Nanoscale Superconducting Quantum Interference Devices Research Articles

Topological insulator based axial superconducting quantum interferometer structures

Abstract Nanoscale superconducting quantum interference devices (SQUIDs) are fabricated in-situ from a single Bi0.26Sb1.74Te3 nanoribbon that is defined using selective-area growth and contacted with superconducting Nb electrodes via a shadow mask technique. We present h/(2e) magnetic flux periodic interference in both, fully and non-fully proximitized nanoribbons. The pronounced oscillations are attributed to interference effects of coherent transport through the topological surface states encompassing the cross-section of the nanoribbon.

Arrays of nano-high-transition temperature superconductor quantum interference devices

We report the fabrication and testing of arrays of nanoscale superconducting quantum interference devices (SQUIDs) directly written into a thin film of the high-transition temperature superconductor YBa2Cu-3O7−δ with a focused helium ion beam. We compare three array configurations with 400 nm by 400 nm nanoSQUIDs connected in series and parallel and a two-dimensional (2D) combination of both. Our electrical transport measurements show that series arrays of three nanoSQUIDs exhibit modulation voltages greater than 1 mV and that combining the devices in parallel greatly enhances the slope of the voltage–magnetic field characteristic. A 2D array with 3 SQUIDS in series and 7 in parallel exhibited a transfer function of 5.51 mV/mT.

PyTDGL: Time-dependent Ginzburg-Landau in Python

Time-dependent Ginzburg-Landau (TDGL) theory is a phenomenological model for the dynamics of superconducting systems. Due to its simplicity in comparison to microscopic theories and its effectiveness in describing the observed properties of the superconducting state, TDGL is widely used to interpret or explain measurements of superconducting devices. Here, we introduce pyTDGL, a Python package that solves a generalized TDGL model for superconducting thin films of arbitrary geometry, enabling simulations of vortex and phase dynamics in mesoscopic superconducting devices. pyTDGL can model the nonlinear magnetic response and dynamics of multiply connected films, films with multiple current bias terminals, and films with a spatially inhomogeneous critical temperature. We demonstrate these capabilities by modeling quasi-equilibrium vortex distributions in irregularly shaped films, and the dynamics and current-voltage-field characteristics of nanoscale superconducting quantum interference devices (nanoSQUIDs). Program summaryProgram Title: pyTDGLCPC Library link to program files:https://doi.org/10.17632/t6z7szt9bj.1Developer's repository link:http://www.github.com/loganbvh/py-tdglCode Ocean capsule:https://codeocean.com/capsule/2460583Licensing provisions:MIT LicenseProgramming language: PythonNature of problem:pyTDGL solves a generalized time-dependent Ginzburg-Landau (TDGL) equation for two-dimensional superconductors of arbitrary geometry, enabling simulations of vortex and phase slip dynamics in thin film superconducting devices.Solution method:: The package uses a finite volume adaptive Euler method to solve a coupled TDGL and Poisson equation in two dimensions.

A Self-Flux-Biased NanoSQUID with Four NbN-TiN-NbN Nanobridge Josephson Junctions

We report the development of a planar 4-Josephson-junction nanoscale superconducting quantum interference device (nanoSQUID) that is self-biased for optimal sensitivity without the application of a magnetic flux of Φ0/4. The nanoSQUID contains novel NbN-TiN-NbN nanobridge Josephson junctions (nJJs) with NbN current leads and electrodes of the nanoSQUID body connected by TiN nanobridges. The optimal superconducting transition temperature of ~4.8 K, superconducting coherence length of ~100 nm, and corrosion resistance of the TiN films ensure the hysteresis-free, reproducible, and long-term stability of nJJ and nanoSQUID operation at 4.2 K, while the corrosion-resistant NbN has a relatively high superconducting transition temperature of ~15 K and a correspondingly large energy gap. FIB patterning of the TiN films and nanoscale sculpturing of the tip area of the nanoSQUID’s cantilevers are performed using amorphous Al films as sacrificial layers due to their high chemical reactivity to alkalis. A cantilever is realized with a distance between the nanoSQUID and the substrate corner of ~300 nm. The nJJs and nanoSQUID are characterized using Quantum Design measurement systems at 4.2 K. The technology is expected to be of interest for the fabrication of durable nanoSQUID sensors for low temperature magnetic microscopy, as well as for the realization of more complex circuits for superconducting nanobridge electronics.

