Strong coupling between a photon and a hole spin in silicon.

Spins in semiconductor quantum dots constitute a promising platform for scalable quantum information processing. Coupling them strongly to the photonic modes of superconducting microwave resonators would enable fast non-demolition readout and long-range, on-chip connectivity, well beyond nearest-neighbour quantum interactions. Here we demonstrate strong coupling between a microwave photon in a superconducting resonator and a hole spin in a silicon-based double quantum dot issued from a foundry-compatible metal-oxide-semiconductor fabrication process. By leveraging the strong spin-orbit interaction intrinsically present in the valence band of silicon, we achieve a spin-photon coupling rate as high as 330 MHz, largely exceeding the combined spin-photon decoherence rate. This result, together with the recently demonstrated long coherence of hole spins in silicon, opens a new realistic pathway to the development of circuit quantum electrodynamics with spins in semiconductor quantum dots.

Gate-based high fidelity spin readout in a CMOS device.

The engineering of a compact qubit unit cell that embeds all quantum functionalities is mandatory for large-scale integration. In addition, these functionalities should present the lowest error rate possible to successfully implement quantum error correction protocols1. Electron spins in silicon quantum dots are particularly promising because of their high control fidelity2-5 and their potential compatibility with complementary metal-oxide-semiconductor industrial platforms6,7. However, an efficient and scalable spin readout scheme is still missing. Here we demonstrate a high fidelity and robust spin readout based on gate reflectometry in a complementary metal-oxide-semiconductor device that consists of a qubit dot and an ancillary dot coupled to an electron reservoir. This scalable method allows us to read out a spin in a single-shot manner with an average fidelity above 98% for a 0.5 ms integration time. To achieve such a fidelity, we combine radio-frequency gate reflectometry with a latched spin blockade mechanism that requires electron exchange between the ancillary dot and the reservoir. We show that the demonstrated high readout fidelity is fully preserved up to 0.5 K. This result holds particular relevance for the future cointegration of spin qubits and classical control electronics.

Germanium Quantum-Well Josephson Field-Effect Transistors and Interferometers.

Hybrid superconductor-semiconductor structures attract increasing attention owing to a variety of potential applications in quantum computing devices. They can serve the realization of topological superconducting systems as well as gate-tunable superconducting quantum bits. Here, we combine a SiGe/Ge/SiGe quantum-well heterostructure hosting high-mobility two-dimensional holes and aluminum superconducting leads to realize prototypical hybrid devices, such as Josephson field-effect transistors (JoFETs) and superconducting quantum interference devices (SQUIDs). We observe gate-controlled supercurrent transport with Ge channels as long as one micrometer and estimate the induced superconducting gap from tunnel spectroscopy measurements. Transmission electron microscopy reveals the diffusion of Ge into the Al contacts, whereas no Al is detected in the Ge channel.

Electrical Spin Driving by g-Matrix Modulation in Spin-Orbit Qubits.

In a semiconductor spin qubit with sizable spin-orbit coupling, coherent spin rotations can be driven by a resonant gate-voltage modulation. Recently, we have exploited this opportunity in the experimental demonstration of a hole spin qubit in a silicon device. Here we investigate the underlying physical mechanisms by measuring the full angular dependence of the Rabi frequency, as well as the gate-voltage dependence and anisotropy of the hole g factor. We show that a g-matrix formalism can simultaneously capture and discriminate the contributions of two mechanisms so far independently discussed in the literature: one associated with the modulation of the g factor, and measurable by Zeeman energy spectroscopy, the other not. Our approach has a general validity and can be applied to the analysis of other types of spin-orbit qubits.

Split-Channel Ballistic Transport in an InSb Nanowire.

We report an experimental study of one-dimensional (1D) electronic transport in an InSb semiconducting nanowire. A total of three bottom gates are used to locally deplete the nanowire, creating a ballistic quantum point contact with only a few conducting channels. In a magnetic field, the Zeeman splitting of the corresponding 1D sub-bands is revealed by the emergence of conductance plateaus at multiples of e2/h, yet we find a quantized conductance pattern largely dependent on the configuration of voltages applied to the bottom gates. In particular, we can make the first plateau disappear, leaving a first conductance step of 2 e2/ h, which is indicative of a remarkable 2-fold sub-band degeneracy that can persist up to several tesla. For certain gate voltage settings, we also observe the presence of discrete resonant states producing conductance features that can resemble those expected from the opening of a helical gap in the sub-band structure. We explain our experimental findings through the formation of two spatially separated 1D conduction channels.

Level Spectrum and Charge Relaxation in a Silicon Double Quantum Dot Probed by Dual-Gate Reflectometry.

We report on dual-gate reflectometry in a metal-oxide-semiconductor double-gate silicon transistor operating at low temperature as a double quantum dot device. The reflectometry setup consists of two radio frequency resonators respectively connected to the two gate electrodes. By simultaneously measuring their dispersive responses, we obtain the complete charge stability diagram of the device. Electron transitions between the two quantum dots and between each quantum dot and either the source or the drain contact are detected through phase shifts in the reflected radio frequency signals. At finite bias, reflectometry allows probing charge transitions to excited quantum-dot states, thereby enabling direct access to the energy level spectra of the quantum dots. Interestingly, we find that in the presence of electron transport across the two dots the reflectometry signatures of interdot transitions display a dip-peak structure containing quantitative information on the charge relaxation rates in the double quantum dot.

