## 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 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 *T* ln *T* 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 amore »

- Authors:

- Harvard Univ., Cambridge, MA (United States); Univ. of California, Santa Barbara, CA (United States)
- Univ. of California at San Diego, La Jolla, CA (United States)
- Harvard Univ., Cambridge, MA (United States); Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Stanford Univ., Stanford, CA (United States)

- Publication Date:

- Research Org.:
- Univ. of California at San Diego, La Jolla, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1438292

- Alternate Identifier(s):
- OSTI ID: 1499002

- Grant/Contract Number:
- SC0009919

- Resource Type:
- Published Article

- Journal Name:
- Physical Review. X

- Additional Journal Information:
- Journal Volume: 8; Journal Issue: 2; Journal ID: ISSN 2160-3308

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Patel, Aavishkar A., McGreevy, John, Arovas, Daniel P., and Sachdev, Subir. Magnetotransport in a Model of a Disordered Strange Metal. United States: N. p., 2018.
Web. doi:10.1103/physrevx.8.021049.
```

```
Patel, Aavishkar A., McGreevy, John, Arovas, Daniel P., & Sachdev, Subir. Magnetotransport in a Model of a Disordered Strange Metal. United States. doi:10.1103/physrevx.8.021049.
```

```
Patel, Aavishkar A., McGreevy, John, Arovas, Daniel P., and Sachdev, Subir. Tue .
"Magnetotransport in a Model of a Disordered Strange Metal". United States. doi:10.1103/physrevx.8.021049.
```

```
@article{osti_1438292,
```

title = {Magnetotransport in a Model of a Disordered Strange Metal},

author = {Patel, Aavishkar A. and McGreevy, John and Arovas, Daniel P. and Sachdev, Subir},

abstractNote = {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 T ln T 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. Here, 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.},

doi = {10.1103/physrevx.8.021049},

journal = {Physical Review. X},

number = 2,

volume = 8,

place = {United States},

year = {2018},

month = {5}

}

DOI: 10.1103/physrevx.8.021049

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