Localization of overdamped bosonic modes and transport in strange metals.

The strange metal phase of correlated electrons materials was described in a recent theory by a model of a Fermi surface coupled a two-dimensional quantum critical bosonic field with a spatially random Yukawa coupling. With the assumption of self-averaging randomness, similar to that in the Sachdev-Ye-Kitaev model, numerous observed properties of a strange metal were obtained for a wide range of intermediate temperatures, including the linear in temperature resistivity. The Harris criterion implies that spatial fluctuations in the local position of the critical point must dominate at lower temperatures. For an [Formula: see text]-component boson with [Formula: see text], we use multiple graphics processing units (GPUs) to compute the real frequency spectrum of the boson propagator in a self-consistent mean-field treatment of the boson self-interactions, but an exact treatment of multiple realizations of the spatial randomness from the random boson mass. We find that Landau damping from the fermions leads to the emergence of the physics of the random transverse-field Ising model at low temperatures, as has been proposed by Hoyos, Kotabage, and Vojta. This regime is controlled by localized overdamped eigenmodes of the bosonic scalar field, also has a resistivity which is nearly linear-in-temperature, and extends into a "quantum critical phase" away from the quantum critical point, as observed in several cuprates. For the [Formula: see text] Ising scalar, the mean-field treatment is not applicable, and so we use Hybrid Monte Carlo simulations running on multiple GPUs; we find a rounded transition and localization physics, with strange metal behavior in an extended region around the transition.

Pair Density Wave Order from Electron Repulsion.

A pair density wave (PDW) is a superconductor whose order parameter is a periodic function of space, without an accompanying spatially uniform component. Since PDWs are not the outcome of a weak-coupling instability of a Fermi liquid, a generic pairing mechanism for PDW order has remained elusive. We describe and solve models having robust PDW phases. To access the intermediate coupling limit, we invoke large-N limits of Fermi liquids with repulsive BCS interactions that admit saddle point solutions. We show that the requirements for long-range PDW order are that the repulsive BCS couplings must be nonmonotonic in space and that their strength must exceed a threshold value. We obtain a phase diagram with both finite temperature transitions to PDW order and a T=0 quantum critical point, where non-Fermi liquid behavior occurs.

Maximal Quantum Chaos of the Critical Fermi Surface.

We investigate the many-body quantum chaos of non-Fermi liquid states with Fermi surfaces in two spatial dimensions by computing their out-of-time-order correlation functions. Using a recently proposed large N theory for the critical Fermi surface, and the ladder identity of Gu and Kitaev, we show that the chaos Lyapunov exponent takes the maximal value of 2πk_{B}T/ℏ, where T is the absolute temperature. We also examine a phenomenological model that can be continuously tuned between a non-Fermi liquid without quasiparticles and a Fermi liquid with quasiparticles. We find that the Lyapunov exponent becomes smaller than the maximal value precisely when quasiparticles are restored.

Strange Metals from Melting Correlated Insulators in Twisted Bilayer Graphene.

Even as the understanding of the mechanism behind correlated insulating states in magic-angle twisted bilayer graphene converges toward various kinds of spontaneous symmetry breaking, the metallic "normal state" above the insulating transition temperature remains mysterious, with its excessively high entropy and linear-in-temperature resistivity. In this Letter, we focus on the effects of fluctuations of the order parameters describing correlated insulating states at integer fillings of the low-energy flat bands on charge transport. Motivated by the observation of heterogeneity in the order-parameter landscape at zero magnetic field in certain samples, we conjecture the existence of frustrating extended-range interactions in an effective Ising model of the order parameters on a triangular lattice. The competition between short-distance ferromagnetic interactions and frustrating extended-range antiferromagnetic interactions leads to an emergent length scale that forms stripy mesoscale domains above the ordering transition. The gapless fluctuations of these heterogeneous configurations are found to be responsible for the linear-in-temperature resistivity as well as the enhanced low-temperature entropy. Our insights link experimentally observed linear-in-temperature resistivity and enhanced entropy to the strength of frustration or, equivalently, to the emergence of mesoscopic length scales characterizing order-parameter domains.

Quantum chaos on a critical Fermi surface.

We compute parameters characterizing many-body quantum chaos for a critical Fermi surface without quasiparticle excitations. We examine a theory of [Formula: see text] species of fermions at nonzero density coupled to a [Formula: see text] gauge field in two spatial dimensions and determine the Lyapunov rate and the butterfly velocity in an extended random-phase approximation. The thermal diffusivity is found to be universally related to these chaos parameters; i.e., the relationship is independent of [Formula: see text], the gauge-coupling constant, the Fermi velocity, the Fermi surface curvature, and high-energy details.

Theory of a Planckian Metal.

We present a lattice model of fermions with N flavors and random interactions that describes a Planckian metal at low temperatures T→0 in the solvable limit of large N. We begin with quasiparticles around a Fermi surface with effective mass m^{*} and then include random interactions that lead to fermion spectral functions with frequency scaling with k_{B}T/ℏ. The resistivity ρ obeys the Drude formula ρ=m^{*}/(ne^{2}τ_{tr}), where n is the density of fermions, and the transport scattering rate is 1/τ_{tr}=fk_{B}T/ℏ; we find f of order unity and essentially independent of the strength and form of the interactions. The random interactions are a generalization of the Sachdev-Ye-Kitaev models; it is assumed that processes nonresonant in the bare quasiparticle energies only renormalize m^{*}, while resonant processes are shown to produce the Planckian behavior.

Coherent Superconductivity with a Large Gap Ratio from Incoherent Metals.

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.

Universal theory of strange metals from spatially random interactions.

Strange metals-ubiquitous in correlated quantum materials-transport electrical charge at low temperatures but not by the individual electronic quasiparticle excitations, which carry charge in ordinary metals. In this work, we consider two-dimensional metals of fermions coupled to quantum critical scalars, the latter representing order parameters or fractionalized particles. We show that at low temperatures (T), such metals generically exhibit strange metal behavior with a T-linear resistivity arising from spatially random fluctuations in the fermion-scalar Yukawa couplings about a nonzero spatial average. We also find a T ln(1/T) specific heat and a rationale for the Planckian bound on the transport scattering time. These results are in agreement with observations and are obtained in the large N expansion of an ensemble of critical metals with N fermion flavors.