High-energy quasiparticle injection into mesoscopic superconductors

High-Performance Gate-Controlled Superconducting Switches: Large Output Voltage and Reproducibility

Logic circuits consist of devices that can be controlled between two distinct states. The recent demonstration that a superconducting current flowing in a constriction can be controlled via a gate voltage (VG)─gate-controlled supercurrent (GCS)─can lead to superconducting logic with better performance than existing logics. However, before such logic is developed, high reproducibility in the functioning of GCS devices and optimization of their performance must be achieved. Here, we report an investigation of gated Nb devices showing GCS with very high reproducibility. Based on the investigation of a statistically significant number of devices, we demonstrate that the GCS is independent of the constriction width, in contrast with previous reports, and confirm a strong correlation between the GCS and the leakage current (Ileak) induced by VG. We also achieve a voltage output in our devices larger than the typical values reported to date by at least 1 order of magnitude, which is relevant for the future interconnection of devices, and show that Ileak can be used as a tool to modulate the operational VG of devices on a SiO2 substrates. These results altogether represent an important step forward toward the optimization of reproducibility and performance of GCS devices, and the future development of a GCS-based logic.

Heat Dissipation Mechanisms in Hybrid Superconductor-Semiconductor Devices Revealed by Joule Spectroscopy

Understanding heating and cooling mechanisms in mesoscopic superconductor-semiconductor devices is crucial for their application in quantum technologies. Owing to their poor thermal conductivity, heating effects can drive superconducting-to-normal transitions even at low bias, observed as sharp conductance dips through the loss of Andreev excess currents. Tracking such dips across magnetic field, cryostat temperature, and applied microwave power allows us to uncover cooling bottlenecks in different parts of a device. By applying this "Joule spectroscopy" technique, we analyze heat dissipation in devices based on InAs-Al nanowires and reveal that cooling of superconducting islands is limited by the rather inefficient electron-phonon coupling, as opposed to grounded superconductors that primarily cool by quasiparticle diffusion. We show that powers as low as 50-150 pW are able to suppress superconductivity on the islands. Applied microwaves lead to similar heating effects but are affected by the interplay of the microwave frequency and the effective electron-phonon relaxation time.

Utilizing Gate-Controlled Supercurrent for All-Metallic Tunable Superconducting Microwave Resonators

Hybridizing a microwave mode with a quantum state requires precise frequency matching of a superconducting microwave resonator and the corresponding quantum object. However, fabrication always brings imperfections in geometry and material properties, causing deviations from the desired operating frequencies. An effective and universal strategy for their resonant coupling is to tune the frequency of a resonator, as quantum states like phonons are hardly tunable. Here, we demonstrate gate-tunable, titanium-nitride (TiN)-based superconducting resonators by implementing a nanowire inductor whose kinetic inductance is tuned via the gate-controlled supercurrent (GCS) effect. We investigate their responses for different gate biases and observe 4% (∼150 MHz) frequency tuning with decreasing internal quality factors. We also perform temperature-controlled experiments to support phonon-related mechanisms in the GCS effect and the resonance tuning. The GCS effect-based method proposed in this study provides an effective route for locally tunable resonators that can be employed in various hybrid quantum devices.

Signatures of Gate-Driven Out-of-Equilibrium Superconductivity in Ta/InAs Nanowires

Understanding the microscopic origin of the gate-controlled supercurrent (GCS) in superconducting nanobridges is crucial for engineering superconducting switches suitable for a variety of electronic applications. The origin of GCS is controversial, and various mechanisms have been proposed to explain it. In this work, we have investigated the GCS in a Ta layer deposited on the surface of InAs nanowires. Comparison between switching current distributions at opposite gate polarities and between the gate dependence of two opposite side gates with different nanowire-gate spacings shows that the GCS is determined by the power dissipated by the gate leakage. We also found a substantial difference between the influence of the gate and elevated bath temperature on the magnetic field dependence of the supercurrent. Detailed analysis of the switching dynamics at high gate voltages shows that the device is driven into the multiple phase slips regime by high-energy fluctuations arising from the leakage current.

