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ac Fingerprints of 2D Electron Hydrodynamics: Superdiffusion and Drude Weight Suppression

Davis Thuillier and Thomas Scaffidi*

  • *Contact author: tscaffid@uci.edu
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Phys. Rev. Lett. 137, 196303 – Published 5 November, 2026

DOI: https://doi.org/10.1103/p8sw-99rn

Abstract

Clean two-dimensional Fermi liquids are now known to exhibit an intermediate tomographic regime, between ballistic and Navier-Stokes transport, caused by the anomalously slow relaxation of parity-odd multipolar deformations of the Fermi surface. Here, we show that this anomaly extends to the dynamical realm. Starting from a microscopic numerical evaluation of the linearized electron-electron collision operator, we find that the finite-frequency nonlocal conductivity is controlled at low frequency by a single hydrodynamic pole, σ(q,ω)=D(q)/(iω+η⋆qz), with dynamical exponent z=4/3 and superdiffusive viscosity η⋆. Remarkably, the pole residue itself is scale dependent and obeys D(q)∼q−α with α=1/3, so the dynamical properties are described by two separate exponents rather than one. We interpret the residue suppression using a Krylov-chain description of current relaxation: As q increases, the longest-lived quasinormal mode ceases to be a nearly pure current excitation and spreads over higher odd angular harmonics. Finally, we show that ac transport in narrow channels provides a direct experimental probe of these phenomena.

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Phys. Rev. Lett. 137, 196303– Published 5 November, 2026
  • Received 26 March 2026
  • Revised 15 June 2026
  • Accepted 21 July 2026
Article part of CHORUS
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