Spin accumulation encoded in electronic noise for mesoscopic billiards with finite tunneling rates

We study the effects of spin accumulation (inside reservoirs) on electronic transport with tunneling and reflections at the gates of a quantum dot. Within the stub model, the calculations focus on the current-current correlation function for the flux of electrons injected into the quantum dot. The linear response theory used allows us to obtain the noise power in the regime of thermal crossover as a function of parameters that reveal the spin polarization at the reservoirs. The calculation is performed employing diagrammatic integration within the universal groups (ensembles of Dyson) for a nonideal, nonequilibrium chaotic quantum dot. We show that changes in the spin distribution determine significant alterations in noise behavior at values of the tunneling rates close to zero, in the regime of strong reflection at the gates.

Figure 1

A schematic picture showing a quantum dot coupled to polarizable reservoirs via several leads with open channels in the presence of temperature and voltage.

Figure 2

We depict the behavior of the noise and its first derivative in the regime of spin accumulation as a function of tunneling rate $\Gamma$ in a quantum dot with nonideal symmetrical contacts. For $\Delta >\Phi$, we observe that the noise suffers abrupt changes, enhanced by the finite tunneling rates.

Figure 3

We depict the behavior of the noise in the regime of spin accumulation as a function of the tunneling rate $\Gamma$ in a QD with nonideal contacts, through the parameter $a=(G_1-G_2)/G_T$. Note that for ideal contacts, ${\Gamma }_1={\Gamma }_2=1$, the noise is highly asymmetrical with respect to this parameter. In the other curves we vary the values of ${\Gamma }_1$ and ${\Gamma }_2$ till we reach the opaque limit, ${\Gamma }_{1,2}\to 0$. In this case the noise becomes symmetrical with respect to $a$.

Figure 4

In this figure we show the concavity and the sign of the noise power for all values of the tunneling rate and of the asymmetry parameter.

Figure 5

We show the behavior of the shot noise in the case of spin accumulation as a function of $a=(G_1-G_2)/G_T$, in a QD with nonideal contacts; see Eq. (13). For any value such that $\delta \mu ⩾\mathit{eV}$, the result will always be the same for the shot noise, which is a direct consequence of the spin accumulation in the reservoirs.