Heat conductance of the quantum Hall bulk

The quantum Hall effect is a prototypical realization of a topological state of matter. It emerges from a subtle interplay between topology, interactions and disorder^1–9. 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 density³. Still, the details of the localized states and their contribution to transport remain beyond the reach of most experimental techniques^10–31. Here we describe an extensive study of the bulk’s heat conductance. Using a novel ‘multiterminal’ short device (on a scale of 10 µm), we separate the longitudinal thermal conductance, \({\kappa }_{xx}T\) ${\kappa }_{xx}T$ (owing to the bulk’s contribution), from the topological transverse value \({\kappa }_{xy}T\) ${\kappa }_{xy}T$ by eliminating the contribution of the edge modes²⁴. When the magnetic field is tuned away from the conductance plateau centre, the localized states in the bulk conduct heat efficiently ( \({\kappa }_{xx}T\propto T\) ${\kappa }_{xx}T\propto T$ ), whereas the bulk remains electrically insulating. Fractional states in the first excited Landau level, such as the \(\nu =7/3\) $\nu =7/3$ and \(\nu =5/2\) $\nu =5/2$ , conduct heat throughout the plateau with a finite \({\kappa }_{xx}T\) ${\kappa }_{xx}T$ . We propose a theoretical model that identifies the localized states as the cause of the finite heat conductance, agreeing qualitatively with our experimental findings.