TiN nanobridge Josephson junctions and nanoSQUIDs on SiN-buffered Si

We report the fabrication and properties of titanium nitride (TiN) nanobridge Josephson junctions (nJJs) and nanoscale superconducting quantum interference devices (nanoSQUIDs) on SiN-buffered Si substrates. The superior corrosion resistance, large coherence length, suitable superconducting transition temperature and highly selective reactive ion etching (RIE) of TiN compared to e-beam resists and the SiN buffer layer allow for reproducible preparation and result in long-term stability of the TiN nJJs. High-resolution transmission electron microscopy reveals a columnar structure of the TiN film on an amorphous SiN buffer layer. High-resolution scanning electron microscopy reveals the variable thickness shape of the nJJs. A combination of wet etching in 20% potassium hydroxide and RIE is used for bulk nanomachining of nanoSQUID cantilevers. More than 20 oscillations of the V(B) dependence of the nanoSQUIDs with a period of ∼6 mT and hysteresis-free I(V) characteristics (CVCs) of the all-TiN nJJs are observed at 4.2 K. CVCs of the low-I c all-TiN nJJs follow theoretical predictions for dirty superconductors down to ∼10 mK, with the critical current saturated below ∼0.6 K. These results pave the way for superconducting electronics based on nJJs operating non-hysteretically at 4.2 K, as well as for all-TiN qubits operating at sub-100 mK temperatures.

Fabrication Process for Deep Submicron SQUID Circuits with Three Independent Niobium Layers.

We present a fabrication technology for nanoscale superconducting quantum interference devices (SQUIDs) with overdamped superconductor-normal metal-superconductor (SNS) trilayer Nb/HfTi/Nb Josephson junctions. A combination of electron-beam lithography with chemical-mechanical polishing and magnetron sputtering on thermally oxidized Si wafers is used to produce direct current SQUIDs with 100-nm-lateral dimensions for Nb lines and junctions. We extended the process from originally two to three independent Nb layers. This extension offers the possibility to realize superconducting vias to all Nb layers without the HfTi barrier, and hence to increase the density and complexity of circuit structures. We present results on the yield of this process and measurements of SQUID characteristics.

High-transition-temperature nanoscale superconducting quantum interference devices directly written with a focused helium ion beam

In this work, we present nanoscale superconducting quantum interference devices (SQUIDs) with dimensions as small as 10 nm from the high-transition-temperature superconductor YBa2Cu3O7−δ (YBCO). The SQUID features and Josephson junctions are directly written into a 35-nm thick YBCO film with a focused helium ion beam. We integrate these nano-SQUIDs with directly written nano-isolated inductively coupled control lines to demonstrate a low power superconducting output driver capable of transimpedance conversion over a very wide temperature range of 4–50 K.

Sputtered Mo 66 Re 34 SQUID-on-Tip for High-Field Magnetic and Thermal Nanoimaging

Scanning nanoscale superconducting quantum interference devices (SQUIDs) are gaining interest as highly sensitive microscopic magnetic and thermal characterization tools of quantum and topological states of matter and devices. Here we introduce a novel technique of collimated differential-pressure magnetron sputtering for versatile self aligned fabrication of SQUID on tip (SOT) nanodevices, which cannot be produced by conventional sputtering methods due to their diffusive, rather than the required directional point-source, deposition. The new technique provides access to a broad range of superconducting materials and alloys beyond the elemental superconductors employed in the existing thermal deposition methods, opening the route to greatly enhanced SOT characteristics and functionalities. Utilizing this method, we have developed MoRe SOT devices with sub-50 nm diameter, magnetic flux sensitivity of 1.2 $\mu\Phi_0/Hz^{1/2}$ up to 3 T at 4.2 K, and thermal sensitivity better than 4 $\mu K/Hz^{1/2}$ up to 5 T, about five times higher than any previous report, paving the way to nanoscale imaging of magnetic and spintronic phenomena and of dissipation mechanisms in previously inaccessible quantum states of matter.

