Powerful and efficient energy harvester with resonant-tunneling quantum dots

We propose a nanoscale heat engine that utilizes the physics of resonant tunneling in quantum dots in order to transfer electrons only at specific energies. The nanoengine converts heat into electrical current in a multiterminal geometry which permits one to separate current and heat flows. By putting two quantum dots in series with a hot cavity, electrons that enter one lead are forced to gain a prescribed energy in order to exit the opposite lead, transporting a single electron charge. This condition yields an ideally efficient heat engine. The energy gain is a property of the composite system rather than of the individual dots. It is therefore tunable to optimize the power while keeping a much larger level spacing for the individual quantum dots. Despite the simplicity of the physical model, the optimized rectified current and power is larger than any other candidate nanoengine. The ability to scale the power by putting many such engines into a two-dimensional layered structure gives a paradigmatic system for harvesting thermal energy at the nanoscale. We demonstrate that the high power and efficiency of the layered structure persists even if the quantum dots exhibit some randomness.

Figure 1

Nanoscale heat engine created from a hot cavity connected to cold reservoirs via resonant tunneling quantum dots, each containing a single relevant energy level at energy $E_{L,R}$. The cavity is kept hot through coupling to an energy reservoir at temperature $T_{\mathrm{C}}$ (not shown) which is considered larger than the reservoir temperature $T_{\mathrm{R}}$. Thermal broadening of the Fermi functions in the three regions (source, cavity, and drain) is shown by the light shading. (a) Rectification configuration. In the absence of bias (short circuit), electrons enter the cavity via the left lead, gain energy $\Delta E=E_R-E_L$ from the cavity, and exit through the right lead, transferring an electrical charge $e$ through the system. (b) Carnot efficient stopping (open circuit) configuration.

Figure 2

(a) Scaled maximum power as a function of energy gain $\Delta E$ for $\Delta T=T$ and level width $\gamma$ and ${\mu }_R$ optimized to give maximum power. (b) Scaled maximum power as a function of $\Delta T/T$ for optimized values of $E_R=\Delta E/2$, $\gamma$, and ${\mu }_R$. (c) Efficiency at maximum power for the values of $E_R=\Delta E/2$, $\gamma$, and ${\mu }_R$ chosen to maximize power. (d) The optimized values are plotted versus $\Delta T/T$. Here, $E_R=\Delta E/2$, ${\mu }_R=\mu /2$.

Figure 3

Scaled heat current $J/[2{\left(k_{\mathrm{B}}T\right)}^2/h]$ leaving (blue) or entering (red) the central cavity vs temperature difference ($x$ axis) and applied bias ($y$ axis) divided by average temperature. The plot is for system parameters optimized for maximal power output, an energy gain of $\Delta E\approx 6k_{B}T$ and level width $\gamma \approx k_{B}T$. The green line is the $J=0$ curve for $\gamma \to 0$ while the black curve is the $J=0$ line for the optimized $\gamma$. The system can work as a heat engine (HE) in the blue region for $\Delta T>0,{\mu }_R=\mu /2>0$ (configuration shown in the inset labeled HE), or as a refrigerator (R) in the blue region for $\Delta T<0,{\mu }_R=\mu /2<0$ (configuration shown in the inset labeled R).

Figure 4

Self-assembled dot engine: A cold bottom electrode (dark blue) is covered with a layer of quantum dots (orange) embedded in an insulating matrix (transparent blue). The quantum dot layer is covered by the hot central region shown in dark red. On top of it, there is another quantum dot layer. The whole structure is terminated by a cold top electrode (dark blue). Importantly, the positions of the quantum dots in the two layers do not have to match each other. Thus, the device can be realized using self-assembled quantum dots. The latter can have charging energies and single-particle level spacings of the order of 10 meV (Refs. 21 and 22), thereby allowing the nanoengine to operate at room temperature.

Figure 5

Schematic of the system operation configuration. Heat enters the engine from the pink hot region, indicated by the red chevrons. The engine itself is signified by the yellow sandwich with black holes indicating the position of the resonant tunneling quantum dots. The position of the holes can be disordered, similar to a slice of Swiss cheese. Electrical current is generated perpendicular to the layers, indicated with the blue arrows flowing in the light blue cold region.

Figure 6

The power per nanoengine is plotted vs the width of Gaussian random distribution of energy levels. The power is normalized to the maximum power a single nanoengine can give (for optimized parameters), while the distribution width is plotted in units of $\Delta E$, the average energy gain between left and right dots. (a) The power is plotted for different level widths of the dots, where ${\gamma }_{\mathrm{opt}}=1.02k_{B}T$. (b) The power is plotted for different applied voltages, where ${\mu }_{R,\mathrm{opt}}=0.7k_{B}T$.

Figure 7

The power per nanoengine is plotted vs the right chemical potential and the average energy gain, $\Delta E$, in units of the optimal power, $P_{\max }$. The level width is taken to be a suboptimal value, $\gamma =0.8k_{B}T$, and the width of Gaussian random distribution is fixed at $\sigma =0.2k_{B}T$. The subscript “opt” refers to the parameter that is optimized for maximal power in the clean case.