Quantized heat flow probing thermal equilibration and edge structures of quantum Hall phases in graphene

The quantization of the electrical Hall conductance in quantum Hall (QH) states was established long back. Although electrical Hall conductance has been widely used to understand the topological order of a QH state, it turns out to be insufficient in the hierarchical fractional quantum Hall (FQH) states, where the edge structure is complicated, and transport may occur via both the downstream (dictated by the external magnetic field) and upstream modes. The electrical Hall conductance only reveals about the downstream charged chiral edge modes and remains insensitive to the total number of the edge modes, their chirality, and character. By contrast, the quantized thermal Hall conductance is not only sensitive to the downstream charged modes, but it can also detect the other upstream modes, including the charge-less neutral modes and the celebrated Majorana modes. Here, we utilize the sensitive Jhonson-Nyquist noise thermometry to measure the quantized thermal conductance to probe the topological edge structure of the various QH states in single-layer and bilayer graphene. We establish the universality of thermal conductance in graphene by measuring its quantized values for integer and “particle-like” FQH states. Further, we show that the thermal conductance for “hole-like” FQH states having counter-propagating downstream (N_d) and upstream (N_u) modes depends on the extent of equilibration between the modes. By tuning the equilibration, we could achieve the crossover between the two asymptotic limits of the quantized values; (N_d + N_u)k_oT and (N_d - N_u)k_oT for ‘NO’ and ‘FULL’ equilibration, respectively. These experimental findings pave the way to resolve the dichotomy between different models of edge structure or, in general, to determine the topological edge quantum numbers of FQH states in graphene.