Few-electron edge-state quantum dots in a silicon nanowire field-effect transistor.

We investigate the gate-induced onset of few-electron regime through the undoped channel of a silicon nanowire field-effect transistor. By combining low-temperature transport measurements and self-consistent calculations, we reveal the formation of one-dimensional conduction modes localized at the two upper edges of the channel. Charge traps in the gate dielectric cause electron localization along these edge modes, creating elongated quantum dots with characteristic lengths of ∼10 nm. We observe single-electron tunneling across two such dots in parallel, specifically one in each channel edge. We identify the filling of these quantum dots with the first few electrons, measuring addition energies of a few tens of millielectron volts and level spacings of the order of 1 meV, which we ascribe to the valley orbit splitting. The total removal of valley degeneracy leaves only a 2-fold spin degeneracy, making edge quantum dots potentially promising candidates for silicon spin qubits.

Spin-resolved Andreev levels and parity crossings in hybrid superconductor-semiconductor nanostructures.

The physics and operating principles of hybrid superconductor-semiconductor devices rest ultimately on the magnetic properties of their elementary subgap excitations, usually called Andreev levels. Here we report a direct measurement of the Zeeman effect on the Andreev levels of a semiconductor quantum dot with large electron g-factor, strongly coupled to a conventional superconductor with a large critical magnetic field. This material combination allows spin degeneracy to be lifted without destroying superconductivity. We show that a spin-split Andreev level crossing the Fermi energy results in a quantum phase transition to a spin-polarized state, which implies a change in the fermionic parity of the system. This crossing manifests itself as a zero-bias conductance anomaly at finite magnetic field with properties that resemble those expected for Majorana modes in a topological superconductor. Although this resemblance is understood without evoking topological superconductivity, the observed parity transitions could be regarded as precursors of Majorana modes in the long-wire limit.

Zero-bias anomaly in a nanowire quantum dot coupled to superconductors.

We studied the low-energy states of spin-1/2 quantum dots defined in InAs/InP nanowires and coupled to aluminum superconducting leads. By varying the superconducting gap Δ with a magnetic field B we investigated the transition from strong coupling Δ << T(K) to weak-coupling Δ >> T(K), where T(K) is the Kondo temperature. Below the critical field, we observe a persisting zero-bias Kondo resonance that vanishes only for low B or higher temperatures, leaving the room to more robust subgap structures at bias voltages between Δ and 2Δ. For strong and approximately symmetric tunnel couplings, a Josephson supercurrent is observed in addition to the Kondo peak. We ascribe the coexistence of a Kondo resonance and a superconducting gap to a significant density of intragap quasiparticle states, and the finite-bias subgap structures to tunneling through Shiba states. Our results, supported by numerical calculations, own relevance also in relation to tunnel-spectroscopy experiments aiming at the observation of Majorana fermions in hybrid nanostructures.

Multifunctional devices and logic gates with undoped silicon nanowires.

We report on the electronic transport properties of multiple-gate devices fabricated from undoped silicon nanowires. Understanding and control of the relevant transport mechanisms was achieved by means of local electrostatic gating and temperature-dependent measurements. The roles of the source/drain contacts and of the silicon channel could be independently evaluated and tuned. Wrap gates surrounding the silicide-silicon contact interfaces were proved to be effective in inducing a full suppression of the contact Schottky barriers, thereby enabling carrier injection down to liquid helium temperature. By independently tuning the effective Schottky barrier heights, a variety of reconfigurable device functionalities could be obtained. In particular, the same nanowire device could be configured to work as a Schottky barrier transistor, a Schottky diode, or a p-n diode with tunable polarities. This versatility was eventually exploited to realize a NAND logic gate with gain well above one.

Joule-assisted silicidation for short-channel silicon nanowire devices.

We report on a technique enabling electrical control of the contact silicidation process in silicon nanowire devices. Undoped silicon nanowires were contacted by pairs of nickel electrodes, and each contact was selectively silicided by means of the Joule effect. By a real-time monitoring of the nanowire electrical resistance during the contact silicidation process we were able to fabricate nickel-silicide/silicon/nickel-silicide devices with controlled silicon channel length down to 8 nm.

Hybrid superconductor-quantum dot devices.

Advances in nanofabrication techniques have made it possible to make devices in which superconducting electrodes are connected to non-superconducting nanostructures such as quantum dots. The properties of these hybrid devices result from a combination of a macroscopic quantum phenomenon involving large numbers of electrons (superconductivity) and the ability to control single electrons, offered by quantum dots. Here we review research into electron transport and other fundamental processes that have been studied in these devices. We also describe potential applications, such as a transistor in which the direction of a supercurrent can be reversed by adding just one electron to a quantum dot.

