we find that the cyclotron resonance frequency in the AC
conductivity shifts linearly with applied magnetic field and is renormalized by
disordered interactions [26], analogously to recent magnetoconductivity experiments on
cuprates [11]. Further work in preparation investigates the DC longitudinal and Hall
resistivities, which we analyze as a function of T and B.

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