SQUID Loop Research Articles

Study of the Effect of Annealing on the Properties of Mn2Ru<italic>x</italic>Ga Thin Films

The effect of vacuum annealing thin films of the compensated ferrimagnetic half-metal Mn2RuxGa at temperatures from 250 to 400 degree Celsius is investigated. The 39.3 nm films deposited on (100) MgO substrates exhibit perpendicular magnetic anisotropy due to a small 1% tetragonal elongation induced by substrate strain. The main change on annealing is a modification in the compensation temperature, which first increases from 50 K for the as-deposited film to 185 K after annealing at 250 degree Celsius, and then falls to 140 K after annealing at 400 degree Celsius. There are minor changes in the atomic order, coercivity, resistivity and anomalous Hall effect (AHE), but the net magnetization measured by SQUID magnetometry with the field applied in-plane or perpendicular-to-the-plane changes more significantly. It saturates at 20 to 30 kA/m at room temperature, and a small soft component is seen in the perpendicular SQUID loops which is absent in the square AHE hysteresis loops. This is explained by the half-metallic nature of the compound; the AHE probes only the 4c Mn sublattice that provides the spin-polarized electrons at the Fermi level, whereas the SQUID measures the sum of the oppositely-aligned 4c and 4a sublattice magnetisations.

Fabrication of YBa2Cu3O7 twin-boundary-junction dc SQUID by using a focused-ion-beam pattern technique

We have fabricated YBa2Cu3O7 (YBCO) dc SQUIDs containing nanobridges across twin boundaries of LaAlO3 (LAO) substrates as Josephson elements by using a focused ion beam (FIB) etching method and measured their transport properties. The beam energy was 30 keV and the current was 1.5 pA for the nanobridge pattern. Each bridge with a nominal width of 200 nm crossed a twin boundary in the (100) direction. The SQUID loop had a 10 μm × 10 μm hole with a 5.7 μm average linewidth. The SQUID voltage showed modulations in response to the external flux with a maximum modulation depth of 350 μV at 77.0 K. HR-XRD spectra showed that the epitaxially grown YBCO film was twinned in commensurate with the twinning of the LAO substrate. Tilting of the c-axis of YBCO across the twin boundary is believed to play a role as a tunnel barrier.

Toward ultra high magnetic field sensitivity YBa2Cu3O7−δ nanowire based superconducting quantum interference devices

We report on measurements of YBa2Cu3O7−δ nanowire based Superconducting QUantum Interference Devices (nanoSQUIDs) directly coupled to an in-plane pick-up loop. The pick-up loop, which is coupled predominantly via kinetic inductance to the SQUID loop, allows for a significant increase of the effective area of our devices. Its role is systematically investigated and the increase in the effective area is successfully compared with numerical simulations. Large effective areas, together with the ultra low white flux noise below 1 μΦ0/Hz, make our nanoSQUIDs very attractive as magnetic field sensors.

Development of Magnetization Measurement Devices Using Micro-dc-SQUIDs and a Sr$$_2$$RuO$$_4$$ Microplate

We developed high-sensitivity magnetization measurement devices composed of micro-dc-SQUIDs and a superconducting Sr\(_2\)RuO\(_4\) microplate, aiming to investigate novel magnetic properties related to a spin-triplet chiral p-wave superconductor with a mesoscopic size. Micron-sized dc-SQUID was fabricated by thin Al electrodes, and the SQUID structure was improved to prevent magnetic fluxes from intruding into SQUID electrodes. A Sr\(_2\)RuO\(_4\) superconducting microplate was fabricated into the size as small as the SQUID loop using a focused ion beam and directly mounted on the SQUID with precise positioning for high-sensitivity magnetization measurements. In the preliminary magnetization measurements of this device, we observed vortices trapped into the plate and thus the lower critical field. The improved magnetization measurement device developed to exclude undesirable flux intrusion successfully enabled high-sensitivity detection of quantized vortex.

