Breakdown of hydrodynamics in a Galilean quantum Hall crystal

2024/12/17 by Xiaoyang Huang, Andrew Lucas, Huang, Xiaoyang +1 · 2 citations
Engineering · #Characterization and Applications of Magnetic Nanoparticles #Electrohydrodynamics and Fluid Dynamics

paper · pdf · doi:10.48550/arxiv.2412.12535

Abstract

We construct a nonlinear fluctuating hydrodynamic effective field theory for Galilean-invariant quantum Hall systems with spontaneously broken translational symmetry. Neglecting the role of energy conservation in a low-temperature regime, the hydrodynamic mode is a magnetophonon with quartic attenuation: ω∼ ± k²-i k^z with z=4. However, this linear response theory is unstable, and flows to a non-trivial dynamical universality class with z≈ 3. We observe this scaling in numerical simulations of many-body classical Hamiltonian dynamics, in a model of an electronic crystal in the lowest Landau level. Observing this magnetophonon decay rate in a quantum Hall crystal represents a promising setting to detect an analogue of a "fractonic dynamical universality class" in a solid-state system, e.g. using microwave impedance microscopy.

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