Long-range vortex transfer in superconducting nanowires

Causes and Consequences of Ordering and Dynamic Phases of Confined Vortex Rows in Superconducting Nanostripes

Understanding the behaviour of vortices under nanoscale confinement in superconducting circuits is important for the development of superconducting electronics and quantum technologies. Using numerical simulations based on the Ginzburg-Landau theory for non-homogeneous superconductivity in the presence of magnetic fields, we detail how lateral confinement organises vortices in a long superconducting nanostripe, presenting a phase diagram of vortex configurations as a function of the stripe width and magnetic field. We discuss why the average vortex density is reduced and reveal that confinement influences vortex dynamics in the dissipative regime under sourced electrical current, mapping out transitions between asynchronous and synchronous vortex rows crossing the nanostripe as the current is varied. Synchronous crossings are of particular interest, since they cause single-mode modulations in the voltage drop along the stripe in a high (typically GHz to THz) frequency range.

Direct-write of tungsten-carbide nanoSQUIDs based on focused ion beam induced deposition

NanoSQUIDs are quantum sensors that excel in detecting a small change in magnetic flux with high sensitivity and high spatial resolution. Here, we employ resist-free direct-write Ga⁺ Focused Ion Beam Induced Deposition (FIBID) techniques to grow W-C nanoSQUIDs, and we investigate their electrical response to changes in the magnetic flux. Remarkably, FIBID allows the fast (3 min) growth of 700 nm × 300 nm nanoSQUIDs based on narrow nanobridges (50 nm wide) that act as Josephson junctions. Albeit the SQUIDs exhibit a comparatively low modulation depth and obtain a high inductance, the observed transfer coefficient (output voltage to magnetic flux change) is comparable to other SQUIDs (up to 1300 μV/Φ ₀), which correlates with the high resistivity of W-C in the normal state. We discuss here the potential of this approach to reduce the active area of the nanoSQUIDs to gain spatial resolution as well as their integration on cantilevers for scanning-SQUID applications.

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.

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.

Superconducting properties of in-plane W-C nanowires grown by He+ focused ion beam induced deposition

Focused ion beam induced deposition (FIBID) is a nanopatterning technique that uses a focused beam of charged ions to decompose a gaseous precursor. So far, the flexible patterning capabilities of FIBID have been widely exploited in the fabrication of superconducting nanostructures, using the W(CO)₆ precursor mostly in combination with a focused beam of Ga⁺ ions. Here, the fabrication and characterization of superconducting in-plane tungsten-carbon (W-C) nanostructures by He⁺ FIBID of the W(CO)₆ precursor is reported. A patterning resolution of 10 nm has been achieved, which is virtually unattainable for Ga⁺ FIBID. When the nanowires are patterned with widths of 20 nm and above, the deposited material is superconducting below 3.5-4 K. In addition, nanowires with widths of 60 and 90 nm have been found to sustain long-range controlled nonlocal superconducting vortex transfer along 3 μm. Overall, these findings strengthen the capabilities of He⁺ FIBID of W-C in the growth and patterning of in-plane superconducting nanodevices.

Optimization of Pt-C Deposits by Cryo-FIBID: Substantial Growth Rate Increase and Quasi-Metallic Behaviour

The Focused Ion Beam Induced Deposition (FIBID) under cryogenic conditions (Cryo-FIBID) technique is based on obtaining a condensed layer of precursor molecules by cooling the substrate below the condensation temperature of the gaseous precursor material. This condensed layer is irradiated with ions according to a desired pattern and, subsequently, the substrate is heated above the precursor condensation temperature, revealing the deposits with the shape of the exposed pattern. In this contribution, the fast growth of Pt-C deposits by Cryo-FIBID is demonstrated. Here, we optimize various parameters of the process in order to obtain deposits with the lowest-possible electrical resistivity. Optimized ~30 nm-thick Pt-C deposits are obtained using ion irradiation area dose of 120 μC/cm² at 30 kV. This finding represents a substantial increment in the growth rate when it is compared with deposits of the same thickness fabricated by standard FIBID at room temperature (40 times enhancement). The value of the electrical resistivity in optimized deposits (~4 × 10⁴ µΩ cm) is suitable to perform electrical contacts to certain materials. As a proof of concept of the potential applications of this technology, a 100 µm × 100 µm pattern is carried out in only 43 s of ion exposure (area dose of 23 μC/cm²), to be compared with 2.5 h if grown by standard FIBID at room temperature. The ion trajectories and the deposit composition have been simulated using a binary-collision-approximation Monte Carlo code, providing a solid basis for the understanding of the experimental results.

3D superconducting hollow nanowires with tailored diameters grown by focused He+ beam direct writing

Currently, the patterning of innovative three-dimensional (3D) nano-objects is required for the development of future advanced electronic components. Helium ion microscopy in combination with a precursor gas can be used for direct writing of three-dimensional nanostructures with a precise control of their geometry, and a significantly higher aspect ratio than other additive manufacturing technologies. We report here on the deposition of 3D hollow tungsten carbide nanowires with tailored diameters by tuning two key growth parameters, namely current and dose of the ion beam. Our results show the control of geometry in 3D hollow nanowires, with outer and inner diameters ranging from 36 to 142 nm and from 5 to 28 nm, respectively; and lengths from 0.5 to 8.9 µm. Transmission electron microscopy experiments indicate that the nanowires have a microstructure of large grains with a crystalline structure compatible with the face-centered cubic WC_{1- x} phase. In addition, 3D electron tomographic reconstructions show that the hollow center of the nanowires is present along the whole nanowire length. Moreover, these nanowires become superconducting at 6.8 K and show high values of critical magnetic field and critical current density. Consequently, these 3D nano-objects could be implemented as components in the next generation of electronics, such as nano-antennas and sensors, based on 3D superconducting architectures.