Universal Quantization of Thermal Conductance in Graphene

As discussed earlier in the Chapter,  2 , the universal quantization of thermal conductance provides information on the topological order of a state beyond the conventional electrical conductance measurement. Although the traditional electrical conductance measurement has been performed extensively in quantum Hall phases of “graphene” and GaAs/AlGaAs two-dimensional electron gas systems, thermal conductance measurement has been lacking since the experimental discoveries of the quantum Hall states. It (thermal conductance) has only become possible recently in GaAs/AlGaAs two-dimensional electron gas systems, demonstrating the universal quantization of thermal conductance for integer and Jain-sequence of the fractional quantum Hall states. In particular, the experimentally measured value of the thermal conductance of the 5/2 state in GaAs/AlGaAs based system raises several essential points, motivating further to reconsider the initial theoretical claims of the ground state of this novel electronic phase. More importantly, the thermal conductance measurement analysis has been complicated by the presence of counter-propagating edge channels arising from edge reconstruction, an inevitable consequence of separating the dopant layer from the GaAs quantum well and the resulting soft confining potential. Fortunately, graphene, a two-dimensional allotrope of carbon, has emerged as a novel two-dimensional material. The edge reconstruction issue is believed to be avoided due to its sharp confining potential. In this Chapter, we present the measurement of the thermal conductance in graphene having atomically sharp confining potential by using sensitive noise thermometry on hexagonal boron nitride encapsulated graphene devices, gated by either SiO \(_{2}\) /Si or graphite back gate. We find the quantization of thermal conductance within \(5\%\) accuracy for \(\nu =1, 4/3, 2,\) and 6 plateaus, emphasizing the universality of the flow of information. These graphene quantum Hall thermal transport measurements will allow us to look into more complex hole-like and even denominator FQH states in “graphene”.