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

Abstract

The heat generation by an electric current flowing through a quantum dot with the dot containing both electron-electron interaction and electron-phonon interaction, is studied. Using the non-equilibrium 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 non-monotonic 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.

Spin Effects on Heat Current Through a Quantum Dot Attached to Ferromagnetic Leads

“…The system under consideration with a QD molecule connected to the left and right ferromagnetic leads is described by the following Hamiltonian [30,31]:…”

“…For example, the heat generation can be very small despite a large current in the resonant tunneling region, which is favorable in device design [31]. The heat generation can even decrease with increasing bias voltage for some chosen parameters, exhibiting the negative differential of the heat generation [31]. In the presence of ac bias voltage, finite time-dependent heat generation emerges without the accompany of electric current [32,33].…”

“…Recently, Sun and Xie have calculated the heat generation from electric current by using the non-equilibrium Keldysh Green's function method and predicted some interesting phenomena unique in nanodevices [30]. For example, the heat generation can be very small despite a large current in the resonant tunneling region, which is favorable in device design [31]. The heat generation can even decrease with increasing bias voltage for some chosen parameters, exhibiting the negative differential of the heat generation [31].…”

“…This heat is a serious technological bottleneck of devices' miniaturization. Properties of local heating in nanostructures have been studied both experimentally [21][22][23][24][25][26][27][28] and theoretically [29][30][31][32][33][34][35][36][37][38][39][40] in recent years. Previous works have shown that although the heat generation in nano-scale or mesoscopic system is caused essentially by the same reasons as those in bulk macroscopic ones, some familiar laws of heat generation applicable in macroscopic systems, for example the Joule law, may not hold true in low-dimensional ones.…”

Transient heat generation in a quantum dot under a step-like pulse bias

“…As for the aspect of theory, on the one hand much efforts have been made to investigate the effects of inelastic e-p scattering on electronic transport through different nanostructures, [16][17][18][19][20][21][22][23][24] on the other hand many theoretical works have devoted to understanding the phenomena of heat, various models and methods were suggested as well. [25][26][27][28][29][30][31][32][33][34][35][36] By using the nonequilibrium Green's function (NEGF) method, a tractable formula of heat generation has been derived. 28 But these works mainly focused on the steady-state cases or, at most, the sinusoidal-like ac bias.…”