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 disorder1-9. 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 techniques10-31. 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, [Formula: see text] (owing to the bulk's contribution), from the topological transverse value [Formula: see text] 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 ([Formula: see text]), whereas the bulk remains electrically insulating. Fractional states in the first excited Landau level, such as the [Formula: see text] and [Formula: see text], conduct heat throughout the plateau with a finite [Formula: see text]. We propose a theoretical model that identifies the localized states as the cause of the finite heat conductance, agreeing qualitatively with our experimental findings.

Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale.

Two-dimensional topological insulators, and in particular quantum Hall states, are characterized by an insulating bulk and a conducting edge. Fractional states may host both downstream (dictated by the magnetic field) and upstream propagating edge modes, which leads to complex transport behavior. Here, we combine two measurement techniques, local noise thermometry and thermal conductance, to study thermal properties of states with counter-propagating edge modes. We find that, while charge equilibration between counter-propagating edge modes is very fast, the equilibration of heat is extremely inefficient, leading to an almost ballistic heat transport over macroscopic distances. Moreover, we observe an emergent quantization of the heat conductance associated with a strong interaction fixed point of the edge modes. Such understanding of the thermal equilibration on edges with counter-propagating modes is a natural route towards extracting the topological order of the exotic 5/2 state.