Spin-Mixing Enhanced Proximity Effect in Aluminum-Based Superconductor-Semiconductor Hybrids

In superconducting quantum circuits, aluminum is one of the most widely used materials. It is currently also the superconductor of choice for the development of topological qubits. However, aluminum-based devices suffer from poor magnetic field compatibility. Herein, this limitation is resolved by showing that adatoms of heavy elements (e.g., platinum) increase the critical field of thin aluminum films by more than a factor of two. Using tunnel junctions, it is shown that the increased field resilience originates from spin-orbit scattering introduced by Pt. This property is exploited in the context of the superconducting proximity effect in semiconductor-superconductor hybrids, where it is shown that InSb nanowires strongly coupled to Al/Pt films can maintain superconductivity up to 7 T. The two-electron charging effect is shown to be robust against the presence of heavy adatoms. Additionally, non-local spectroscopy is used in a three-terminal geometry to probe the bulk of hybrid devices, showing that it remains free of sub-gap states. Finally, it is demonstrated that proximitized semiconductor states maintain their ability to Zeeman-split in an applied magnetic field. Combined with the chemical stability and well-known fabrication routes of aluminum, Al/Pt emerges as the natural successor to Al-based systems and is a compelling alternative to other superconductors, whenever high-field resilience is required.

Dimensional crossovers in the Gaussian critical fluctuations above Tc of two-layer and three-layer superconductors

By using a Ginzburg–Landau functional in the Gaussian approximation, we calculate the energy of superconducting fluctuations above the transition, at zero external magnetic field, of a system composed by a small number N of parallel two-dimensional superconducting planes, each of them Josephson coupled to its first neighbour, with special focus in the N = 2 and 3 cases. This allows us to obtain expressions for the critical contributions to various observables (fluctuation specific heat and magnetic susceptibility and Aslamazov–Larkin paraconductivity). Our results suggest that these systems may display deviations from pure 2D behaviour and interesting crossover effects, with both similitudes and differences to those known to occur in infinite-layers superconductors. Some challenges for future related research are also outlined.

Superconducting Materials and Devices Grown by Focused Ion and Electron Beam Induced Deposition

Since its discovery in 1911, superconductivity has represented an equally inciting and fascinating field of study in several areas of physics and materials science, ranging from its most fundamental theoretical understanding, to its practical application in different areas of engineering. The fabrication of superconducting materials can be downsized to the nanoscale by means of Focused Ion/Electron Beam Induced Deposition: nanopatterning techniques that make use of a focused beam of ions or electrons to decompose a gaseous precursor in a single step. Overcoming the need to use a resist, these approaches allow for targeted, highly-flexible nanopatterning of nanostructures with lateral resolution in the range of 10 nm to 30 nm. In this review, the fundamentals of these nanofabrication techniques are presented, followed by a literature revision on the published work that makes use of them to grow superconducting materials, the most remarkable of which are based on tungsten, niobium, molybdenum, carbon, and lead. Several examples of the application of these materials to functional devices are presented, related to the superconducting proximity effect, vortex dynamics, electric-field effect, and to the nanofabrication of Josephson junctions and nanoSQUIDs. Owing to the patterning flexibility they offer, both of these techniques represent a powerful and convenient approach towards both fundamental and applied research in superconductivity.

An electron turnstile for frequency-to-power conversion

Single-electron transport relates an operation frequency f to the emitted current I through the electron charge e as I = ef (refs. ^1-5). Similarly, direct frequency-to-power conversion (FPC) links both quantities through a known energy. FPC is a natural candidate for a power standard resorting to the most basic definition of the watt: energy emitted per unit of time. The energy is traceable to Planck's constant and the time is in turn traceable to the unperturbed ground state hyperfine transition frequency of the caesium 133 atom. Hence, FPC comprises a simple and elegant way to realize the watt⁶. In this spirit, single-photon emission^7,8 and detection⁹ at known rates have been proposed as radiometric standards and experimentally realized^10-14. However, power standards are so far only traceable to electrical units, that is, to the volt and the ohm^6,15-17. In this Letter, we demonstrate an alternative proposal based on solid-state direct FPC using a hybrid single-electron transistor (SET). The SET injects n (integer) quasi-particles (QPs) per cycle into the two superconducting leads with discrete energies close to their superconducting gap Δ, even at zero source-drain voltage. Furthermore, the application of a bias voltage can vary the distribution of the power among the two leads, allowing for an almost equal power injection nΔf into the two. While in single-electron transport current is related to a fixed universal constant (e), in our approach Δ is a material-dependent quantity. We estimate that under optimized conditions errors can be well below 1%.

