Shot noise induced by electron-nuclear spin-flip scattering in a nonequilibrium quantum wire

We study the shot noise (nonequilibrium current fluctuation) associated with dynamic nuclear polarization in a nonequilibrium quantum wire (QW) fabricated in a two-dimensional electron gas. We observe that the spin-polarized conductance quantization of the QW in the integer quantum Hall regime collapses when the QW is voltage biased to be driven to nonequilibrium. By measuring the shot noise, we prove that the spin polarization of electrons in the QW is reduced to $\sim$$0.7$ instead of unity as a result of electron-nuclear spin-flip scattering. The result is supported by Knight shift measurements of the QW using resistively detected NMR.

Figure 1

(a) Schematic diagram of the measurement setup with a SEM image of a QW fabricated on GaAs/AlGaAs 2DEG. (b) Equilibrium QW conductance as a function of $V_g$. At the conductance plateau at $e^2/h$, which we focus on in this paper, only the outer edge channel transmits electrons whereas the inner one is reflected. The two channels are spin polarized, as schematically shown in (a) by $\uparrow$ and $\downarrow$.

Figure 2

(a) Differential conductance $G$ at 4.5 T as a function of $V_{sd}$ obtained for $V_g=-1.6$, $-1.5$, $-1.4$, and $-1.3$ V. (b) Corresponding excess noise $S$. In the top part of (a) and (b), the (quasi)equilibrium, transient, and steady regimes are indicated by the arrows labeled “Eq,” “Tr,” and “Steady,” respectively. (c) Corresponding Fano factor $S/2eI$. The straight dashed curves indicate the Fano factor in the steady regime. (d) The spin polarization in the steady regime obtained by the noise measurement $P_F$ (upper panel) and the equilibrium conductance as a function of $V_g$ (lower panel). The dashed curve in the upper panel is a guide to the eye.

Figure 3

(a) Typical differential conductance, where the hysteresis is observed in the transient regime for $50\lesssim V_{sd}\lesssim 200\mu$V. (b) Temporal variation of $G$ in the transient regime obtained at $B=5.0$ T. The data shown by the open circles are obtained with applying a rf with the NMR frequency for ${}^{75}$As and that shown by the solid circles shows the result without rf irradiation.

Figure 4

(a) Image plot of the conductance obtained through the RDNMR as functions of the rf frequency and the elapsed time after rf irradiation. The QW was set at $V_g=-1.60$ V and at the transient regime at $V_{sd}=180\mu$V in the irradiation step. (b) NMR spectrum obtained at the cross section of (a) at an elapsed time of 10 s. The solid curve is a Gaussian fit for the spectrum. Also shown is the NMR spectrum “Steady,” in which the QW was set at the steady regime at $V_{sd}=280\mu$V in the irradiation step. Reference NMR spectra corresponding to $P_K=0$ and $P_K=1$ are shown at the top and the bottom, respectively. All the data shown in (b) were taken at $V_g=-1.60$ V. (c) $P_K$ obtained by the RDNMR (upper panel) and the equilibrium conductance (lower panel) as a function of $V_g$. The dotted curve in the upper panel is a guide to the eye.