On the origin of the controversial electrostatic field effect in superconductors

Switching dynamics in Al/InAs nanowire-based gate-controlled superconducting switch

The observation of the gate-controlled supercurrent (GCS) effect in superconducting nanostructures increased the hopes for realizing a superconducting equivalent of semiconductor field-effect transistors. However, recent works attribute this effect to various leakage-based scenarios, giving rise to a debate on its origin. A proper understanding of the microscopic process underlying the GCS effect and the relevant time scales would be beneficial to evaluate the possible applications. In this work, we observed gate-induced two-level fluctuations between the superconducting state and normal state in Al/InAs nanowires (NWs). Noise correlation measurements show a strong correlation with leakage current fluctuations. The time-domain measurements show that these fluctuations have Poissonian statistics. Our detailed analysis of the leakage current measurements reveals that it is consistent with the stress-induced leakage current (SILC), in which inelastic tunneling with phonon generation is the predominant transport mechanism. Our findings shed light on the microscopic origin of the GCS effect and give deeper insight into the switching dynamics of the superconducting NW under the influence of the strong gate voltage.

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.

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.

Gate-Tunable Critical Current of the Three-Dimensional Niobium Nanobridge Josephson Junction

Recent studies have shown that the critical currents of several metallic superconducting nanowires and Dayem bridges can be locally tuned by using a gate voltage (Vg). Here, we report a gate-tunable Josephson junction structure constructed from a three-dimensional (3D) niobium nanobridge junction (NBJ) with a voltage gate on top. Measurements up to 6 K showed that the critical current of this structure can be tuned to zero by increasing Vg. The critical gate voltage was reduced to 16 V and may possibly be reduced further by reducing the thickness of the insulation layer between the gate and the NBJ. Furthermore, the flux modulation generated by Josephson interference of two parallel 3D NBJs can also be tuned by using Vg in a similar manner. Therefore, we believe that this gate-tunable Josephson junction structure is promising for superconducting circuit fabrication at high integration levels.

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.

Diamagnetic mechanism of critical current non-reciprocity in multilayered superconductors

The suggestion that non-reciprocal critical current (NRC) may be an intrinsic property of non-centrosymmetric superconductors has generated renewed theoretical and experimental interest motivated by an analogy with the non-reciprocal resistivity due to the magnetochiral effect in uniform materials with broken spatial and time-reversal symmetry. Theoretically it has been understood that terms linear in the Cooper pair momentum do not contribute to NRC, although the role of higher-order terms remains unclear. In this work we show that critical current non-reciprocity is a generic property of multilayered superconductor structures in the presence of magnetic field-generated diamagnetic currents. In the regime of an intermediate coupling between the layers, the Josephson vortices are predicted to form at high fields and currents. Experimentally, we report the observation of NRC in nanowires fabricated from InAs/Al heterostructures. The effect is independent of the crystallographic orientation of the wire, ruling out an intrinsic origin of NRC. Non-monotonic NRC evolution with magnetic field is consistent with the generation of diamagnetic currents and formation of the Josephson vortices. This extrinsic NRC mechanism can be used to design novel devices for superconducting circuits.

Microwave response of a metallic superconductor subject to a high-voltage gate electrode

Processes that lead to the critical-current suppression and change of impedance of a superconductor under the application of an external voltage is an active area of research, especially due to various possible technological applications. In particular, field-effect transistors and radiation detectors have been developed in the recent years, showing the potential for precision and sensitivity exceeding their normal-metal counterparts. In order to describe the phenomenon that leads to the critical-current suppression in metallic superconducting structures, a field-effect hypothesis has been formulated, stating that an electric field can penetrate the metallic superconductor and affect its characteristics. The existence of such an effect would imply the incompleteness of the underlying theory, and hence indicate an important gap in the general comprehension of superconductors. In addition to its theoretical value, a complete understanding of the phenomenon underneath the electric-field response of the superconductor is important in the light of the related technological applications. In this paper, we study the change of the characteristics of a superconductor implementing a coplanar-waveguide resonator as a tank circuit, by relating our measurements to the reactance and resistance of the material. Namely, we track the state of the superconductor at different voltages and resulting leakage currents of a nearby gate electrode which is not galvanically connected to the resonator. By comparing the effects of the leakage current and of a change in the temperature of the system, we conclude that the observed behaviour in the superconductor is mainly caused by the heat that is deposited by the leakage current, and bearing the experimental uncertainties, we are not able to observe the effect of the applied electric field in our sample. In addition, we present a relatively good quantitative agreement between the Mattis–Bardeen theory of a heated superconductor and the experimental observations. Importantly, we do not claim this work to nullify the results of previous works, but rather to provide inspiration for future more thorough experiments and analysis using the methods presented here.

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.

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.

Ionic gating in metallic superconductors: A brief review

Ionic gating is a very popular tool to investigate and control the electric charge transport and electronic ground state in a wide variety of different materials. This is due to its capability to induce large modulations of the surface charge density by means of the electric-double-layer field-effect transistor (EDL-FET) architecture, and has been proven to be capable of tuning even the properties of metallic systems. In this short review, I summarize the main results which have been achieved so far in controlling the superconducting (SC) properties of thin films of conventional metallic superconductors by means of the ionic gating technique. I discuss how the gate-induced charge doping, despite being confined to a thin surface layer by electrostatic screening, results in a long-range ‘bulk’ modulation of the SC properties by the coherent nature of the SC condensate, as evidenced by the observation of suppressions in the critical temperature of films much thicker than the electrostatic screening length, and by the pronounced thickness-dependence of their magnitude. I review how this behavior can be modelled in terms of proximity effect between the charge-doped surface layer and the unperturbed bulk with different degrees of approximation, and how first-principles calculations have been employed to determine the origin of an anomalous increase in the electrostatic screening length at ultrahigh electric fields, thus fully confirming the validity of the proximity effect model. Finally, I discuss a general framework—based on the combination of ab-initio Density Functional Theory and the Migdal-Eliashberg theory of superconductivity—by which the properties of any gated thin film of a conventional metallic superconductor can be determined purely from first principles.