Concentric transmon qubit featuring fast tunability and an anisotropic magnetic dipole moment

We present a planar qubit design based on a superconducting circuit that we call concentric transmon. While employing a straightforward fabrication process using Al evaporation and lift-off lithography, we observe qubit lifetimes and coherence times in the order of 10 μs. We systematically characterize loss channels such as incoherent dielectric loss, Purcell decay and radiative losses. The implementation of a gradiometric SQUID loop allows for a fast tuning of the qubit transition frequency and therefore for full tomographic control of the quantum circuit. Due to the large loop size, the presented qubit architecture features a strongly increased magnetic dipole moment as compared to conventional transmon designs. This renders the concentric transmon a promising candidate to establish a site-selective passive direct Ẑ coupling between neighboring qubits, being a pending quest in the field of quantum simulation.

Superconducting Quantum Interference Devices Arranged in Pyramid Shaped Arrays

We explore SQUID array designs that could be beneficial in a robust 3-D structure involving several substrates and find a design for which there may be some advantages in linearity and dynamic range. Traditional substrates are square in shape, for a 3-D structure three squares would need to be attached together to create a structure with three sides of a cube. We explored how we would arrange an array of SQUIDs on this structure if the substrates were cut into triangles. This would result in a three-sided pyramid (or tetrahedron) shape. The arrays have a feed line at the top entering a single SQUID (or small array) and the number of SQUIDs (small arrays) increased in number each row and a decreasing critical current. We simulated the effects of varying the critical currents and SQUID loop sizes on the average response output and determined that for arrays of 21 10 × 10 bi-SQUIDs have a more linear anti-peak and larger voltage swing than a comparable size 35 × 60 array.

HfTi-nanoSQUID gradiometers with high linearity

We have developed a family of HfTi nanoSQUID gradiometers for different applications. These Nb-based nanoSQUIDs contain overdamped superconductor–normal conductor–superconductor (SNS) Josephson junctions with HfTi as a normal conducting barrier. The lateral dimensions of the junctions are about 200 nm × 200 nm, and the barrier thickness is nominally 30 nm. In order to enhance their practical use, the nanoSQUIDs are implemented with gradiometric SQUID and feedback loops, gradiometric transformers, and rf filters. The devices can be operated in an excitation field of up to a few mT with very low levels of nonlinearity. Due to the small loop size and the resulting low loop inductance, a white noise level down to 110 nΦ0/√Hz was achieved. The 1/f noise with a typical corner frequency below 1 kHz is dominated by critical current fluctuations. It can be reduced by applying bias reversal. A noise level of 600 nΦ0/√Hz was achieved at 1 Hz in a two-stage flux locked loop with bias reversal.

Experimental observation of induced stochastic transitions in a multiwall potential of an rf-SQUID loop

Experimental observation of a weak low-frequency harmonic signal in a point (superconductor-constriction-superconductor, ScS) contact superconducting quantum interference device (rf-SQUID loop), being amplified due to the stochastic transitions between two or more metastable states of the loop, under the influence of applied noise flux of varying intensity (the effect of stochastic resonance, SR). In addition to the usual SR effect found in a bi-stable system with Gaussian noise, there were observed transitions between several metastable states of the multiwell SQUID loop potential, due to the influence of binary noise, which can be interpreted as a kind of noise “spectroscopy” of the loop's metastable states, with varying values of trapped magnetic flux.

Investigation of Helium-Cooled Planar Transformer-Coupled SQUID Magnetometer

We investigated helium-cooled planar transformer-coupled SQUID magnetometers with regard to their field resolution δB by varying the SQUID loop inductance Ls, input coils and the pick-up loop Lp. It was found that the pick-up-loop area Ap is the most important parameter for δB of transformer-coupled magnetometers. δB with Ap = 10 × 10 mm2 reached about 3 fTA/□Hz, even using direct readout scheme without any feedback circuitries.

Analytical approximations to the dynamics of an array of coupled DC SQUIDs

Coupled dynamical systems that operate near the onset of a bifurcation can lead, under certain conditions, to strong signal amplification effects. Over the past years we have studied this generic feature on a wide range of systems, including: magnetic and electric fields sensors, gyroscopic devices, and arrays of loops of superconducting quantum interference devices, also known as SQUIDs. In this work, we consider an array of SQUID loops connected in series as a case study to derive asymptotic analytical approximations to the exact solutions through perturbation analysis. Two approaches are considered. First, a straightforward expansion in which the non-linear parameter related to the inductance of the DC SQUID is treated as the small perturbation parameter. Second, a more accurate procedure that considers the SQUID phase dynamics as non-uniform motion on a circle. This second procedure is readily extended to the series array and it could serve as a mathematical framework to find approximate solutions to related complex systems with high-dimensionality. To the best of our knowledge, an approximate analytical solutions to an array of SQUIDs has not been reported yet in the literature.

