Vanishing bulk heat flow in the ν=0 quantum Hall ferromagnet in monolayer graphene

Undoped graphene is a gapless semiconductor; however, when placed under a high perpendicular magnetic field and cooled to low temperature, it develops an insulating state. This state, dubbed nu = 0, is due to the interplay between electronic interactions and the four-fold spin and valley degeneracies in the flat band formed by the n = 0 Landau level. The nature of the ground state of nu = 0, including its spin and valley polarization, is still under debate. Here we observe vanishing bulk thermal transport in monolayer at nu = 0, in contradiction with the expected ground state, which is predicted to have finite thermal conductance even at very low temperature. Our results highlight the need for further investigations on the nature of nu = 0. Charge-neutral graphene in the quantum Hall regime is known to be an insulator. Now thermal transport measurements show that it also does not conduct heat. This sheds light on the nature of the ground state in this regime.