High-Efficiency Thermoelectric Transport in Aharonov-Bohm-Casher Rings

TL;DR

This paper addresses how spin-dependent interference in an asymmetric Aharonov-Bohm ring, enhanced by Rashba spin-orbit interaction in one arm, can boost thermoelectric performance. Using a scattering-matrix and Landauer-Büttiker framework, it computes spin-resolved transmissions and linear-response coefficients to obtain the Seebeck coefficient, thermal conductance, and the figure of merit $ZT$. The main finding is that Rashba SOI, together with geometric asymmetry, yields prominent spin-dependent interference that drives $ZT$ well above unity, with a maximum near $ZT_{ ext{max}}\approx 6$ for $ ilde{\eta}\approx 0.2$ and AB flux $ ext{Φ}_{AB}=0$ or $rac{1}{2}\text{Φ}_0$, and that $ZT$ is electrically tunable. This points to a viable, tunable nanoscale thermoelectric device platform with potential for efficient energy conversion and control via gate-induced SOI strength.

Abstract

Quantum heat engines are nanoscale devices that convert heat into work by exploiting quantum effects, such as coherence and interference. Previous studies of these devices did not consider spin-dependent effects, which can influence the thermoelectric performance of the engine. In this work, we study the thermoelectric behavior of a quantum heat engine based on an Aharonov-Bohm ring - a mesoscopic ring where electrons exhibit interference depending on the magnetic flux it encloses - incorporating Rashba spin-orbit interaction (SOI), which couples the electron's motion and spin. We find that Rashba SOI enhances the figure of merit $ZT$, measure of the engine's conversion efficiency. Our results suggest that controlling spin-dependent interference could lead to improvements in the fabrication of efficient thermoelectric devices.

Figures (4)

• Figure 1: (a) Schematic representation of a two-terminal Aharonov-Bohm quantum heat engine. The upper arm, of length $\ell_1$, is affected by Rashba SOI, while the lower arm, of length $\ell_2$, remains spin-independent, as indicated. The ring encloses a magnetic flux $\Phi_{AB}$ and is connected to two reservoirs at temperatures $T_{\rm hot}$ and $T_{\rm cold}$ through junctions of coupling strength $\epsilon$. $V_g$ represents the applied gate voltage. (b) Parametrization of the AB ring, where the junctions act as scatterers. At each junction, the incoming (red) and outgoing (black) wavefunctions are related by the scattering matrix $\mathcal{S}$.
• Figure 2: Transmission probability of the quantum ring. (a) Energy dependence of the transmission in absence of Rashba SOI for different coupling strength $\epsilon$, for $eV_g = \pi \mu$, and $\Phi = 1/14 \Phi_0$. (b) Energy dependence of the spin-resolved transmission probabilities ($\mathcal{T}_\uparrow, \mathcal{T}_\downarrow$) and total transmission ($\mathcal{T}_{tot}$) for $\tilde{\eta} = 0.1$ and $\epsilon = 0.2$. (c) Same quantities as in (b) as a function of $\tilde{\eta}$ at fixed energy $E = \mu$. In (a), both channels are degenerate and the plotted transmission correspond to a single channel. In (b) and (c), the total transmission can exceed unity since the contributions of both channels are shown separately.
• Figure 3: Thermoelectric behavior of the Aharonov-Bohm ring-based quantum heat engine. (a) Contour plots of the normalized conductance $G$, charge Seebeck $S$ and thermal conductance $\kappa_{th}$ for the case of no Rashba SOI ($\tilde{\eta} = 0$) vs gate voltage $V_g$ and magnetic flux $\Phi_{AB}$. (b) Same quantities in the presence of Rashba spin-orbit coupling with $\tilde{\eta} = 0.2$.
• Figure 4: Figure of merit of the Aharonov-Bohm ring-based heat engine: (a) configuration in the absence of Rashba SOI, as shown in Fig. \ref{['fig:coefficients']}, (b) configuration with $\tilde{\eta} = 0.2$, as shown in Fig. \ref{['fig:coefficients']} and (c) Maximum value of $ZT$ obtained for different Rashba strengths $\tilde{\eta}$. The dotted line represents the maximum $ZT$ obtained in the absence of Rashba SOI.