Out-of-equilibrium phonons in gated superconducting switches

Recent experiments have suggested that superconductivity in metallic nanowires can be suppressed by the application of modest gate voltages. The source of this gate action has been debated and either attributed to an electric-field effect or to small leakage currents. Here we show that the suppression of superconductivity in titanium nitride nanowires on silicon substrates does not depend on the presence or absence of an electric field at the nanowire, but requires a current of high-energy electrons. The suppression is most efficient when electrons are injected into the nanowire, but similar results are obtained when electrons are passed between two remote electrodes. This is explained by the decay of high-energy electrons into phonons, which propagate through the substrate and affect superconductivity in the nanowire by generating quasiparticles. By studying the switching probability distribution of the nanowire, we also show that high-energy electron emission leads to a much broader phonon energy distribution compared with the case where superconductivity is suppressed by Joule heating near the nanowire.

Electrostatic Field-Driven Supercurrent Suppression in Ionic-Gated Metallic Superconducting Nanotransistors

Recent experiments have shown the possibility of tuning the transport properties of metallic nanosized superconductors through a gate voltage. These results renewed the longstanding debate on the interaction between electrostatic fields and superconductivity. Indeed, different works suggested competing mechanisms as the cause of the effect: an unconventional electric field-effect or quasiparticle injection. Here, we provide conclusive evidence for the electrostatic-field-driven control of the supercurrent in metallic nanosized superconductors, by realizing ionic-gated superconducting field-effect nanotransistors (ISFETs) where electron injection is impossible. Our Nb ISFETs show giant suppression of the superconducting critical current of up to ∼45%. Moreover, the bipolar supercurrent suppression observed in different ISFETs, together with invariant critical temperature and normal-state resistance, also excludes conventional charge accumulation/depletion. Therefore, the microscopic explanation of this effect calls upon a novel theory able to describe the nontrivial interaction of static electric fields with conventional superconductivity.

Gate-Controlled Supercurrent in Epitaxial Al/InAs Nanowires

Gate-controlled supercurrent (GCS) in superconducting nanobridges has recently attracted attention as a means to create superconducting switches. Despite the clear advantages for applications, the microscopic mechanism of this effect is still under debate. In this work, we realize GCS for the first time in a highly crystalline superconductor epitaxially grown on an InAs nanowire. We show that the supercurrent in the epitaxial Al layer can be switched to the normal state by applying ≃±23 V on a bottom gate insulated from the nanowire by a crystalline hBN layer. Our extensive study of the temperature and magnetic field dependencies suggests that the electric field is unlikely to be the origin of GCS in our device. Though hot electron injection alone cannot explain our experimental findings, a very recent non-equilibrium phonons based picture is compatible with most of our results.

Gate Control of the Current-Flux Relation of a Josephson Quantum Interferometer Based on Proximitized Metallic Nanojuntions

We demonstrate an Al superconducting quantum interference device in which the Josephson junctions are implemented through gate-controlled proximity Cu mesoscopic weak links. This specific kind of metallic weak links behaves analogously to genuine superconducting metals in terms of the response to electrostatic gating and provides a good performance in terms of current-modulation visibility. We show that through the application of a static gate voltage we can modify the interferometer current-flux relation in a fashion that seems compatible with the introduction of π-channels within the gated weak link. Our results suggest that the microscopic mechanism at the origin of the suppression of the switching current in the interferometer is apparently phase coherent, resulting in an overall damping of the superconducting phase rigidity. We finally tackle the performance of the interferometer in terms of responsivity to magnetic flux variations in the dissipative regime and discuss the practical relevance of gated proximity-based all-metallic SQUIDs for magnetometry at the nanoscale.

