Magnetotransport in a model of a disordered strange metal

Abstract

Despite much theoretical effort, there is no complete theory of the 'strange' metal state of the high temperature superconductors, and its linear-in-temperature, $T$, resistivity. Recent experiments showing an unexpected linear-in-field, $B$, magnetoresistivity have deepened the puzzle. We propose a simple model of itinerant electrons, interacting via random couplings with electrons localized on a lattice of quantum 'dots' or 'islands'. This model is solvable in a large-$N$ limit, and can reproduce observed behavior. The key feature of our model is that the electrons in each quantum dot are described by a Sachdev-Ye-Kitaev model describing electrons without quasiparticle excitations. For a particular choice of the interaction between the itinerant and localized electrons, this model realizes a controlled description of a diffusive marginal-Fermi liquid (MFL) without momentum conservation, which has a linear-in-$T$ resistivity and a $T\ln T$ specific heat as $T\to 0$. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite-$T$ crossover to a fully incoherent regime that also has a linear-in-$T$ resistivity. We show that the MFL regime has conductivities which scale as a function of $B/T$; however, its magnetoresistance saturates at large $B$. We then consider a macroscopically disordered sample with domains of MFLs with varying densities of electrons. Using an effective-medium approximation, we obtain a macroscopic electrical resistance that scales linearly in the magnetic field $B$ applied perpendicular to the plane of the sample, at large $B$. The resistance also scales linearly in $T$ at small $B$, and as $Tf(B/T)$ at intermediate $B$. We consider implications for recent experiments reporting linear transverse magnetoresistance in the strange metal phases of the pnictides and cuprates.

21 pages + Appendices + References, 4 figures

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• Quantum Criticality
• Quantum quench of the Sachdev-Ye-Kitaev Model
• Visualizing the emergence of the pseudogap state and the evolution to superconductivity in a lightly hole-doped Mott insulator
• Eigenstate thermalization in the Sachdev-Ye-Kitaev model
• Dispersive SYK model: band structure and quantum chaos
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Cited by in corpus (80)

• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• An introduction to the SYK model
• Theory of a Planckian metal
• Universal theory of strange metals from spatially random interactions
• Translationally invariant non-Fermi liquid metals with critical Fermi-surfaces: Solvable models
• Large $N$ theory of critical Fermi surfaces
• Large $N$ theory of critical Fermi surfaces II: conductivity
• Transport and chaos in lattice Sachdev-Ye-Kitaev models
• Coexistence of orbital and quantum critical magnetoresistance in FeSe${}_{1-x}$S${}_x$
• A critical strange metal from fluctuating gauge fields in a solvable random model
• Coherent superconductivity with large gap ratio from incoherent metals
• Thermoelectric power of Sachdev-Ye-Kitaev islands: Probing Bekenstein-Hawking entropy in quantum matter experiments
• $T$-linear resistivity in models with local self-energy
• Traversable wormhole and Hawking-Page transition in coupled complex SYK models
• Bad metallic transport in a modified Hubbard model
• Quench, thermalization and residual entropy across a non-Fermi liquid to Fermi liquid transition
• Intrinsic superconducting instabilities of a solvable model for an incoherent metal
• Dirac Fast Scramblers
• Superconducting instabilities in a spinful Sachdev-Ye-Kitaev model
• Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models
• Family of Sachdev-Ye-Kitaev models motivated by experimental considerations
• SYK Superconductivity: Quantum Kuramoto and Generalized Richardson Models
• Renyi entanglement entropy of Fermi liquids and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories
• A candidate Theory for the "Strange Metal" phase at Finite Energy Window
• Magneto-thermal transport implies an incoherent Hall conductivity
• Theory of shot noise in strange metals
• Excitation spectra of quantum matter without quasiparticles II: random $t$-$J$ models
• Strongly coupled quantum phonon fluid in a solvable model
• Strange Metals from Melting Correlated Insulators in Twisted Bilayer Graphene
• A toy model for anomalous transport and Griffiths effects near the Many-Body Localization transition
• Anisotropy in the Magnetoresistance Scaling of BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$
• Single-parameter scaling in the magnetoresistance of optimally doped La${}_{2-x}$Sr${}_x$CuO${}_4$
• Variational wavefunctions for Sachdev-Ye-Kitaev models
• Solvable models of two-level systems coupled to itinerant electrons: Robust non-Fermi liquid and quantum critical pairing
• $Z_2$ fractionalized phases of a solvable, disordered, $t$-$J$ model
• Superconducting critical temperature in the extended diffusive SYK model
• $B^2$ to $B$-linear magnetoresistance due to impeded orbital motion
• Linear-in-$T$ resistivity from semiholographic non-Fermi liquid models
• On the temperature scaling behaviour of the linear magnetoresistance observed in high-temperature superconductors
• Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite $N$
• Superconductor--Insulator Transition in a non-Fermi Liquid
• Strongly coupled phonon fluid and Goldstone modes in an anharmonic quantum solid: transport and chaos
• Bosonization of Fermi liquids in a weak magnetic field
• Schwarzian correction to quantum correlation in SYK model
• One SYK SET
• Violation of the viscosity/entropy bound in translationally invariant non-Fermi liquids
• Many-body energy invariant for $T$-linear resistivity
• Lattice models for Non-Fermi Liquids with Tunable Transport Scalings
• Strange metal from incoherent bosons
• Solvable Theory of a Strange Metal at the Breakdown of a Heavy Fermi Liquid
• Bad metallic transport in geometrically frustrated models
• Collective density fluctuations of strange metals with critical Fermi surfaces
• Fluctuation Spectrum of Critical Fermi Surfaces
• Isolated zeros in the spectral function as signature of a quantum continuum
• Excitation Transmission through a non-Hermitian traversable wormhole
• Incoherent transport in a model for the strange metal phase: Memory-matrix formalism
• Non-Fermi liquid behavior in the Sachdev-Ye-Kitaev model for a one dimensional incoherent semimetal
• Linear magnetoresistance with a universal energy scale in a strong-coupling superconductor
• Marginal Fermi liquid at magnetic quantum criticality from dimensional confinement
• Defect conformal field theory from Sachdev-Ye-Kitaev interactions
• The Future of the Correlated Electron Problem
• SYK does not Transit Gloria Mundi just yet
• Symmetry breaking in zero-field two-dimensional electron bilayers
• Superconducting gap ratio from strange metal phase in the absence of quasiparticles
• Wormhole-induced effective coupling in SYK chains
• Fractionalized Fermi liquids and the cuprate phase diagram
• Strong non-linear response of strange metals
• Longitudinal Magnetoresistance in YBa${}_2$Cu${}_3$O${}_7$ at High Magnetic Fields of up to 100 T
• Dynamic charge order from strong correlations in the cuprates
• Superlinear Hall angle and carrier mobility from non-Boltzmann magnetotransport in the spatially disordered Yukawa-Sachdev-Ye-Kitaev model on a square lattice
• Non-Landau Quantum Phase Transitions and nearly-Marginal non-Fermi Liquid
• Strange Metal to Insulator Transitions in the Lowest Landau Level
• Theory of Linear Magnetoresistance in a Strange Metal
• Lyapunov exponents in a Sachdev-Ye-Kitaev-type model with population imbalance in the conformal limit and beyond
• Power-Law Spectra and Asymptotic $\omega /T$ Scaling in the Orbital-Selective Mott Phase of a Three-Orbital Hubbard Model
• Near-Equilibrium Approach to Transport in Complex Sachdev-Ye-Kitaev Models
• Stranger than Metals
• Landau Quasiparticles in Weak Power-Law Liquids
• Upper bound on $T_c$ in a strongly coupled electron-boson superconductor
• Phonon Induced Energy Relaxation in Quantum Critical Metals