Nuclear polarization in quantum point contacts in an in-plane magnetic field

Nuclear spin polarization is typically generated in GaAs quantum point contacts (QPCs) when an out-of-plane magnetic field gives rise to spin-polarized quantum-Hall edge states and a voltage bias drives transitions between the edge states via electron-nuclear flip-flop scattering. Here, we report a similar effect for QPCs in an in-plane magnetic field, where currents are spin polarized but edge states are not formed. The nuclear polarization gives rise to hysteresis in the dc transport characteristics with relaxation time scales around 100 s. The dependence of anomalous QPC conductance features on nuclear polarization provides a useful test of their spin sensitivity.

Figure 1

QPC nonlinear conductance and hysteresis. (a) Nonlinear conductance $G$ versus dc bias $V_{\text{dc}}$ for a range of gate voltages at $B_{\parallel }=0\text{T}$ and (b) $B_{\parallel }=4.9\text{T}$. (c) Nonlinear conductance curves showing hysteresis for $V_{\text{dc}}$ swept from negative to positive (solid) and from positive to negative (dashed). Labels 1–7 denote select curves from (b). (d) Hysteresis measured as deviation from average conductance (described in text) for corresponding curves 1–7 in (c). Arrow indicates vertical scale.

Figure 2

Evolution of ZBP and hysteresis in an in-plane magnetic field $B_{\parallel }$ from 0.12T to 1.46T (different QPC to that used for Fig. 1). Inset: $B_{\parallel }$ dependence of peak-height difference $\Delta Ph$ extracted from curves in main panel.

Figure 3

(a) Relaxation of zero-bias conductance away from its equilibrium value, $G_{eq}$, for various $T_{\text{P}}$ at $B_{\parallel }=4.4\text{T}$ (dot). Solid lines are fits of data to Eq. (1). Curves are offset horizontally by 500 s for clarity. Inset: zero-bias peak measured at the same gate voltage and $B_{\parallel }$. (b) Fits of Eq. (1) (solid) to conductance relaxation curves (dot) of another QPC defined in the same wafer. Black and gray curves represent polarizing bias $V_{\text{dc}}=-300\mu \text{V}$ and $+300\mu \text{V}$, respectively. Inset: hysteresis measured at the same gate voltage and $B_{\parallel }$.

Figure 4

[(a) and (b)] Examples of hysteresis effect that are more complicated than those shown in Fig. 2. [(c)–(f)] A transition between symmetric and antisymmetric conductance relaxation curves at $B_{\parallel }=4.9\text{T}$ as readout conductance decreases from $G=1.27e^2/h$ to $0.35e^2/h$ while keeping the conductance during the polarization step unchanged at $1.27e^2/h$. Black and gray curves correspond to $V_{\text{dc}}=-300\mu \text{V}$ and $+300\mu \text{V}$, respectively. (g) Zero-bias peaks measured at the same readout gate voltage as in (c)–(f).

Figure 5

(a) Comparison between measured ZBP at $B_{\parallel }=4.9\text{T}$ and the expected curve based on a simple Kondo-type splitting. The dashed line was calculated by taking the ZBP at $B_{\parallel }=0\text{T}$ and splitting it by $2g{\mu }_{\text{B}}{B}_{\parallel }$, using $g=0.44$. (b) Zero-bias conductance relaxation curves measured at settings for panel (a) $\left(B_{\parallel }=4.9\text{T}\right)$, indicating dependence of zero-bias-peak height on nuclear polarization in the QPC.