Optimal Quantum Interference Thermoelectric Heat Engine with Edge States

We show theoretically that a thermoelectric heat engine, operating exclusively due to quantum-mechanical interference, can reach optimal linear-response performance. A chiral edge state implementation of a close-to-optimal heat engine is proposed in an electronic Mach-Zehnder interferometer with a mesoscopic capacitor coupled to one arm. We demonstrate that the maximum power and corresponding efficiency can reach 90% and 83%, respectively, of the theoretical maximum. The proposed heat engine can be realized with existing experimental techniques and has a performance robust against moderate dephasing.

Figure 1

(a) Schematic of a thermoelectric two-path interferometer. Each path $i=1$, 2 from the hot ($H$) to the cold ($C$) terminal contains a phase coherent scatterer with energy-dependent transmission amplitude $t_i(\omega )$. (b) Realization of (a) in a two-terminal Mach-Zehnder interferometer implemented with edge states. The active edge state is denoted with a solid line, chirality shown with arrows. A mesoscopic capacitor (MC) is coupled to one interferometer arm via a quantum point contact with transparency $\tau$. Two additional quantum point contacts, transparencies ${\tau }_A$, ${\tau }_B$, form beam splitters. The hot (cold) terminal is kept at temperature $T_H$ ($T_C$) and potential $V_H$ ($V_C$). By tuning $\tau$ and the path phase difference ${\varphi }_0$, the interferometer transmission probability can become steplike in energy. Close-to-optimal linear-response thermoelectric performance is obtained by adjusting step height and position, via ${\tau }_A$, ${\tau }_B$ and the capacitor resonance energy.

Figure 2

(a) Phase $\alpha (\omega )$ for different transparencies $\tau$ of the capacitor-edge coupling. (b) Interferometer transmission probability $\mathcal{T}(\omega )$ for ${\varphi }_0=\pi /2$ and same $\tau$ as in (a). (c) Transmission probability $\mathcal{T}(\omega )$ for $\tau =0.61$ and different ${\varphi }_0$. (d) Close-up of $\mathcal{T}(\omega )$ defining magnitude of ripple $R$ and transition width $\mathrm{\Delta }\omega$ for effective energy filter.

Figure 3

(a) Maximal power in units of $P_0=(k_B\mathrm{\Delta }T{)}^2/h$ (left) and efficiency at maximum power in units of ${\eta }_C$ (right) as functions of ${\varphi }_0$ and ${\omega }_0$. Parameters are $\mathrm{\Delta }=24.2k_{B}T$ and $\tau =0.61$. (b) Maximum power in units of $P_0$ and efficiency at maximum power in units of ${\eta }_C$, as a functions of dephasing strength $0\le \epsilon \le 1$ and (c) effective arm length difference $\mathrm{\Delta }L{k}_{B}T/(\hslash v_D)$.