Coherent effects in magnetotransport through Zeeman-split levels

We study nonequilibrium electronic transport through a quantum dot or an impurity weakly coupled to ferromagnetic leads. Based on the rate equation formalism we derive the noise spectra for the transport current. We show that, due to quantum interference between different spin components of the current, the spectrum develops peaks or dips at frequencies corresponding to the Zeeman splitting in the quantum dot. A detailed analysis of the spectral structure of the current is carried out for noninteracting electrons as well as for the regime of Coulomb blockade.

Figure 1

(Color online) Resonant tunneling of a polarized electron through a quantum dot. Here the $\Omega$’s denote the tunneling transition amplitudes between the reservoir states and the Zeeman doublets $\left(E_{1,2}\right)$ of the quantum dot. ${\mu }_{L,R}$ are the chemical potentials in the left and right reservoirs. The unit vectors $\mathbf{n}$, $\overline{\mathbf{n}}$, and ${\mathbf{n}}^{\prime }$ show the polarization axes in the emitter, quantum dot, and the collector, respectively.

Figure 2

(Color online) Four available states of the quantum dot. The indices $n,m$ denote the number of electrons with the spin components $s^{\prime }=\pm \frac{1}{2}$ in the right reservoir.

Figure 3

Spin-up and total resonant currents through the Zeeman doublet as a function of time for ${\theta }_L={\theta }_R=\pi ∕2$ and ${\Gamma }_L={\Gamma }_R=0.1ϵ$.

Figure 4

The polarized resonant current through the Zeeman doublet with ferromagnetic reservoirs and ${\theta }_L={\theta }_R=\pi ∕2$. The solid line corresponds to ${\Gamma }_L={\Gamma }_R=0.1ϵ$ and the dashed line to ${\Gamma }_L=ϵ$ and ${\Gamma }_R=0.1ϵ$.

Figure 5

The Fano factor versus $\omega$ for a polarized electron current with ferromagnetic reservoirs and ${\theta }_L$, ${\theta }_R=\pi ∕2$. The solid line corresponds to ${\Gamma }_L={\Gamma }_R=0.1ϵ$ and the dashed line to ${\Gamma }_L=ϵ$ and ${\Gamma }_R=0.1ϵ$.

Figure 6

The Fano factor versus $\omega$ for a polarized collector current with ferromagnetic reservoirs and Coulomb blockade and ${\theta }_L$, ${\theta }_R=\pi ∕2$. The solid line corresponds to ${\Gamma }_L={\Gamma }_R=0.1ϵ$ and the dashed line to ${\Gamma }_L=ϵ$ and ${\Gamma }_R=0.1ϵ$.

Figure 7

The Fano factor for the circuit $(\alpha =\beta =\frac{1}{2})$ versus $\omega$ for a polarized electron current with ferromagnetic reservoirs and Coulomb blockade and ${\theta }_L,{\theta }_R=\pi ∕2$. The solid line corresponds to ${\Gamma }_L={\Gamma }_R=0.1ϵ$ and the dashed line to ${\Gamma }_L=ϵ$ and ${\Gamma }_R=0.1ϵ$.