Spin-polarized transport through weakly coupled double quantum dots in the Coulomb-blockade regime

We analyze cotunneling transport through two quantum dots in series weakly coupled to external ferromagnetic leads. In the Coulomb-blockade regime, the electric current flows due to third-order tunneling, while the second-order single-barrier processes have indirect impact on the current by changing the occupation probabilities of the double dot system. We predict a zero-bias maximum in the differential conductance, whose magnitude is conditioned by the value of the interdot Coulomb interaction. This maximum is present in both magnetic configurations of the system and results from asymmetry in cotunneling through different virtual states. Furthermore, we show that tunnel magnetoresistance exhibits a distinctively different behavior depending on temperature, being rather independent of the value of interdot correlation. Moreover, we find negative tunnel magnetoresistance in some range of the bias voltage.

Figure 1

(Color online) Schematic of a double quantum dot coupled to ferromagnetic leads. The magnetic moments of the leads can form either parallel or antiparallel configuration. The system is symmetrically biased.

Figure 2

(Color online) Examples of possible tunneling processes through double quantum dot in the Coulomb-blockade regime. The third-order process (a) from left to right lead, where ∣↑↓⟩ is the initial state (1) and ∣↑↑⟩ is the final state (7), takes place via five virtual states (2)–(6). This process contributes directly to the current flowing through the system. The second-order process (b) through the left barrier, with $\mid \uparrow \sigma ⟩$ $\left(\mid \downarrow \sigma ⟩\right)$ being the initial (1) [finite (4)] state, where $\sigma =\uparrow ,\downarrow$, affects the occupations of the double quantum dot. This process takes place via two virtual states [(2) and (3)].

Figure 3

(Color online) Differential conductance as a function of the bias voltage for different interdot interaction parameter $U^{\prime }$, as indicated in the figure. The other parameters are $k_{\mathrm{B}}T=0.1\Gamma$, $\epsilon =-10\Gamma$, $U=20\Gamma$, $t=\Gamma$, and $p=0$.

Figure 4

(Color online) Bias dependence of the differential conductance in the (a) parallel and (b) antiparallel magnetic configurations for different interdot interaction parameter $U^{\prime }$, as indicated. The other parameters are $k_{\mathrm{B}}T=0.1\Gamma$, $\epsilon =-10\Gamma$, $U=20\Gamma$, $t=\Gamma$, and $p=0.5$.

Figure 5

(Color online) Bias dependence of the differential conductance in the (a) parallel and (b) antiparallel magnetic configurations for different temperatures and for $U^{\prime }=2\Gamma$. The other parameters are the same as in Fig. 4.

Figure 6

(Color online) Bias dependence of the TMR for different interdot interaction parameter $U^{\prime }$ and for $k_{\mathrm{B}}T=0.1\Gamma$. The other parameters are the same as in Fig. 4.

Figure 7

(Color online) Tunnel magnetoresistance as a function of the bias voltage for different temperatures and for $U^{\prime }=2\Gamma$. The other parameters are the same as in Fig. 4.