Under high magnetic field and at low temperatures, electronic interactions in a two-dimensional electron gas give rise to exotic, strongly correlated many-body quantum Hall states. These states have been proposed for the implementation of new quantum circuits, for instance realizing topologically protected quantum computing. Although exciting, these states remain poorly understood, because the conventional experimental approach for their investigation, dc electron transport, only yields limited information. In particular, electron transport only probes the physics of the current-carrying edge channels of the quantum Hall effect propagating along the edges of the electron gas, leaving the physics of the bulk unexplored. To gain a better understanding of these exotic states and their origin, I propose a new, unconventional approach, based on heat transport measurements, which directly probes the charge-neutral, heat-carrying collective modes characterizing these interactions-induced states. I will focus on the debated ν=0 quantum Hall state of monolayer and bilayer graphene, which is thought to arise from spontaneous spin- and valley- symmetry breakings due to interactions, and on the fractional quantum Hall effect, where the competition between interaction and disorder gives rise to low-energy, heat-carrying neutral modes which have not yet been observed in graphene. Investigating the neutral modes through heat transport will address two important questions regarding these exotic new states: does ν=0 indeed arise from spontaneous symmetry breakings, and what is the origin of the low-energy neutral modes in the fractional quantum Hall effect, particularly in graphene. Furthermore, it will be possible to apply my approach to the investigation of other exotic quantum states in two-dimensions, such as the superfluid excitonic condensate in electron-hole bilayer systems.
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