This book describes the quantized thermal conductance measurements of integer and several fractional quantum Hall (QH) states realized in graphene devices. Although the electrical conductance quantization of the QH effect in graphene was demonstrated in 2005, a heat flow study of QH states needed to be included. This becomes particularly essential for the hole-conjugate fractional QH phases, where counterpropagating edge modes lead to complex transport behavior. The experimental results reported in this thesis are the first set of experiments done for the quantized heat flow in graphene devices since the first mechanical isolation of graphene flakes. The book devotes two detailed introductory chapters to the electronic properties of the graphene and its bilayer and trilayer parts at zero magnetic fields, and to the essential physics of the integer and fractional quantum Hall (FQH) states, the topological order of FQH phases and the experiments that can detect them.

The book has a dedicated chapter for the details of the device fabrication and thermal conductance measurement technique. The rest of the chapters are dedicated to the systematic and detailed documentation of the new experimental findings of quantized heat flow in quantum Hall phases in graphene.