Stochastic resonance in an RF SQUID with shunted ScS junction

Using a point (superconductor–constriction–superconductor, ScS) contact in a single-Josephson-junction superconducting quantum interference device (RF SQUID) provides stochastic resonance conditions at any arbitrary small value of loop inductance and contact critical current, unlike SQUIDs with more traditional tunnel (superconductor–insulator–superconductor, SIS) junctions. This is due to the unusual potential energy of the ScS RF SQUID which always has a barrier between two wells, thus making the device bistable. This paper presents the results of a numerical simulation of the stochastic dynamics of the magnetic flux in an ScS RF SQUID loop affected by band-limited white Gaussian noise and low-frequency sine signals of small and moderate amplitudes. The difference in stochastic amplification of RF SQUID loops incorporating ScS and SIS junctions is discussed.

Coupled NanoSQUIDs and Nano-Electromechanical Systems (NEMS) Resonators

Recent developments in cryogenic nano-electromechanical (NEMS) resonators have shown that they can address some fundamental physics, for example in achieving the ground state of a mechanical resonator and entanglement with an electromagnetic resonator. In contrast, little work has been reported on using what is arguably the most sensitive measuring device, a SQUID, to directly interact with, and thus interrogate, a NEMS resonator. We report here our initial experimental results aimed towards forming an optimized coupled micro/nano-mechanical resonator and a focused ion beam patterned Nb SQUID, possessing exceptionally low noise (~200nΦ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0/</sub> Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> above 1 kHz), and operating above 4.2 K. We describe our first results from a paddle-shaped mechanical resonator with a diameter of 15 μm coupled to a Nb SQUID loop. Finally, we describe the construction of our first true nanoscale-coupled, double-clamped cantilever and nanoSQUID (rectangular loop area 100 nm × 900 nm).

Statistical characterization of voltage-biased SQUIDs with weakly damped junctions

Recently, it has been shown that voltage-biased readout of SQUIDs with weakly damped junctions (large Stewart–McCumber parameter βc, due to high shunt resistance) is useful for suppression of preamplifier noise. We experimentally studied the characteristics of 53 planar niobium–SQUID magnetometers with junction shunt resistors RJ nominally of 30 Ω fabricated on 5 × 5 mm2 chips. The field-to-flux transfer coefficient ∂B/∂Φ of the magnetometers was 1.5 nT/Φ0, with a SQUID loop inductance Ls of about 350 pH. The distributions of important SQUID parameters, such as the current swing Iswing, the dynamic resistance Rd, and the flux-to-voltage transfer coefficient ∂V/∂Φ, are given. Nearly all the SQUIDs could be stably operated in the voltage bias mode and their ∂V/∂Φ reached a large mean value of 380 μV/Φ0. In this case, the SQUIDs can be read out directly by a commercial operational amplifier without any additional means to suppress preamplifier noise. The mean flux noise of the SQUIDs was found to be 4.5 μΦ0 Hz−1/2, corresponding to a field resolution of 7 fT Hz−1/2. To demonstrate the applicability of these SQUIDs in the direct readout scheme, a simple four-channel SQUID gradiometer system was set up to perform magnetocardiography and magnetoencephalography measurements in a magnetically shielded room.

Nano-sized SQUID-on-tip for scanning probe microscopy

We present a SQUID of novel design, which is fabricated on the tip of a pulled quartz tube in a simple 3-step evaporation process without need for any additional processing, patterning, or lithography. The resulting devices have SQUID loops with typical diameters in the range 75–300 nm. They operate in magnetic fields up to 0.6 T and have flux sensitivity of 1.8 μΦ0/Hz1/2 and magnetic field sensitivity of 10−7 T/Hz1/2, which corresponds to a spin sensitivity of 65 μB/Hz1/2 for aluminum SQUIDs. The shape of the tip and the small area of the SQUID loop, together with its high sensitivity, make our device an excellent tool for scanning SQUID microscopy: With the SQUID-on-tip glued to a tine of a quartz tuning fork, we have succeeded in obtaining magnetic images of a patterned niobium film and of vortices in a superconducting film in a magnetic field.

