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.

Teasing out the topological order Quantum Hall states, which form in two-dimensional electron gases at low temperatures and in the presence of strong magnetic fields, have long been known to have nontrivial topological properties. Among the most intriguing is the state that arises at the Landau level filling factor of 5/2. Theoretical calculations suggest several possibilities for the 5/2 ground state and associated topological order but distinguishing among them experimentally is tricky. Dutta et al . developed a method for doing so by interfacing a region in the 5/2 state with a region at an integer filling, and the measurements provided support for the particle-hole Pfaffian order. The technique can be used for the investigation of other exotic states in the quantum Hall setting. —JS

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. This new 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.

Thermal conductance measurements, sensitive to charge and chargeless energy flow, are evolving as an essential measurement technique in Condensed Matter Physics. For twodimensional topological insulators, the measurements of the thermal Hall conductance, 𝜿 𝐱𝐲 𝑻, and the longitudinal one 𝜿 𝐱𝐱 𝑻, are crucial for the understanding of their underlying topological order. Such measurements are thus far lacking, even in the extensively studied quantum Hall effect (QHE) regime. Here, we report a new local power measurement technique that reveals the topological thermal Hall conductance (not the ubiquitous twoterminal one). For example, we find 𝜿 𝐱𝐲 ~𝟎 of the challenging 𝝂 = 𝟐 𝟑 particle-hole conjugated state. This is in contrast to the two-terminal measurement, which provides a non-universal value that depends on the extent of thermal equilibration between the counter-propagating edge modes. Moreover, we use this technique to study the power carried by the current fluctuations in a partitioned edge mode with an out-of-equilibrium distribution.The importance of heat flow in electronic systems is being appreciated in recent years, as a growing number of thermal transport 1, 2 and microscopy 3,4 techniques are being developed. The significance of thermal transport is especially apparent in topologically non-trivial materials. For two-dimensional topological insulators, the bulk of the electron gas is insulating, while gapless excitations flow in 1D-like chiral or helical modes next to the sample's edge 5,6,7 . The nature of the edge modes is a manifestation of the wavefunction in the bulk (due to 'bulk-boundary' correspondence 8 ), making edge transport experiments a compelling route for studying bulk properties 9 . In addition to the quantization of the electrical conductance of the edge modes, the thermal Hall conductance 𝜅 -. 𝑇 (𝑇 the temperature) is also expected to be quantized in units of the thermal conductance quanta 𝜅 0 𝑇 = 1 2 3 4 2 56 𝑇 (𝑘 8 is the Boltzmann constant and ℎ is the Planck's constant) 10 . Sensitive to all types of edge modes, the thermal measurement supplements the