National Graphene Institute, The University of Manchester, UK In the integer Quantum Hall effect (QHE) regime, heat in a two-dimensional (2D) electron gas is carried by electrons in the edge states of Landau levels.Here we study phonon-emission cooling of such heat-carrying electron at the edge of graphene at the filling factor and determine the temperature profile extended from a hot spot where Hall current is injected into graphene from a metallic contact. Our calculations, performed for a mechanically free edge of graphene coupled by van der Waals forces to a substrate shows that losses in chiral heat transportobserved by Nahm, Hwang and Lee [PRL 110, 226801 (2013)] can be attributed to the phonon cooling mechanism. Sergey Slizovskiy is currently a postdoctoral member of theory group of Prof. V.Fal'ko at National Graphene Institute, The University of Manchester, UK. He is interested in electronic properties of 2D materials, Quantum Hall Effect devices, topological insulators, edge states, Dirac and Weyl semimetals, topological Lifshitz transitions in interacting systems. He received his B.S. and M.S. degrees in theoretical physics from Saint-Petersburg State University and a PhD in physics from Uppsala University where he studied instantons and non-perturbative effects in Yang-Mills theory and topological field theories. After finishing his PhD, he spent 5 years in Loughborough University studying interacting electronic systems with strong spin fluctuations and graphene in magnetic field. His awards include EPSRC post-doctoral fellowship, PhD stipend of Russian non-commercial foundation Dynasty and RFBR (Russia) grants. |

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