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Strange Metals and Planckian Transport in a Gapless Phase from Spatially Random Interactions

Aavishkar A. Patel1,*, Peter Lunts2,3,†, and Michael S. Albergo4,5,6,‡

  • *Contact author: apatel@flatironinstitute.org
  • †Contact author: plunts@fas.harvard.edu
  • ‡Contact author: malbergo@fas.harvard.edu
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Phys. Rev. X 15, 031064 – Published 8 September, 2025

DOI: https://doi.org/10.1103/611k-yxb9

Abstract

“Strange” metals that do not follow the predictions of Fermi liquid theory are prevalent in materials that feature superconductivity arising from electron interactions. In recent years, it has been hypothesized that spatial randomness in electron interactions must play a crucial role in strange metals for their hallmark linear-in-temperature (T) resistivity to survive down to low temperatures where phonon and umklapp processes are ineffective, as is observed in experiments. However, a clear picture of how this happens has not yet been provided in a realistic model free from artificial constructions, such as large-N limits and replica tricks. We study a realistic model of two-dimensional metals with spatially random antiferromagnetic interactions in a nonperturbative regime, using numerically exact high-performance, large-scale hybrid Monte Carlo simulation and exact averages over the quenched spatial randomness. Our simulations reproduce strange metals’ key experimental signature of linear-in-T resistivity with a universal “Planckian” transport scattering rate Γtr∼kBT/ℏ that is independent of coupling constants. We further find that strange metallicity in these systems is not associated with a quantum critical point and, instead, arises from a phase of matter with gapless antiferromagnetic fluctuations that lacks long-range correlations and spans an extended region of parameter space: A feature that is also observed in several experiments. These gapless antiferromagnetic fluctuations take the form of spatially localized overdamped modes, whose presence could possibly be detected using recently developed nanoscale magnetometry methods. Our work paves the way for an eventual microscopic understanding of the role of spatial disorder in determining important properties of correlated-electron materials.

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Popular Summary

Strange metals are mysterious states that appear in high-temperature superconductors above their superconducting transition temperature. They are unusual because their electrical resistance grows linearly with temperature, and the electron scattering rate is set by a universal ratio of temperature to fundamental constants. Even more striking, these properties are robust against changes in chemical composition and persist over large regions of the material’s phase diagram. In this work, we introduce a simple but realistic model that explains these puzzling features and provides a framework for understanding strange metals.

Our model describes a 2D system of electrons interacting with each other through magnetic fluctuations, a hallmark of high-temperature superconductors. To capture the effects of chemical disorder, we allow these interactions to be spatially heterogeneous. We then solve the model exactly using high-performance quantum Monte Carlo simulations, which can account for nonperturbative interaction effects that analytical methods miss. The simulations reveal that the interactions generate spatially localized magnetic modes, and it is the scattering of electrons off these modes that gives rise to the strange metal behavior. This mechanism naturally explains the linear temperature dependence of resistance and the universality of the scattering rate.

Our results suggest that these localized magnetic modes could be directly detected using advances in nanoscale magnetometry, opening the possibility of experimental validation. More broadly, the model provides a foundation for future computational and theoretical studies on how strange metals evolve into superconducting states, bringing us closer to solving the long-standing mystery of high-temperature superconductivity.

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Phys. Rev. X 15, 031064– Published 8 September, 2025
  • Received 8 November 2024
  • Revised 27 April 2025
  • Accepted 19 August 2025
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