Electric-current-induced heat generation in a strongly interacting quantum dot in the Coulomb blockade regime

The heat generation by electric current flowing through a quantum dot with the dot containing both electron-electron interaction and electron-phonon interaction is studied. Using the nonequilibrium Keldysh Green's-function method, the current-induced heat generation is obtained. We find that for a small phonon frequency, heat generation is proportional to the current. However, for a large phonon frequency, heat generation is in general qualitatively different from the current. It is nonmonotonic with current, and many unique and interesting behaviors emerge. The heat generation could be very large in the Coulomb blockade region in which the current is very small due to the Coulomb blockade effect. On the other hand, in the resonant tunneling region, the heat generation is very small despite a large current, an ideal condition for device operation. In the curve of heat generation versus the bias, a negative differential of the heat generation is exhibited, although the current is always monotonously increasing with the bias voltage.