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Suppression of quantized heat flow by the dielectric response of a compressible strip at the quantum Hall edge

Eugene V. Sukhorukov, Adrien Tomà

TL;DR

This work develops a unified perturbative framework for energy transport along a chiral quantum Hall edge coupled to a disordered compressible strip, expressing edge heat-current corrections and plasmon-spectrum shifts entirely through the strip’s retarded susceptibility. It identifies distinct environmental responses—gapped local dielectric, diffusive hydrodynamic, and long-range dipolar back-action—and derives universal relations linking heat-flux suppression to spectral curvature. The framework yields concrete predictions for how the edge heat flux deviates from quantized values (including $T^4$, $T^{3/2}$, and $T^3$ scalings in various regimes) while preserving total heat quantization via reversible drag into the strip. These results offer a coherent explanation for the observed missing heat flux anomaly and provide diagnostic universal ratios to identify the dominant mechanism in experiments, thereby unifying thermal and spectral signatures of quantum Hall edge dynamics.

Abstract

We develop a unified perturbative framework for energy transport along a chiral quantum Hall edge coupled to a disordered, compressible strip. Treating the strip as a generic linear response environment characterized by its retarded susceptibility, we obtain leading corrections to both the heat flux carried by the edge plasmon and to its spectrum. Two generic regimes emerge: (i) a gapped, local dielectric response with finite-range coupling, producing a negative correction to the quantized heat flux that scales as T^4 at low temperatures together with a convex cubic shift of the plasmon dispersion; and (ii) a hydrodynamic (diffusive) response with relaxation, yielding a crossover from T^4 to T^{3/2} scaling and a change of sign in the correction. We further introduce a microscopic dipolar model in which the edge couples electrostatically to localized dipole moments inside a wide compressible strip. This long-range interaction amplifies the nonlocal dielectric back-action and generates new suppression laws, T^3 or even T^2 for smooth disorder profiles, together with a universal ratio connecting spectral curvature to thermal response. Across all regimes, the total heat flux remains quantized: the apparent deficit of the plasmon contribution reflects reversible heat drag into the compressible strip rather than a breakdown of quantization. The framework thus provides a coherent and quantitatively plausible explanation of the "missing heat flux" anomaly and unifies the thermal and spectral signatures of quantum Hall edge dynamics.

Suppression of quantized heat flow by the dielectric response of a compressible strip at the quantum Hall edge

TL;DR

This work develops a unified perturbative framework for energy transport along a chiral quantum Hall edge coupled to a disordered compressible strip, expressing edge heat-current corrections and plasmon-spectrum shifts entirely through the strip’s retarded susceptibility. It identifies distinct environmental responses—gapped local dielectric, diffusive hydrodynamic, and long-range dipolar back-action—and derives universal relations linking heat-flux suppression to spectral curvature. The framework yields concrete predictions for how the edge heat flux deviates from quantized values (including , , and scalings in various regimes) while preserving total heat quantization via reversible drag into the strip. These results offer a coherent explanation for the observed missing heat flux anomaly and provide diagnostic universal ratios to identify the dominant mechanism in experiments, thereby unifying thermal and spectral signatures of quantum Hall edge dynamics.

Abstract

We develop a unified perturbative framework for energy transport along a chiral quantum Hall edge coupled to a disordered, compressible strip. Treating the strip as a generic linear response environment characterized by its retarded susceptibility, we obtain leading corrections to both the heat flux carried by the edge plasmon and to its spectrum. Two generic regimes emerge: (i) a gapped, local dielectric response with finite-range coupling, producing a negative correction to the quantized heat flux that scales as T^4 at low temperatures together with a convex cubic shift of the plasmon dispersion; and (ii) a hydrodynamic (diffusive) response with relaxation, yielding a crossover from T^4 to T^{3/2} scaling and a change of sign in the correction. We further introduce a microscopic dipolar model in which the edge couples electrostatically to localized dipole moments inside a wide compressible strip. This long-range interaction amplifies the nonlocal dielectric back-action and generates new suppression laws, T^3 or even T^2 for smooth disorder profiles, together with a universal ratio connecting spectral curvature to thermal response. Across all regimes, the total heat flux remains quantized: the apparent deficit of the plasmon contribution reflects reversible heat drag into the compressible strip rather than a breakdown of quantization. The framework thus provides a coherent and quantitatively plausible explanation of the "missing heat flux" anomaly and unifies the thermal and spectral signatures of quantum Hall edge dynamics.
Paper Structure (17 sections, 83 equations, 1 figure)

This paper contains 17 sections, 83 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Model of QH edge
  3. Formal expression for the heat flux correction
  4. Plasmon self-energy and spectrum
  5. Diffusive and relaxing medium
  6. Thermodynamic derivation of the hydrodynamic response
  7. Heat flux kernel ${\cal S}(\omega)$ and $\Delta J_{\rm th}(T)$
  8. Plasmon self-energy and spectrum in the diffusive medium
  9. Finite-range coupling to independent local centers
  10. Small–frequency expansion and the sign of $\Delta J_{\rm th}$
  11. Plasmon spectrum: finite range self–energy
  12. Microscopic dipolar model of the dielectric response
  13. Narrow compressible strip: $Wk\ll 1$.
  14. Wide compressible strip: $Wk\gg 1$.
  15. Discussion
  16. ...and 2 more sections

Figures (1)

  • Figure 1: Models of dissipation and disorder at a quantum Hall (QH) edge. (a) Phenomenological description in which the compressible strip (gradient-shaded region) acts as a dissipative medium coupled to the chiral plasmon at the QH edge (solid line). (b) Microscopic picture of the compressible strip as a network of closed loops (“QH puddles”) connected by tunneling (dotted red lines) and capacitively coupled to the QH edge. (c) TLS model of the compressible strip, where two-level systems are randomly coupled to the edge (red dotted lines) or interact with the edge density field via a long-range potential (shaded triangles), resulting in a self-averaged dielectric response.