Thermoelectric performance of nanojunctions subjected to microwave-driven spin-orbit coupling

Coherent charge and heat transport through periodically driven nanodevices provide a platform for studying thermoelectric effects on the nanoscale. Here we study a junction composed of a quantum dot connected to two fermionic terminals by two weak links. An AC electric field induces time-dependent spin-orbit interaction in the weak links. We show that this setup supports DC charge and heat currents and that thermoelectric performance can be improved, as reflected by the effect of the spin-orbit coupling on the Seebeck coefficient and the electronic thermal conductance. Our analysis is based on the nonequilibrium Keldysh Green's function formalism in the time domain and reveals an interesting distribution of the power supply from the AC source among the various components of the device.

Figure 1

(a) Schematic plot of the model system: a single-level (of energy ${\varepsilon }_d^{}$) quantum dot is attached by two weak links (of lengths $d_{L,R}^{}$) lying along $\widehat{\mathbf{x}}$ with two electrons' baths, denoted $L$ and $R$. An electric AC field $U_z^{}\left(t\right)$ along $\widehat{\mathbf{z}}$, the amplitude of which oscillates with frequency $\mathrm{\Omega }$, induces a Rashba spin-orbit interaction in the links. The two fermionic terminals are held at different temperatures ($T_{L,R}^{}$) and different chemical potentials (${\mu }_{L,R}^{}$). (b) Upon averaging the charge and energy fluxes over a period of the AC field, the AC field supplies the power $P_{L,R}^{}$ to the left (right) terminals.

Figure 2

The Seebeck coefficient (in units of $k_B^{}/\left|e\right|$), Eq. (34). The solid (blue) curves are obtained by calculating the integrals $I_n^{\left(\ell \right)}$ numerically, for $\beta \mathrm{\Gamma }=0.2$ and $K_{\mathrm{SO}}^{}/{({\varepsilon }_d^{}-\mu )}^2=1/16$ (thick lines) or $K_{\mathrm{SO}}^{}=0$ (thin lines) [42]. In each case, the other two curves are the approximations of the integrals discussed in Appendix pp4: dashed (red) line, low-temperature approximation; dash-dotted (black) line, high-temperature approximation.

Figure 3

Same as Fig. 2, for ${\kappa }_e^{}$, the electronic thermal conductance (divided by the amplitude $4{\mathrm{\Gamma }}_L^{}{\mathrm{\Gamma }}_R^{}/\pi$).