Nanobridge superconducting quantum interference devices: Beyond the Josephson limit

Nano-scale superconducting quantum interference devices (nano-SQUIDS) where the weak-links are made from nano-bridges --- i.e., nano-bridge--SQUIDs (NBSs) --- are one of the most sensitive magnetometers for nano-scale magnetometry. Because of very strong non-linearity in the nano-bridge--electrode joints, the applied magnetic flux ($\Phi_{a}$) -- critical current ($I_{c}$) characteristics of NBSs differ very significantly from conventional tunnel-junction-SQUIDs, especially when nano-bridges are long and/or the screening parameter is large. However, in most of the theoretical descriptions, NBSs have been treated like conventional tunnel-junction-SQUIDs, which are based on d.c. Josephson effect. Here, I present a model demonstrating that for long nano-bridges and/or large screening parameter the $I_{c}(\Phi_{a})$ of a NBS can be explained by merely considering the fluxoid quantization in the NBS loop and the energy of the NBS; it is not necessary to take the Josephson effect into consideration. I also demonstrate that using the model, we can derive useful expressions like modulation depth and transfer function. I also discuss the role of kinetic inductance fraction ($\kappa$) in determining $I_{c}(\Phi_{a})$.

Meissner effect measurement of single indium particle using a customized on-chip nano-scale superconducting quantum interference device system

As many emergent phenomena of superconductivity appear on a smaller scale and at lower dimension, commercial magnetic property measurement systems (MPMSs) no longer provide the sensitivity necessary to study the Meissner effect of small superconductors. The nano-scale superconducting quantum interference device (nano-SQUID) is considered one of the most sensitive magnetic sensors for the magnetic characterization of mesoscopic or microscopic samples. Here, we develop a customized on-chip nano-SQUID measurement system based on a pulsed current biasing method. The noise performance of our system is approximately 4.6 × 10−17 emu/Hz1/2, representing an improvement of 9 orders of magnitude compared with that of a commercial MPMS (~10−8 emu/Hz1/2). Furthermore, we demonstrate the measurement of the Meissner effect of a single indium (In) particle (of 47 μm in diameter) using our on-chip nano-SQUID system. The system enables the observation of the prompt superconducting transition of the Meissner effect of a single In particle, thereby providing more accurate characterization of the critical field Hc and temperature Tc. In addition, the retrapping field Hre as a function of temperature T of single In particle shows disparate behavior from that of a large ensemble.

Heat propagation models for superconducting nanobridges at millikelvin temperatures

Nanoscale superconducting quantum interference devices (nanoSQUIDs) most commonly use Dayem bridges as Josephson elements to reduce the loop size and achieve high spin sensitivity. Except at temperatures close to the critical temperature Tc, the electrical characteristics of these bridges exhibit undesirable thermal hysteresis which complicates device operation. This makes proper thermal analysis an essential design consideration for optimising nanoSQUID performance at ultralow temperatures. However the existing theoretical models for this hysteresis were developed for micron-scale devices operating close to liquid helium temperatures, and are not fully applicable to a new generation of much smaller devices operating at significantly lower temperatures. We have therefore developed a new analytic heat model which enables a more accurate prediction of the thermal behaviour in such circumstances. We demonstrate that this model is in good agreement with experimental results measured down to 100 mK and discuss its validity for different nanoSQUID geometries.

