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The microscopic origins of Fourier's venerable law of thermal transport inquantum electron systems has remained somewhat of a mystery, given thatprevious derivations were forced to invoke intrinsic scattering rates farexceeding those occurring in real systems. We propose an alternativehypothesis, namely, that Fourier's law emerges naturally if many quantum statesparticipate in the transport of heat across the system. We test this hypothesissystematically in a graphene flake junction, and show that the temperaturedistribution becomes nearly classical when the broadening of the individualquantum states of the flake exceeds their energetic separation. We develop athermal resistor network model to investigate the scaling of the sample andcontact thermal resistances, and show that the latter is consistent withclassical thermal transport theory in the limit of large level broadening.

Emergence of Fourier's law of heat transport in quantum electron systems