Wiedemann–Franz Relation and Thermal-Transistor Effect in Suspended Graphene

We extract experimentally the electronic thermal conductivity, K_e, in suspended graphene that we dope using a back-gate electrode. We make use of two-point dc electron transport at low bias voltages and intermediate temperatures (50–160 K), where the electron and lattice temperatures are decoupled. The thermal conductivity is proportional to the charge conductivity times the temperature, confirming that the Wiedemann–Franz relation is obeyed in suspended graphene. We extract an estimate of the Lorenz coefficient as 1.1–1.7 × 10^–8 W ΩK^–2. K_e shows a transistor effect and can be tuned with the back-gate by more than a factor of 2 as the charge carrier density ranges from ∼0.5 to 1.8 × 10¹¹ cm^–2.