Modern technology allows us to fabricate uniquely pure graphene samples that contain only a few impurities. Recent results on ultra-precise experimental thermal measurements [1] demonstrate that it is possible to probe local heating due to the remaining impurities. In the present work, we theoretically describe this phenomenon. Specifically, we study the effect of strong rare impurities on heat transfer in a coupled electron-phonon system in disordered graphene. We analyze in detail the electron-phonon heat exchange assisted by such an impurity through the “resonant supercollisions”, that is, combined collisions in which impurities and phonons are simultaneously involved. We further explore the local modification of heat transfer in a weakly disordered graphene due to a resonant scatterer and determine spatial profiles of the phonon and electron temperature around the scatterer under electrical driving. Our results are consistent with experimental findings of Ref. [1].

References
[1] Dorri Halbertal, Moshe Ben Shalom, Aviram Uri, Kousik Bagani, Alexander Y Meltzer, Ido Marcus, Yuri Myasoedov, John Birkbeck, Leonid S Levitov, Andre K Geim, Eli Zeldov, Imaging resonant dissipation from individual atomic defects in graphene, Science, 358, 1303 (2017)