Critical current modulation induced by an electric field in superconducting tungsten-carbon nanowires

The critical current of a superconducting nanostructure can be suppressed by applying an electric field in its vicinity. This phenomenon is investigated throughout the fabrication and electrical characterization of superconducting tungsten-carbon (W-C) nanostructures grown by Ga[Formula: see text] focused ion beam induced deposition (FIBID). In a 45 nm-wide, 2.7 [Formula: see text]m-long W-C nanowire, an increasing side-gate voltage is found to progressively reduce the critical current of the device, down to a full suppression of the superconducting state below its critical temperature. This modulation is accounted for by the squeezing of the superconducting current by the electric field within a theoretical model based on the Ginzburg-Landau theory, in agreement with experimental data. Compared to electron beam lithography or sputtering, the single-step FIBID approach provides with enhanced patterning flexibility and yields nanodevices with figures of merit comparable to those retrieved in other superconducting materials, including Ti, Nb, and Al. Exhibiting a higher critical temperature than most of other superconductors, in which this phenomenon has been observed, as well as a reduced critical value of the gate voltage required to fully suppress superconductivity, W-C deposits are strong candidates for the fabrication of nanodevices based on the electric field-induced superconductivity modulation.

On the origin of the controversial electrostatic field effect in superconductors

Superconducting quantum devices offer numerous applications, from electrical metrology and magnetic sensing to energy-efficient high-end computing and advanced quantum information processing. The key elements of quantum circuits are (single and double) Josephson junctions controllable either by electric current or magnetic field. The voltage control, commonly used in semiconductor-based devices via the electrostatic field effect, would be far more versatile and practical. Hence, the field effect recently reported in superconducting devices may revolutionise the whole field of superconductor electronics provided it is confirmed. Here we show that the suppression of the critical current attributed to the field effect, can be explained by quasiparticle excitations in the constriction of superconducting devices. Our results demonstrate that a miniscule leakage current between the gate and the constriction of devices perfectly follows the Fowler-Nordheim model of electron field emission from a metal electrode and injects quasiparticles with energies sufficient to weaken or even suppress superconductivity.

A recent report on electrostatic field effect in superconducting devices provides a high potential for advanced quantum technology, but it remains controversial. Here, the authors report that the suppression of critical current, which was attributed to the field effect, can instead be explained by quasiparticle excitations in the constriction of superconducting devices.

Sauter-Schwinger Effect in a Bardeen-Cooper-Schrieffer Superconductor

Since the 1960s a deep and surprising connection has followed the development of superconductivity and quantum field theory. The Anderson-Higgs mechanism and the similarities between the Dirac and Bogoliubov-de Gennes equations are the most intriguing examples. In this last analogy, the massive Dirac particle is identified with a quasiparticle excitation and the fermion mass energy with the superconducting gap energy. Here we follow further this parallelism and show that it predicts an outstanding phenomenon: the superconducting Sauter-Schwinger effect. As in the quantum electrodynamics Schwinger effect, where an electron-positron couple is created from the vacuum by an intense electric field, we show that an electrostatic field can generate two coherent excitations from the superconducting ground-state condensate. Differently from the dissipative thermal excitation, these form a new macroscopically coherent and dissipationless state. We discuss how the superconducting state is weakened by the creation of this kind of excitations. In addition to shedding a different light and suggesting a method for the experimental verification of the Sauter-Schwinger effect, our results pave the way to the understanding and exploitation of the interaction between superconductors and electric fields.

Gate Control of Superconductivity in Mesoscopic All-Metallic Devices

The possibility to tune, through the application of a control gate voltage, the superconducting properties of mesoscopic devices based on Bardeen-Cooper-Schrieffer metals was recently demonstrated. Despite the extensive experimental evidence obtained on different materials and geometries, a description of the microscopic mechanism at the basis of such an unconventional effect has not been provided yet. This work discusses the technological potential of gate control of superconductivity in metallic superconductors and revises the experimental results, which provide information regarding a possible thermal origin of the effect: first, we review experiments performed on high-critical-temperature elemental superconductors (niobium and vanadium) and show how devices based on these materials can be exploited to realize basic electronic tools, such as a half-wave rectifier. Second, we discuss the origin of the gating effect by showing gate-driven suppression of the supercurrent in a suspended titanium wire and by providing a comparison between thermal and electric switching current probability distributions. Furthermore, we discuss the cold field-emission of electrons from the gate employing finite element simulations and compare the results with experimental data. In our view, the presented data provide a strong indication regarding the unlikelihood of the thermal origin of the gating effect.