Shot noise and tunnel magnetoresistance in multilevel quantum dots: Effects of cotunneling

Spin-dependent transport through a multilevel quantum dot weakly coupled to ferromagnetic leads is analyzed theoretically by means of the real-time diagrammatic technique. Both the sequential and cotunneling processes are taken into account, which makes the results on tunnel magnetoresistance (TMR) and shot noise applicable in the whole range of relevant bias and gate voltages. Suppression of the TMR due to inelastic cotunneling and super-Poissonian shot noise has been found in some of the Coulomb blockade regions. Furthermore, in the Coulomb blockade regime, there is an additional contribution to the noise due to bunching of cotunneling processes involving the spin-majority electrons. On the other hand, in the sequential tunneling regime, TMR oscillates with the bias voltage, while the current noise is generally sub-Poissonian.

Figure 1

(Color online) (a) The differential conductance $G$ in the parallel configuration and (b) the TMR as a function of the bias voltage $V$ and level position $\epsilon ={\epsilon }_1$. (c)–(e) show the TMR as a function of $\epsilon$ for several values of $V$, whereas (f)–(h) display the bias voltage dependence of TMR for several values of $\epsilon$. The dashed lines in (c)–(h) show the first-order contributions. The parameters are $k_{B}T=0.15\mathrm{meV}$, ${\epsilon }_2-{\epsilon }_1=1.5\mathrm{meV}$, $U=5\mathrm{meV}$, $U^{\prime }=2\mathrm{meV}$, $\Gamma =0.1\mathrm{meV}$, and $p=0.5$.

Figure 2

(Color online) The Fano factor $F$ as a function of the bias voltage and level position for the (a) parallel and (b) antiparallel magnetic configurations. (c)–(h) show $F$ in the parallel configuration as a function of [(c)–(e)] the level position and [(f)–(h)] the bias voltage. The dashed lines present the first-order contributions. The parameters are the same as in Fig. 1.

Figure 3

(Color online) (a) The differential conductance $G$ and (c) the Fano factor in the parallel configuration, and (b) the TMR as a function of the bias voltage $V$ and level position $\epsilon ={\epsilon }_1$. The parameters are $k_{B}T=0.15\mathrm{meV}$, ${\epsilon }_2-{\epsilon }_1=U=3\mathrm{meV}$, $U^{\prime }=2\mathrm{meV}$, $\Gamma =0.1\mathrm{meV}$, and $p=0.5$.

Figure 4

(Color online) (a) The bias voltage dependence of the TMR and (b) the Fano factor in the parallel configuration for the same parameters as in Fig. 3. The dashed curves show the first-order calculation.