Electrically Tunable Multiterminal SQUID-on-Tip

We present a new nanoscale superconducting quantum interference device (SQUID) whose interference pattern can be shifted electrically in situ. The device consists of a nanoscale four-terminal-four-junction SQUID fabricated at the apex of a sharp pipet using a self-aligned three-step deposition of Pb. In contrast to conventional two-terminal-two-junction SQUIDs that display optimal sensitivity when flux biased to about a quarter of the flux quantum, the additional terminals and junctions allow optimal sensitivity at arbitrary applied flux, thus eliminating the magnetic field "blind spots". We demonstrate spin sensitivity of 5 to 8 μB/Hz1/2 over a continuous field range of 0 to 0.5 T with promising applications for nanoscale scanning magnetic imaging.

Nanoscale Superconducting Quantum Interference Devices Add Another Dimension.

Over the past decade, nanoscale superconducting quantum interference devices (nanoSQUIDs) have rapidly risen from nowhere to forge a new sphere of applications of these macroscopic quantum devices. New fabrication techniques have enabled these advances. In this Perspective, we highlight another recent major development in this area-the demonstration of a three-axis nanoSQUID magnetometer, which enables the vector magnetization of a nanoscale magnetic particle to be measured in the presence of an applied magnetic field. We illustrate the technological demands and developments that have driven the development of nanoSQUIDs and make suggestions for future directions for applications.

Fabrication of high sensitivity 3D nanoSQUIDs based on a focused ion beam sculpting technique

In this paper a nanofabrication process, based on a focused ion beam (FIB) nanosculpting technique, for high sensitivity three-dimensional nanoscale superconducting quantum interference devices (nanoSQUIDs) is reported. The crucial steps of the fabrication process are described, as are some peculiar features of the superconductor–normal metal–insulator–superconductor (SNIS) Josephson junctions, which may useful for applications in cryocooler systems. This fabrication procedure is employed to fabricate sandwich nanojunctions and high sensitivity nanoSQUIDs. Specifically, the superconductive nanosensors have a rectangular loop of 1 × 0.2–0.4 μm2 interrupted by two square Nb/Al–AlOx/Nb SNIS Josephson junctions with side lengths of 0.3 μm. The characterization of a typical nanoSQUID has been carried out and a spectral density of magnetic flux noise as low as 0.8 μΦ0 Hz–1/2 has been measured.

Three-junction SQUID-on-tip with tunable in-plane and out-of-plane magnetic field sensitivity.

Nanoscale superconducting quantum interference devices (SQUIDs) demonstrate record sensitivities to small magnetic moments but are typically sensitive only to the field component that is normal to the plane of the SQUID and out-of-plane with respect to the scanned surface. We report on a nanoscale three-junction Pb SQUID, which is fabricated on the apex of a sharp tip. Because of its three-dimensional structure, it exhibits a unique tunable sensitivity to both in-plane and out-of-plane fields. We analyze the two-dimensional interference pattern from both numerical and experimental points of view. This device is integrated into a scanning microscope, and its ability to independently measure the different components of the magnetic field with outstanding spin sensitivity better than 5 μB/Hz(1/2) is demonstrated. This highlights its potential as a local probe of nanoscale magnetic structures.

Proximity effect bilayer nano superconducting quantum interference devices for millikelvin magnetometry

Superconducting quantum interference devices (SQUIDs) incorporating thin film nanobridges as weak links have sensitivities approaching that required for single spin detection at 4.2 K. However, due to thermal hysteresis they are difficult to operate at much lower temperatures which hinder their application to many quantum measurements. To overcome this, we have developed nanoscale SQUIDs made from titanium-gold proximity bilayers. We show that their electrical properties are consistent with a theoretical model developed for heat flow in bilayers and demonstrate that they enable magnetic measurements to be made on a sample at system temperatures down to 60 mK.

