Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale

Abstract

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.

Does delta-$T$ noise probe quantum statistics?

“…Such delta-T noise was recently measured in Ref. [55]. We note also that C (1) vanishes at ∆ T = 1/2 in accordance with Ref.…”

“…In contrast to the voltage-induced noise, the delta-T noise does not require a net flow of a non-equilibrium charge current. Since initial theoretical [42][43][44][45][46][47][48][49] and experimental [41,[50][51][52][53][54][55] work, it has been shown that non-equilibrium noise in the absence of currents is, in fact, a more general phenomenon than delta-T noise [56]. Still, what properties of nanoscale conductors-and, in particular, facets of their strongly-correlated nature-this class of zerocurrent non-equilibrium noise might reveal, remains an open and interesting question.…”

Determination of topological edge quantum numbers of fractional quantum Hall phases

“…( 3) requires that L also satisfies L L T , where L T ∼ T −1 is the thermal length. In the intermediate regime L T L H eq , a correction to this value emerges due to backscattering of heat at interfaces with contacts 8,20,25 . For the sake of simplicity, we discard this correction in our analysis in the present work.…”

“…1(b,c) for ν = 2/3. While the fullyequilibrated and non-equilibrated limiting cases of G Q have been reported in disparate GaAs/AlGaAs based 2DEG devices 15,16,20 , and in graphene only the non-equilibrated values have been observed 18 , a crossover of G Q from the non-equilibrated to the fully equilibrated limit in a single device has remained unattainable. This has remained one of the long-standing challenges on the path to reveal the detailed edge structure of FQH states.…”

“…This is fulfilled under an additional condition L L T where L T ∼ T −1 is the thermal length. In the intermediate regime L T L H eq , a correction to this value is expected to emerge 8,20,25 . Thus, the non-equilibrated regime may, in fact, be expected to be split into two plateaus, which is, however, not observed in our experiment.…”