Spin filtering and thermopower in star-coupled quantum dot devices

We analyze the linear thermoelectric transport properties of devices with three quantum dots in a star configuration. A central quantum dot is tunnel-coupled to source and drain electrodes and to two additional quantum dots. For a wide range of parameters, in the absence of an external magnetic field, the system is a singular Fermi liquid with a nonanalytic behavior of the electric transport properties at low energies. The singular behavior is associated with the development of a ferromagnetic or an underscreened Kondo effect, depending on the parameter regime. A magnetic field drives the system into a regular Fermi liquid regime and leads to a large peak $\left(\sim k_B/\left|e\right|\right)$ in the spin thermopower as a function of the temperature, and to a $\sim 100\%$ spin polarized current for a wide range of parameters due to interference effects. We find a qualitatively equivalent behavior for systems with a larger number of side-coupled quantum dots, with the maximum value of the spin thermopower decreasing as the number of side-coupled quantum dots increases.

Figure 1

Schematic representation of a three QD device in a star configuration. The central QD which is labeled with 0 is tunnel-coupled to two QDs and to left (L) and right (R) electrodes.

Figure 2

Conductance as function of the temperature for different values of the tunnel coupling $t$. $t/D$ takes the values 0.012, 0.014, 0.016, 0.018, 0.02, 0.025, 0.05, and 0.1. Other parameters are $U=0.4D,V=0.2D$, and ${\epsilon }_{\ell }=-U/2$. (Inset) Plot of $G^{-1/2}$ as a function of $ln(k_{B}T/T_K^0)$ to make clear the singular behavior of the conductance at low energies for $t\ne 0$.

Figure 3

Conductance $G$ vs total occupation $\mathcal{N}$ of the QDs. (a) Conductance for different couplings $t$. (Inset) Kondo coupling as a function of $\delta$ for $t=0.2D$. The arrow indicates the value of $\delta ={\delta }^{☆}\simeq 0.44U$ where $J_K$ vanishes. (b) Conductance for $t=0.04D$ at different temperatures. $k_{B}T$ changes from ${10}^{-13}D$ to ${10}^{-4}D$ in steps of 1 in the exponent. (Inset) $\mathcal{N}$ as a function of $\delta$ for $t=0.04D$ (solid line) and $t=0.2D$ (dashed line). In (a) and (b), the expected zero-temperature conductance for a singular Fermi liquid $G_0{sin}^2(\pi \mathcal{N}/2-\pi /2)$ (red thick line) and a regular Fermi liquid $G_0{sin}^2(\pi \mathcal{N}/2)$ (black thin line), are presented.

Figure 4

Charge Seebeck coefficient $S_c$ in the ferromagnetic Kondo regime $\left(t=0.2D\right)$ for $B=0$. There is a change in the sign of $S$ near $\delta \sim U/2$ where the total occupation of the QDs changes between $\sim 3$ and $\sim 2$. Other parameters as in Fig. 2.

Figure 5

(Top to bottom) Conductance, Seebeck coefficient $S_c$, and Lorentz number, as a function of the temperature for a system in the ferromagnetic Kondo regime $t=0.2$ and $\delta =0.23U$. Other parameters as in Fig. 2.

Figure 6

(a) Spectral density of the central QD at low energies for $k_{B}T=0.3{\mu }_{B}B=3\times {10}^{-6}D$ in the ferromagnetic regime $\left(t=0.2D\right)$ and $\delta =0$. For $B=0$, the spectral density is electron-hole symmetric and presents a singular behavior at low energies. (b) Same as (a) for $\delta =0.23U$ and $k_{B}T={10}^{-6}D$. (Inset) Spectral density in a wide range of energies that includes the Hubbard peaks at $\omega \sim \pm U/2$ and shows the spin polarization under an applied magnetic field.

Figure 7

(a) Spin Seebeck coefficient in the ferromagnetic Kondo regime $\left(t=0.2D\right)$ and $g{\mu }_{B}B={10}^{-5}D$. There are two peaks associated with with a maximum of $S_{\uparrow }$ at $\delta =0.23U$ and a minimum of $S_{\downarrow }$ at $\delta \sim U/2$. (b) Zero-temperature current polarization $I_p$ as a function of $\delta$. There is a broad range of values of $\delta$ around $\delta \sim 0.23U$ and where the current is $\sim 100\%$ polarized.

Figure 8

Spin Seebeck as function of the temperature and the magnetic field at $\delta =0$ for (a) $t=0.02D$ and (b) $t=0.2D$. The magnetic field changes from ${10}^{-11}D$ to ${10}^{-6}D$ in steps of 1 in the exponent.