Heat Conductance of the Quantum Hall Bulk

The Quantum Hall Effect (QHE) is a prototypical realization of a topological state of matter. It emerges from a subtle interplay between topology, interactions, and disorder. The disorder enables the formation of localized states in the bulk that stabilize the quantum Hall states with respect to the magnetic field and carrier density. Still, the details of the localized states and their contribution to transport remain beyond the reach of most experimental techniques. Here, we describe an extensive study of the bulk's heat conductance. Using a novel 'multi-terminal' short device (on a scale of $10 \mu m$), we separate the longitudinal thermal conductance, $\kappa_{xx}T$ (due to bulk's contribution), from the topological transverse value $\kappa_{xy}T$, by eliminating the contribution of the edge modes. When the magnetic field is tuned away from the conductance plateau center, the localized states in the bulk conduct heat efficiently ($\kappa_{xx}T \propto T$), while the bulk remains electrically insulating. Fractional states in the first excited Landau level, such as the $\nu=7/3$ and $\nu=5/2$, conduct heat throughout the plateau with a finite $\kappa_{xx} T$. We propose a theoretical model that identifies the localized states as the cause of the finite heat conductance, agreeing qualitatively with our experimental findings.