Thermal control across a chain of electronic nanocavities

We study a chain of alternating hot and cold electronic nanocavities—connected to one another via resonant-tunneling quantum dots—with the intent of achieving precise thermal control across the chain. This is accomplished by positioning the dots' energy levels such that a predetermined distribution of heat currents is realized across the chain in the steady state. The number of electrons in each cavity must be conserved in the steady state which constrains the cavities' chemical potentials. Determining these chemical potentials is a challenging task, but can be performed analytically in the linear response regime where the energy differences between the dots' resonant levels and the neighboring chemical potentials are much smaller than the thermal energy. In this regime, the thermal control problem can then be solved exactly.