Vanishing Thermal Equilibration for Hole-Conjugate Fractional Quantum Hall States in Graphene

Abstract

Transport through edge channels is responsible for conduction in quantum Hall (QH) phases. Robust quantized values of charge and thermal conductances dictated by bulk topology appear when equilibration processes become dominant. We report on measurements of electrical and thermal conductances of integer and fractional QH phases, realized in hexagonal boron nitride encapsulated graphite-gated bilayer graphene devices for both electron and hole doped sides with different valley and orbital symmetries. Remarkably, for complex edges at filling factors ν ¼ 53 and 8 3 , closely related to the paradigmatic hole-conjugate ν ¼ 2 3 phase, we find quantized thermal conductance whose values (3κ 0 T and 4κ 0 T, respectively where κ 0 T is the thermal conductance quantum) are markedly inconsistent with the values dictated by topology (1κ 0 T and 2κ 0 T, respectively). The measured thermal conductance values remain insensitive to different symmetries, suggesting its universal nature. Our findings are supported by a theoretical analysis, which indicates that, whereas electrical equilibration at the edge is established over a finite length scale, the thermal equilibration length diverges for strong electrostatic interaction. Our results elucidate the subtle nature of crossover from coherent, mesoscopic to topology-dominated transport.

Observation of ballistic upstream modes at fractional quantum Hall edges of graphene

“…This is entirely consistent with the data of Ref. 18 on thermal conductance in graphene. There, a dramatic difference between the charge and heat equilibration lengths was explained by the vicinity of a system to a strong-interaction fixed point, where the bare modes of the ν = 2/3 edge are renormalized into a charge and a neutral mode.…”

“…Such a model would be consistent not only with measured electrical conductance but also with the thermal conductance measurements reported in Ref. 18 . On a broader scope, several alternative approaches attempting to establish the presence of upstream current of heat at edges of a variety of FQH states in GaAs/AlGaAs structures were employed in Refs.…”

“…For the noise measurement, an LCR resonant circuit with the resonance frequency of ~763 kHz is utilized together with an amplifier chain and a spectrum analyzer (see methods and SI(S4)) 44 – 47 . At zero bias, the equilibrium voltage noise measured at the amplifier contact is given by 18 , 44 where k B is the Boltzmann constant, T is the temperature, R is the resistance of the QH state, G is the gain of the amplifier chain, and B W is the bandwidth. The first term, 4 k B T R , corresponds to the thermal noise, and and are the intrinsic voltage and current noise of the amplifier.…”

“…This decay can be attributed to one of two mechanisms mentioned above: thermal equilibration within the edge (which would imply a crossover from ballistic to diffusive regime of heat flow) or loss of heat to the bulk. Both mechanisms are expected to be enhanced at higher temperature 18 , 49 – 51 , but further work is needed to understand which of them is dominant.…”

“…In this case, Λ becomes x -independent within the edge segment, so that the x -integral is straightforwardly calculated, yielding for the ν = 2/3 edge the noise where the dependence of Λ on the bias voltage V and the interaction between edge modes (parameter Δ) is noted. We take Δ ≈ 1, which corresponds to the strong-interaction fixed point 5 , at which the heat equilibration length is much larger than the charge equilibration length 18 , as observed experimentally. To determine the dependence of Λ on the voltage, we first calculate the effective temperatures of the downstream and upstream modes on the edge.…”