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

In the previous chapter, we discussed the thermal conductance measurement of integer ( \(\nu =1, 2, 6\) ) and a particle-like fractional ( \(\nu =4/3\) ) quantum Hall states of the single-layer graphene, where the edge structures harbour only downstream edge modes. The measured values of quantized thermal conductance for these fillings were consistent with the expected theoretical limit of \(G_Q = N_d\kappa _0 T\) , where \(N_d\) is the number of downstream edge modes. However, for a certain class of fractional quantum Hall states, called hole-conjugate states, in addition to the downstream edge modes, the edge structure harbours the upstream edge modes propagating anti-parallel to the downstream edge modes. In the presence of such counter-propagating edge modes, measured electrical and thermal conductances depend on the extent of the ‘equilibration’ between the counter-propagating edge modes. In this chapter, we focus 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 \(\nu =\frac{5}{3}\) and \(\frac{8}{3}\) , closely related to the paradigmatic hole-conjugate \(\nu =\frac{2}{3}\) phase, we find quantized thermal conductance whose values ( \(3\kappa _{0}T\) and \(4\kappa _{0}T\) , respectively where \(\kappa _{0}T\) is the thermal conductance quantum) are markedly inconsistent with the values dictated by topology ( \(1\kappa _{0}T\) and \(2\kappa _{0}T\) , respectively). The measured thermal conductance values remain insensitive to different symmetries, suggesting its universal nature. A theoretical analysis further supports these findings, which indicates that while charge equilibration at the edge is established over a finite length scale, the thermal equilibration length diverges for strong electrostatic interaction. These results elucidate the subtle nature of crossover from coherent, mesoscopic to topology-dominated transport.