Coherent oscillations of current due to nuclear spins

We propose a mechanism for very slow coherent oscillations of current and nuclear spins in a quantum dot system, that may qualitatively explain some recent experimental observations. We concentrate on an experimentally relevant double dot setup where hyperfine interaction lifts the spin blockade. We study the dependence of the magnitude and period of the oscillations on magnetic field and anisotropy.

Figure 1

The period as a function the integral of motion $L$ for various values of $x_B$. The asymmetry is $ϵ=0.1$, $k_R=0.9$, and $k_S^z=0.0$. The inset shows the period as a function of $x_B$ for fixed values of $L$.

Figure 2

The current shown as a function of time for $ϵ=0.1$, $x_B=1.6$, but for different initial conditions, i.e., different $L$. The inset shows current for $L=-0.14$ in the case of $N_b=1$ and 25, where $N_b$ is the number of blocks. Note that the long period oscillations are still present for $N_b⪢1$.