Detection and Measurement of Spin-Dependent Dynamics in Random Telegraph Signals

A quantum point contact was used to observe single-electron fluctuations of a quantum dot in a GaAs heterostructure. The resulting random telegraph signals (RTS) contain statistical information about the electron spin state if the tunneling dynamics are spin dependent. We develop a statistical method to extract information about spin-dependent dynamics from RTS and use it to demonstrate that these dynamics can be studied in the thermal energy regime. The tunneling rates of each spin state are independently measured in a finite external magnetic field. We confirm previous findings of a decrease in overall tunneling rates for the spin excited state compared to the ground state as an external magnetic field is increased.

Figure 1

(a) Scanning electron microscope image of the active area of the device. A quantum dot is formed in the region highlighted by the dashed circle, connected by a tunnel barrier to a reservoir of free electrons at the lower right. A QPC channel through the upper half of the device is used to monitor the charge state of the quantum dot. (b) Schematic of the chemical potential levels of the quantum dot and occupancy of states in the lead. Indicated are the chemical potentials ${\mu }^{\downarrow }$ and ${\mu }^{\uparrow }$ for spin-down and spin-up electrons, respectively, the Fermi level of the lead $E_f$, the detuning $ϵ$, and the Zeeman energy $E_Z$. The red curve represents the Fermi distribution of occupied states in the lead. (c) Example of part of one RTS data trace. (d) Most likely state sequence reconstructed from a two-state model fit to the RTS shown in (c). (e) Most likely state sequence from a three-state model fit. (f) Overall tunneling rates ${\Gamma }_{\mathrm{IN}}$ (red circles) and ${\Gamma }_{\mathrm{OUT}}$ (blue triangles) as a function of detuning, determined by the two-state model at $B=0\mathrm{T}$.

Figure 2

Results of fitting a three-state MMGP model to two sets of RTS. (a)–(d): magnetic field $B=0\mathrm{T}$. (e)–(h) $B=3\mathrm{T}$. (a) and (e) show the model selection statistic $\Delta \mathrm{BIC}$ as a function of detuning $ϵ$. Negative $\Delta \mathrm{BIC}$ indicates that differences between two spins are statistically significant. (b) and (f) Tunnel-out rates ${\Gamma }_{\mathrm{OUT}}^{\downarrow }$ and ${\Gamma }_{\mathrm{OUT}}^{\uparrow }$ extracted from the three-state model fits. Those detuning points for which the three-state model is selected are emphasized by solid symbols and 90% confidence intervals. (c) and (g) Tunnel-in rates ${\Gamma }_{\mathrm{IN}}^{\downarrow }$ and ${\Gamma }_{\mathrm{IN}}^{\uparrow }$. (d) and (h) Spin-flip transition rates $W_{\downarrow \uparrow }$ and $W_{\uparrow \downarrow }$. Solid lines in (f) indicate fits of Eq. (2) to those data points where the three-state model was selected.

Figure 3

(a) Gross tunnel-out rates for the two spin states, ${\Gamma }_0^{\downarrow }$ and ${\Gamma }_0^{\uparrow }$, as a function of applied magnetic field. These were determined by fits to the rates extracted from a series of RTS such as shown in Fig. 2f for $B=3\mathrm{T}$. (b) Ratio of the gross tunnel-out rates for the two spin states, ${\Gamma }_0^{\downarrow }/{\Gamma }_0^{\uparrow }$, as a function of applied magnetic field. The tunneling rate for spin-down electrons decreases relative to the spin-up tunneling rate as the Zeeman energy difference between the two states increases.