When two-dimensional electron gas is cooled to millikelvin temperature regime and then subjected to a high magnetic field, well resolved Landau levels get developed. For the particulars electron density and magnetic field, electron-electron interactions give rise to strongly correlated topological phase, known as the fractional Quantum Hall (QH) states whose edge structures are not as simple as in integer QH state, which is the precursor of fractional QH phase. In particular, for hole like states, initially proposed model is that at the edge of sample, there are downstream charge mode accompanied by the upstream neutral mode. These fractional quantum Hall phases are topological in nature and are characterized by a topological number, related to the conductance of the state. In fact, some of them are believed to be possible candidate for the fault tolerant quantum computation. We are currently exploring the exotic property of these quantum Hall states realized in graphene via the electrical, thermal and noise measurement techniques, particularly focusing on the thermal conductance measurement. Measurement of thermal conductance reveals the detailed topological structure of the edges, which are usually limited in the electrical conductance measurement. We have successfully measured the thermal conductance of the integer quantum Hall states and particle like fractional quantum Hall state, to its quantized value. Our observation, re-establish the fact that the quantized thermal conductance is independent of the statistics of the carriers. Currently, we are focusing other exotic states like Neutral mode and Majorana modes.
(Top-left): Schematic of the measurement setup used for the thermal conductance measurement. (Top-right): Electronic temperature measured as a function of dissipated power. (Bottom-left): Electrical conductance and thermal noise response as a function of gate voltage. (Bottom-right): Dissipated power as a function of square of temperature, Slope of the lines gives thermal conductance. Interestingly, the thermal conductance of 4/3 quantum Hall state matches with the ν=2 integer quantum Hall state.