Andreev reflection versus Coulomb blockade in hybrid semiconductor nanowire devices.

Semiconductor nanowires provide promising low-dimensional systems for the study of quantum transport phenomena in combination with superconductivity. Here we investigate the competition between the Coulomb blockade effect, Andreev reflection, and quantum interference, in InAs and InP nanowires connected to aluminum-based superconducting electrodes. We compare three limiting cases depending on the tunnel coupling strength and the characteristic Coulomb interaction energy. For weak coupling and large charging energies, negative differential conductance is observed as a direct consequence of the BCS density of states in the leads. For intermediate coupling and charging energy smaller than the superconducting gap, the current-voltage characteristic is dominated by Andreev reflection and Coulomb blockade produces an effect only near zero bias. For almost ideal contact transparencies and negligible charging energies, we observe universal conductance fluctuations whose amplitude is enhanced because of Andreev reflection at the contacts.

Manganese-induced growth of GaAs nanowires.

GaAs nanowires have been grown on SiO2 and GaAs by molecular beam epitaxy using manganese as growth catalyst. Transmission electron microscopy shows that the wires have a wurtzite-type lattice and that alpha-Mn particles are found at the free end of the wires. X-ray absorption fine structure measurements reveal the presence of a significant fraction of Mn-As bonds, suggesting Mn diffusion and incorporation during wire growth. Transport measurements indicate that the wires are p-type, as expected from doping of GaAs with Mn.

Supercurrent reversal in quantum dots.

When two superconductors are electrically connected by a weak link--such as a tunnel barrier--a zero-resistance supercurrent can flow. This supercurrent is carried by Cooper pairs of electrons with a combined charge of twice the elementary charge, e. The 2e charge quantum is clearly visible in the height of voltage steps in Josephson junctions under microwave irradiation, and in the magnetic flux periodicity of h/2e (where h is Planck's constant) in superconducting quantum interference devices. Here we study supercurrents through a quantum dot created in a semiconductor nanowire by local electrostatic gating. Owing to strong Coulomb interaction, electrons only tunnel one-by-one through the discrete energy levels of the quantum dot. This nevertheless can yield a supercurrent when subsequent tunnel events are coherent. These quantum coherent tunnelling processes can result in either a positive or a negative supercurrent, that is, in a normal or a pi-junction, respectively. We demonstrate that the supercurrent reverses sign by adding a single electron spin to the quantum dot. When excited states of the quantum dot are involved in transport, the supercurrent sign also depends on the character of the orbital wavefunctions.

Tunable supercurrent through semiconductor nanowires.

Nanoscale superconductor/semiconductor hybrid devices are assembled from indium arsenide semiconductor nanowires individually contacted by aluminum-based superconductor electrodes. Below 1 kelvin, the high transparency of the contacts gives rise to proximity-induced superconductivity. The nanowires form superconducting weak links operating as mesoscopic Josephson junctions with electrically tunable coupling. The supercurrent can be switched on/off by a gate voltage acting on the electron density in the nanowire. A variation in gate voltage induces universal fluctuations in the normal-state conductance, which are clearly correlated to critical current fluctuations. The alternating-current Josephson effect gives rise to Shapiro steps in the voltage-current characteristic under microwave irradiation.

Orbital Kondo effect in carbon nanotubes.

Progress in the fabrication of nanometre-scale electronic devices is opening new opportunities to uncover deeper aspects of the Kondo effect--a characteristic phenomenon in the physics of strongly correlated electrons. Artificial single-impurity Kondo systems have been realized in various nanostructures, including semiconductor quantum dots, carbon nanotubes and individual molecules. The Kondo effect is usually regarded as a spin-related phenomenon, namely the coherent exchange of the spin between a localized state and a Fermi sea of delocalized electrons. In principle, however, the role of the spin could be replaced by other degrees of freedom, such as an orbital quantum number. Here we show that the unique electronic structure of carbon nanotubes enables the observation of a purely orbital Kondo effect. We use a magnetic field to tune spin-polarized states into orbital degeneracy and conclude that the orbital quantum number is conserved during tunnelling. When orbital and spin degeneracies are present simultaneously, we observe a strongly enhanced Kondo effect, with a multiple splitting of the Kondo resonance at finite field and predicted to obey a so-called SU4 symmetry.

Epitaxial growth of InP nanowires on germanium.

The growth of III-V semiconductors on silicon would allow the integration of their superior (opto-)electronic properties with silicon technology. But fundamental issues such as lattice and thermal expansion mismatch and the formation of antiphase domains have prevented the epitaxial integration of III-V with group IV semiconductors. Here we demonstrate the principle of epitaxial growth of III-V nanowires on a group IV substrate. We have grown InP nanowires on germanium substrates by a vapour-liquid-solid method. Although the crystal lattice mismatch is large (3.7%), the as-grown wires are monocrystalline and virtually free of dislocations. X-ray diffraction unambiguously demonstrates the heteroepitaxial growth of the nanowires. In addition, we show that a low-resistance electrical contact can be obtained between the wires and the substrate.