Quantum mechanics

Electrical resistivity and conductivity

Magnetic field

Hubbard model

Crossover

Fermi liquid theory

Computer science

Physics

Magnetoresistance

Superconductivity

Free electron model

Condensed matter physics

Artificial intelligence

Quantum

Electron

Quasiparticle

Physical Review X

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 particular 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 TlnT specific heat as T→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 describe the magnetotransport properties of this model and show that the MFL regime has conductivities that scale as a function of B/T; however, the magnetoresistance saturates at large B. We then consider a macroscopically disordered sample with domains of such MFLs with varying densities of electrons and islands. 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.Received 30 December 2017Revised 4 March 2018DOI:https://doi.org/10.1103/PhysRevX.8.021049Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Physical SystemsStrongly correlated systemsTechniquesKondo lattice modelNon-Fermi-liquid theoryCondensed Matter, Materials & Applied Physics

Magnetotransport in a Model of a Disordered Strange Metal