A dispersive nanoSQUID magnetometer for ultra-low noise, high bandwidth flux detection

We describe a dispersive nanoSQUID (nanoscale superconducting quantum interference device) magnetometer comprised of two variable thickness aluminum weak-link Josephson junctions shunted in parallel with an on-chip capacitor. This arrangement forms a nonlinear oscillator with a tunable 4–8 GHz resonant frequency with a quality factor Q = 30 when coupled directly to a 50 Ω transmission line. In the presence of a near-resonant microwave carrier signal, a low frequency flux input generates sidebands that are readily detected using microwave reflectometry. If the carrier excitation is sufficiently strong, then the magnetometer also exhibits parametric gain, resulting in a minimum effective flux noise of 30 nΦ0 Hz−1/2 with 20 MHz of instantaneous bandwidth. If the magnetometer is followed with a near-quantum-noise-limited Josephson parametric amplifier, we can increase the bandwidth to 60 MHz without compromising sensitivity. This combination of high sensitivity and wide bandwidth with no on-chip dissipation makes this device ideal for local sensing of spin dynamics, both classical and quantum.

Phonon-mediated superconductivity in graphene by lithium deposition

Graphene exhibits many extraordinary properties. But, despite many attempts to find ways to induce it, superconductivity is not one of them. First-principles calculations suggest that by decorating the surface of graphene with lithium atoms, it could yet be made to superconduct. Graphene1 is the physical realization of many fundamental concepts and phenomena in solid-state physics2. However, in the list of graphene’s many remarkable properties3,4,5,6, superconductivity is notably absent. If it were possible to find a way to induce superconductivity, it could improve the performance and enable more efficient integration of a variety of promising device concepts including nanoscale superconducting quantum interference devices, single-electron superconductor–quantum dot devices7,8, nanometre-scale superconducting transistors9 and cryogenic solid-state coolers10. To this end, we explore the possibility of inducing superconductivity in a graphene sheet by doping its surface with alkaline metal adatoms, in a manner analogous to which superconductivity is induced in graphite intercalated compounds11,12 (GICs). As for GICs, we find that the electrical characteristics of graphene are sensitive to the species of adatom used. However, contrary to what happens in GICs, Li-covered graphene is superconducting at a much higher temperature with respect to Ca-covered graphene.

Noise theory of dc nano-SQUIDs based on Dayem nanobridges

In the recent years, nanoscale superconducting quantum interference devices (nano-SQUIDs) played a fundamental role in the study of small spin systems. Nano-SQUIDs typically employ nano-Dayem bridges having dimensions (length $L$ and/or width $W$) greater than coherence length $\ensuremath{\xi}$ of the superconducting film. They exhibit characteristics different from those of standard SQUIDs because the current-phase relationship (CPR) is nonsinusoidal, rendering most of the theoretical predictions based on the standard SQUID theory usually unreliable. Here, we present a noise theory of dc nano-SQUIDs based on Dayem nanobridges. We have computed the main characteristics of this quantum device including current-voltage and voltage-magnetic flux characteristics, magnetic flux-to-voltage transfer factor, and spectral densities of voltage and magnetic flux noise for $L$/$\ensuremath{\xi}$ ratios ranging from 1 (sinusoidal limit) to 3.5 (hysteretic limit). The CPRs have been computed by using the theory of Josephson weak links based on the Ginzburg--Landau equation. The results show a dependence of the magnetic flux noise spectral density on ($L$/$\ensuremath{\xi}$)${}^{4/3}$ involving a degradation of about a factor of five between the two extreme cases and are consistent with experimentally measured magnetic flux noises reported in the literature. These results provide useful information for both device physics and their applications.

Three-dimensional nanoscale superconducting quantum interference device pickup loops

Nanoscale superconducting quantum interference devices (SQUIDs) have sensitivities approaching that required for single-spin detection, but they only measure fields perpendicular to their plane and can be difficult to tightly couple to magnetic sources on the same chip. To remove these limitations we used focused-ion-beam-induced chemical vapor deposition to directly write a SQUID structure with three-dimensional, freestanding pickup loops using superconducting tungsten nanowires. By applying a localized field, we investigated the pickup loop response, and found that it exhibits Meissner screening corresponding to a penetration depth λ(T) consistent with BCS theory in the dirty limit and λ(0)=330 nm.