Quantum limit of thermal conductance in Graphene

In condensed matter physics, last one decade, the graphene, a single carbon atomic layer, has emerged as an ideal platform to experimentally verify many theoretical predictions. One of those predictions are to see the quantum limit of electrical conductance as well as thermal conductance. Although the quantization of electrical conductance (in e²/h) has been observed in graphene quantum Hall (QH) but the demonstration of quantization of thermal conductance in terms of its quantum limit (p²k_b²/3h T) remains challenging due to the requirement of accurate measurement of very small temperature change. The quantum limit of thermal conductance has been demonstrated recently in GaAs-AlGaAs heterostructures but its determination in graphene QH will open a new path to study the unique exotic phases near the Dirac point, which can be uniquely identified by the thermal conductance measurements. Motivated by this we have carried out the thermal conductance measurement in the integer QH regime of graphene by sensitive noise thermometry setup. We have measured the thermal conductance for n =1, 2 and 6 plateaus and its values agree with the quantum limit of it by more than 95% accuracy.