Suppression of Spin Relaxation in an InAs Nanowire Double Quantum Dot

We investigate the triplet-singlet relaxation in a double quantum dot defined by top gates in an InAs nanowire. In the Pauli spin blockade regime, the leakage current can be mainly attributed to spin relaxation. While at weak and strong interdot coupling relaxation is dominated by two individual mechanisms, the relaxation is strongly reduced at intermediate coupling and finite magnetic field. In addition we observe a characteristic bistability of the spin-nonconserving current as a function of magnetic field. We propose a model where these features are explained by the polarization of nuclear spins enabled by the interplay between hyperfine and spin-orbit mediated relaxation.

Figure 1

(a) Scanning electron microscope image of a device equivalent to the one measured. The current $I_{\mathrm{SD}}$ for an applied source-drain voltage $V_{\mathrm{SD}}$ is measured between the outer contacts to the NW. Voltages on the top gates $G1$, $G2$, $GC$ create a double quantum dot. (b) Level scheme and relaxation rates inside the spin blockaded region. A small magnetic field splits the triplets by $\Delta E_Z$. Fluctuating nuclear spins lead to relaxation of the triplets to the singlets with rates ${\Gamma }_{0,\pm }$ over the splitting $ϵ$. The singlet $S(0,2)$ is coupled to the drain lead with the rate ${\Gamma }_D$. Alternative processes such as spin-orbit mediated relaxation (${\Gamma }^{\prime }$) and cotunneling (${\Gamma }^{\prime \prime }$) are sketched. (c) Current $I_{\mathrm{SD}}$ as a function of gate voltages $V_{G1}$ and $V_{G2}$ for $V_{\mathrm{SD}}=3\mathrm{mV}$. Spin blockade suppresses current in the base region of the triangle. Variation of $V_{G1}$, $V_{G2}$ along the dotted white line detunes the levels in the dot with respect to each other by an energy ${\Delta }_{12}$. At large detuning, current can flow via $T(0,2)$ (red dashed line in inset, white arrow in main panel). (d) For reverse bias, current can always flow via $(0,1)\to (0,2)\to (1,1)\to (0,1)$ (inset). The white arrow indicates the onset of transport via $T(0,2)$.

Figure 2

(a) Plot of $I_{\mathrm{SD}}$ for weakly coupled dots $V_{GC}=-175\mathrm{mV}$). The $B$ field is stepped after each gate sweep. $V_{G1}$ and $V_{G2}$ are changed together to vary the detuning ${\Delta }_{12}$ [see Fig. 1c]. (b) Same for strong coupling ($V_{GC}=-128\mathrm{mV}$). (b) For slightly decreased coupling ($V_{GC}=-129\mathrm{mV}$), relaxation current is suppressed in a region of size $\Delta B$.

Figure 3

Measurements corresponding to Fig. 2c, but sweeping the magnetic field and stepping the gate voltages after each trace. (a) Up sweeps $-120\mathrm{mT}$ to $+100\mathrm{mT}$. Inset: Size $\Delta B$ of the region with reduced relaxation current as defined in Fig. 2c for different coupling, tuned by $V_{GC}$. (b) Down sweeps. Inset: Current traces for variation of the gate voltages starting from point $X$ demonstrating the bistability. The high-current state is stable, once the gates are tuned out of the region of suppressed relaxation.

Figure 4

(a) Dependence of the singlet branches $S$ and triplets $T_{0,\pm }(1,1)$ on the detuning ${\Delta }_{12}$ of the dot levels. (b) Evolution of the triplet energies at fixed ${\Delta }_{12}$ for up and down sweeps of the magnetic field, including the influence of DNSP. Arrows indicate the sweep direction. (c) Current traces along the dashed line in Fig. 3a. Up sweeps (green) and down sweeps (black). The dotted curve for strong coupling [along dashed line in Fig. 2b] does not exhibit bistability. (d) Same for different temperatures.