Electronic statistics on demand: Bunching, antibunching, positive, and negative correlations in a molecular spin valve

One of the long-standing goals of quantum transport is to use the noise, rather than the average current, for information processing. However, achieving this requires on-demand control of quantum fluctuations in the electric current. In this paper, we demonstrate theoretically that transport through a molecular spin valve provides access to many different statistics of electron tunneling events. Simply by changing highly tunable parameters, such as electrode spin polarization, magnetization angle, and voltage, one is able to switch between Poisson behavior, bunching and antibunching of electron tunnelings, and positive and negative temporal correlations. The molecular spin valve is modeled by a single spin-degenerate molecular orbital with local electronic repulsion coupled to two ferromagnetic leads with magnetization orientations allowed to rotate relative to each other. The electron transport is described via Born-Markov master equation and fluctuations are studied with higher-order waiting time distributions. For highly magnetized parallel-aligned electrodes, we find that strong positive temporal correlations emerge in the voltage range where the second transport channel is partially open. These are caused by a spin-induced electron-bunching, which does not manifest in the stationary current alone.

Figure 1

Examples of different statistics for electronic transport. Each peak represent electron detection event in the drain. In addition to the standard Poisson process, one can also observe: (a) electron bunching (super-Poisson statistics), (b) electron antibunching (sub-Poisson statistics), (c) positive temporal correlations, and (d) negative temporal correlations. All these different statistics can be observed in a molecular spin valve.

Figure 2

Schematic of a molecular spin valve, which consists of an Anderson model coupled to ferromagnetic electrodes. The spin-quantization axis of the source electrode is aligned with the $z$ axis, whereas the drain electrode is allowed to rotate along the $x\text{−}z$ plane, enclosing an angle $\varphi$ with the $z\mathrm{axis}$.

Figure 3

Randomness parameter $R$ as a function of bias voltage for different spin polarizations and relative magnetization angles: (a) $\varphi =0$, (b) $\varphi =\frac{\pi }{2}$, (c) $\varphi =\pi$. Both electrodes have the same spin polarization: $p_S=p_D=p$. Other parameters are $\varepsilon =10k_{B}T, U=30k_{B}T, k_{B}T=0.1\text{meV}, \gamma =0.01\text{meV}$.

Figure 4

Pearson correlation coefficient $P{C}_{{\tau }_2,{\tau }_1}$ between the first two successive waiting times ${\tau }_1$ and ${\tau }_2$ as a function of bias voltage for different spin polarizations and relative magnetization angles: (a) $\varphi =0$, (b) $\varphi =\frac{\pi }{2}$, (c) $\varphi =\pi$. All parameters are the same as in Figs. 3–3.

Figure 5

Relative correlation between successive waiting times $C({\tau }_2,{\tau }_1)$ plotted for parallel magnetizations: $\varphi =0$. Spin polarization within the leads is $p=0.99$ and the voltage is $V_{SD}=75k_{B}T$, corresponding to the peak in the positive correlations from Fig. 4. All other parameters are the same as in Figs. 3–3.

Figure 6

$\langle S_z\rangle$ The $z$ component of the measurement-averaged spin (a) as a function of the initial waiting time ${\tau }_1$, and (b) as a function of the second waiting time ${\tau }_2$, given a long initial waiting time: ${\tau }_1=5\langle {\tau }_1\rangle$. All parameters are the same as in Fig. 5.

Figure 7

Transport characteristics of the spin valve across the relevant voltage range $V_{SD}$, and half-rotation of the drain electrode $\varphi$. In (a) the successive waiting time correlation $P{C}_{{\tau }_2,{\tau }_1}$ is plotted, while (b) contains the randomness parameter $R$. The spin polarization is $p=0.99$ and other parameters are the same as in Fig. 5.

Figure 8

Higher-order temporal correlations between ${\tau }_1$ and ${\tau }_n, P{C}_{{\tau }_n,{\tau }_1}$, as a function of bias voltage $V_{SD}$. All parameters are the same as in Fig. 4.