Field Tuning the $g$ Factor in InAs Nanowire Double Quantum Dots

We study the effects of magnetic and electric fields on the $g$ factors of spins confined in a two-electron InAs nanowire double quantum dot. Spin sensitive measurements are performed by monitoring the leakage current in the Pauli blockade regime. Rotations of single spins are driven using electric-dipole spin resonance. The $g$ factors are extracted from the spin resonance condition as a function of the magnetic field direction, allowing determination of the full $g$ tensor. Electric and magnetic field tuning can be used to maximize the $g$-factor difference and in some cases altogether quench the electric-dipole spin resonance response, allowing selective single spin control.

Figure 1

(a) Scanning electron microscope image illustrating the device geometry. Four gates are sufficient to fully define the double quantum dot with this device, resulting in a double well confinement potential. The double dot’s coupling to the right and left leads are controlled with voltages $V_{\mathrm{rw}}$ and $V_{\mathrm{lw}}$, respectively, while $V_{\mathrm{rp}}$ and $V_{\mathrm{lp}}$ control the interdot coupling and occupation. (b) Current measured through the device as a function of gate voltages $V_{\mathrm{rp}}$ and $V_{\mathrm{lp}}$, with source drain bias $V_{\mathrm{sd}}=-4\mathrm{mV}$. Dashed lines are superimposed to illustrate the double dot charge stability diagram. Left inset: $(1,1)\leftrightarrow (2,0)$ transition at $V_{\mathrm{sd}}=+4\mathrm{mV}$. The apparent excited state is a resonance associated with the one-dimensional leads that contact the double quantum dot [12]. Right inset: $(1,1)\leftrightarrow (2,0)$ transition at $V_{\mathrm{sd}}=-4\mathrm{mV}$. The current in the insets has been multiplied by a factor of 2.

Figure 2

Leakage current measured as a function of the magnetic field and applied frequency for (a) $\mathbf{B}\parallel \widehat{z}$ and (b) $\mathbf{B}\parallel (\widehat{x}+\widehat{z})$. The zero field peak, shown in (c), is due to hyperfine field mixing of the spin states, with a fit to the data yielding $B_N=3.3\mathrm{mT}$. The spin resonance condition is satisfied when $hf=g{\mu }_B|\mathbf{B}|$, resulting in a peak in the leakage current. Cuts through the data in (a) and (b) are shown in (d), demonstrating the dependence of the $g$ factors on magnetic field direction. The upper trace is offset by 0.3 pA for clarity.

Figure 3

(a)–(c) Leakage current measured as a function of magnetic field direction and frequency for the rotations depicted in the insets below. The $y$ axes have been rescaled from frequency to units of $g$, taking a fixed magnetic field amplitude of 80 mT; all angles are radians. In this coordinate system, the unit vector describing the nanowire axis is approximately $(\theta ,\varphi )=(1.2,3.1)$. A fit to Eq. (1) has been superimposed on the data. (d)–(f) Pumped current extracted from the upper resonances in (a)–(c), along with a fit to Eq. (3).

Figure 4

(a) Measured current through the double dot as a function of $V_{\mathrm{lp}}$ and $V_{\mathrm{rp}}$ for $V_{\mathrm{sd}}=-4\mathrm{mV}$ in the case of unbalanced tuning. (b)–(d) Evolution of the resonance condition for magnetic field rotations about the $x$, $y$, and $z$ axes, respectively. In (b)–(d) the $y$ axes have been rescaled into units of $g$, taking a fixed magnetic field amplitude of 80 mT.