Few-Electron Single and Double Quantum Dots in an $\mathrm{In}\mathrm{As}$ Two-Dimensional Electron Gas

Most proof-of-principle experiments for spin qubits have been performed with $\mathrm{Ga}\mathrm{As}$-based quantum dots because of the excellent control they offer over tunneling barriers and the orbital and spin degrees of freedom. Here we present the first realization of high-quality single and double quantum dots hosted in an $\mathrm{In}\mathrm{As}$ two-dimensional electron gas, demonstrating accurate control down to the few-electron regime, where we observe a clear Kondo effect and singlet-triplet spin blockade. We measure an electronic $g$ factor of 16 and a typical magnitude of the random hyperfine fields on the quantum dots of approximately $0.6\mathrm{mT}$. We estimate the spin-orbit length in the system to be approximately $5-10\mu \mathrm{m}$ (which is almost 2 orders of magnitude longer than typically measured in $\mathrm{In}\mathrm{As}$ nanostructures), achieved by a very symmetric design of the quantum well. These favorable properties put the $\mathrm{In}\mathrm{As}$ two-dimensional electron gas on the map as a compelling host for studying fundamental aspects of spin qubits. Furthermore, having weak spin-orbit coupling in a material with a large Rashba coefficient potentially opens up avenues for engineering structures with spin-orbit coupling that can be controlled locally in space and/or time.

Popular Summary

A future quantum computer requires quantum bits, called “qubits,” that can be precisely controlled and offer long lifetimes of their quantum states. The intrinsic magnetic moment of an electron described by the so-called spin is a natural qubit. Spins of a single electron or a few electrons trapped in semiconductor quantum dots have emerged as one of the contenders in the worldwide competition for the best qubit, which also includes approaches using superconducting circuits or ion traps. The quest for the best qubit system is open. For spin qubits, several material platforms are competing in view of being compatible with standard semiconductor technology, offering long lifetimes and exquisite control and readout of the quantum states.

The basic properties of spins in quantum dots have so far been investigated mostly in gallium arsenide. For industrial applications, silicon offers straightforward integration into commercial production lines. Here we succeed in investigating for the first time gate-defined indium arsenide quantum dots, which offer advantages in view of the intrinsic material properties.

We fabricate quantum dots in indium arsenide electron gases that are as stable and controllable as the well-established gallium arsenide quantum dots considered to be the benchmark in this field. We observe fundamental quantum effects, such as the spin-related Kondo effect, controlled trapping of a few electrons, and Pauli spin blockade, a prerequisite for the readout of spin states. Compared with gallium arsenide, indium arsenide offers a smaller effective electron mass, leading to larger confinement energies and possibly higher operation temperatures, as well as a factor of 30 larger $g$ factor promising faster spin manipulation

Figure 1

(a) Three-dimensional view of sample geometry with a cross section of the heterostructure used. The 24-nm-wide $\mathrm{In}\mathrm{As}$ quantum well (lower blue layer) is sandwiched by two 20-nm ($\mathrm{Al}$,$\mathrm{Ga}$)$\mathrm{Sb}$ barriers (red) and capped with a 1.5-nm $\mathrm{In}\mathrm{As}$ layer (upper blue layer). Multiple layers of gates separated by ${\mathrm{Al}}_2{\mathrm{O}}_3$ dielectric layers create a device used to form single and double quantum dots. (b) Scanning electron micrograph of the gate layout of a device similar to the one used in this study. (c) Coulomb resonances in the conductance $G$ through the left quantum dot as a function of $V_{\mathrm{PGL}}$. (d) Coulomb blockade diamond visible in the differential conductance as a function of $V_{\mathrm{PGL}}$ and $V_{\mathrm{dc}}$. Uninterrupted Coulomb resonances up to $V_{\mathrm{dc}}=\pm 10\mathrm{mV}$ and the absence of additional resonances indicate the loading of the first electron.

Figure 2

(a) Coulomb blockade diamonds corresponding to the loading of the first two electrons. A resonance corresponding to the transition to an excited state branches off the two-electron Coulomb blockade diamond at $V_{\mathrm{dc}}=-3.9\mathrm{mV}$. (b) Magnetic field dependence of the resonances along the dashed white line in (a). (c) Enlargement of the dashed yellow box in (b). A linear Zeeman splitting of the resonances corresponding to the loading of the first electron is visible. (d) Enlargement the dashed blue box in (b), where a direct crossing of the resonances corresponding to the spin singlet and a spin triplet state is observed.

