Difference in charge and spin dynamics in a quantum dot–lead coupled system

We analyze time evolution of charge and spin states in a quantum dot coupled to an electric reservoir. Utilizing high-speed single-electron detection, we focus on dynamics induced by the first-order tunneling. We find that there is a difference between the spin and the charge relaxation: The former appears slower than the latter. The difference depends on the Fermi occupation factor and the spin relaxation becomes slower when the energy level of the quantum dot is lowered. We explain this behavior by a theory including the first-order tunneling processes and find a good agreement between the experiment and the theory.

Figure 1

(a) SEM image of the device and the schematic of the measurement circuit. The target QD1 is connected to the ancillary QD2 for the spin initialization and readout. The charge state is monitored by the QD sensor connected to the RF resonator circuit. (b) Schematics of the measurement procedure. The spin state is initialized in QD2 and the electron is transferred to QD1. After that, the charge and spin states evolve by the interaction with the lead. The charge state is monitored by the QD sensor. The final spin state after some interaction duration is measured utilizing the spin blockade. (c) Charge stability diagram $\mathrm{\Delta }{V}_{\mathrm{sensor}}$ as a function of $V_{\mathrm{P}2}$ and $V_{\mathrm{P}1}$. I, O, and M correspond to gate voltage conditions for initialization, operation, and readout, respectively. The number of electrons in each QD is shown as $(n_1,n_2)$.

Figure 2

(a) Observed charge and spin signals as a function of the interaction time. Red circles show the charge signal $\langle V_{\mathrm{sensor}}\left(t\right)\rangle$ calculated as the average of the sensor signal $V_{\mathrm{sensor}\alpha }\left(t\right)$ over the experimental runs indexed by $\alpha$. Blue circles show the spin signal (the probability to find a singlet in M). The solid lines are exponential fits resulting in a relaxation time of $1.7\mu \mathrm{s}$ for the charge and $3.0\mu \mathrm{s}$ for the spin. The QD level is close to the Fermi level of the reservoir ($\epsilon =5.4$ mV). (b) Observed charge and spin signals as a function of the interaction time for a lowered QD level ($\epsilon =5.0$ mV). The spin relaxation time becomes slower. (c) Schematic of the first-order tunneling process. The first-order tunneling event between the QD and the lead changes the charge and spin states.

Figure 3

[(a)–(e)] The observed charge (red) and spin (blue) signals for different energy alignment of the QD with respect to the Fermi level of the lead. The charge and spin signals are normalized. Panels (a)–(e) correspond to $\epsilon =5.8,5.6,5.4,5.2,5.0$ mV, respectively. (f) The relaxation time obtained by single-exponential fitting in the case of charge (red) and spin (blue) signals as a function of $\epsilon$.

Figure 4

[(a) and (b)] Calculated charge and spin dynamics using the model in Eq. (1) and the parameters of the experiment (magnetic field $B=0.5$ T, electron temperature $T_{\mathrm{e}}=0.25$ K). Panels (a) and (b) are results for $f=0$ and 0.6, respectively.