Figure 3

(a) Coulomb blockade diamond in the conduction of the left quantum dot for strong coupling to the leads as a function of $V_{\mathrm{dc}}$ and $V_{\mathrm{PGL}}$ at $B=0$. A clear zero-bias conductance peak indicates the observation of the Kondo effect. (b) Same as in (a) but at an external magnetic field of $B_{\parallel }=150\mathrm{mT}$ causing a Zeeman splitting of the Kondo resonance. (c) Dependence of the Zeeman splitting of the Kondo resonance on $B_{\parallel }$ recorded at $V_{\mathrm{PGL}}=-933\mathrm{mV}$ marked by the dashed arrow in (a). (d) Temperature dependence of the peak conductance of the Kondo resonance.

Figure 4

Charge stability diagram visible in the logarithm of the conductance $G$ of the double quantum dot system. Regions of stable charge occupancy are labeled with tuples $(N_L,N_R)$ where $N_L$ ($N_R$) indicates the occupancy of the left (right) quantum dot.

Figure 5

(a) Magnitude of the current $|I_{\mathrm{dc}}|$ through the double quantum dot system at finite bias of $V_{\mathrm{dc}}=+500\mathrm{mV}$ ($V_{\mathrm{dc}}=-500\mathrm{mV}$) in the left (right) panel. Electron transport involves the internal (1,2) to (0,3) transition (left) and (0,3) to (1,2) transition (right). As expected, in both cases current can flow, resulting in finite bias triangles. (b) $|I_{\mathrm{dc}}|$ involving the (1,3) to (0,4) transition (left) and the (0,4) to (1,3) transition (right). The triangles involving the transition from (1,3) to (0,4) occupancy at $V_{\mathrm{dc}}=+500\mathrm{mV}$ show an absence of current due to singlet-triplet spin blockade by Pauli exclusion. (c) $|I_{\mathrm{dc}}|$ involving the (2,2) to (1,3) transition (left) and the (1,3) to (2,2) transition (right). The transition from (1,3) to (2,2) occupancy at $V_{\mathrm{dc}}=-500\mathrm{mV}$ is blocked.

Figure 6

(a) Dependence of the magnitude of the leakage current $|I_{\mathrm{dc}}|$ through the spin blockade involving the (1,3) to (0,4) transition for strong interdot tunnel coupling on $\delta$ and $B_{\parallel }$. A dip around zero external magnetic field is visible in the data. (b) High-resolution trace of $|I_{\mathrm{dc}}|$ as a function of $B_{\parallel }$ around zero detuning. (c) $\delta$-dependent leakage current $|I_{\mathrm{dc}}|$ at $B_{\parallel }=700\mathrm{mT}$ (blue) and a Lorentzian fit to the onset of the peak (green) disregarding the inelastic current tail. (d) Peak current values $I_{\max }$ for $|B_{\parallel }|>500\mathrm{mT}$, where the gray shaded area indicates the magnitude of the error of each fit. Their field-independent height suggests spin-orbit coupling as the main mechanism responsible for spin-flip tunneling rather than hyperfine coupling.

Figure 7

(a) Magnitude of the current $|I_{\mathrm{dc}}|$ through the double quantum dot system for weak interdot tunnel coupling and at a finite bias of $V_{\mathrm{dc}}=+500\mu \mathrm{V}$, close to the triple points involving the (2,2) to (1,3) transition. (b) Transitions from (1,3) to (2,2) at $V_{\mathrm{dc}}=-500\mu \mathrm{V}$ are suppressed due to singlet-triplet spin blockade. For weak interdot tunnel coupling, a leakage current is observed when the tunneling process is resonant. (c) Dependence of this leakage current on $\delta$ and $B_{\parallel }$. A narrow resonance around zero external magnetic field is observed. (d) Enlargement of the dashed yellow box in (c) showing more clearly the zero-field resonance arising from hyperfine coupling to the nuclear spins of the host crystal. The offset from $B_{\parallel }=0$ is due to residual magnetization in our experimental setup.