Decoherence of superconducting qubits caused by quasiparticle tunneling

In superconducting qubits, the interaction of the qubit degree of freedom with quasiparticles defines a fundamental limitation for the qubit coherence. We develop a theory of the pure dephasing rate \Gamma_{\phi} caused by quasiparticles tunneling through a Josephson junction and of the inhomogeneous broadening due to changes in the occupations of Andreev states in the junction. To estimate \Gamma_{\phi}, we derive a master equation for the qubit dynamics. The tunneling rate of free quasiparticles is enhanced by their large density of states at energies close to the superconducting gap. Nevertheless, we find that \Gamma_{\phi} is small compared to the rates determined by extrinsic factors in most of the current qubit designs (phase and flux qubits, transmon, fluxonium). The split transmon, in which a single junction is replaced by a SQUID loop, represents an exception that could make possible the measurement of \Gamma_{\phi}. Fluctuations of the qubit frequency leading to inhomogeneous broadening may be caused by the fluctuations in the occupation numbers of the Andreev states associated with a phase-biased Josephson junction. This mechanism may be revealed in qubits with small-area junctions, since the smallest relative change in frequency it causes is of the order of the inverse number of transmission channels in the junction.

Voltage response of non-uniform arrays of bi-superconductive quantum interference devices

Multi-loop arrays of Josephson junctions (JJs) with non-uniform area distributions, which are known as superconducting quantum interference filters (SQIFs), are the most highly sensitive sensors of changes in applied magnetic field as well as the absolute magnitude of magnetic fields. The non-uniformity of the loop sizes allows the array to produce a unique collective voltage response that has a pronounced single peak with a large voltage swing around zero magnetic field. To obtain high linear dynamic range, which is critical for a wide variety of applications, the linearity of the slope of the anti-peak response must be improved. We propose a novel scheme for enhancing linearity—a new configuration combining the SQIF array concept with the recently introduced bi-superconductive quantum interference device (SQUID) configuration, in which each individual SQUID loop is made up of three JJs as opposed to using two JJs per loop in standard dc SQUIDs. We show, computationally, that the additional junction offers a viable linearization method for optimizing the voltage response and dynamic range of SQIF arrays. We have realized SQIF arrays based on bi-SQUID cells and present first experimental results.

The Renormalization Effects in the Microstrip-SQUID Amplifier

The peculiarities of the microstrip-DC SQUID amplifier caused by the resonant structure of the input circuit are analyzed. It is shown that the mutual inductance, that couples the input circuit and the SQUID loop, depends on the frequency of electromagnetic field. The renormalization of the SQUID parameters due to the screening effect of the input circuit vanishes when the Josephson frequency is much greater than the signal frequency.

Josephson junctions fabrication in multi-layer deposition and post annealing MgB&lt;sub&gt;2&lt;/sub&gt; thin films

Josephson junctions are fabricated by focused ion beam in MgB₂ thin films. The films were prepared by deposite multi-layer Mg and B films at room temperature first and then annealed at about 700°C. These films have <italic>T</italic>_c of 32 K. Strips and SQUID loops were defined by photolithography and Ar ion beam milling. Then nanobridges of 150-300 nm wide were made by focused ion beam etching. The <italic>R-T</italic> characteristics of the strip is the same as that of the raw film while SQUIDs have a “foot” near the critical temperature. The <italic>I-V</italic> curve of one of the SQUIDs is hysteretic below about 10 K. Nanobridges show features of the resistively shunted junction like, and the temperature dependence of the critical current turns out to be of SINS weaklink. At 9.8 K, the critical current density is about 1.5×10⁷ A/cm².

Highly sensitive miniature SQUID magnetometer fabricated with cross-type Josephson tunnel junctions

We report on a new method suitable for the fabrication of highly sensitive SQUID magnetometers exhibiting very small effective areas. In contrast to commonly used approaches, which mostly make use of constrictions in a superconducting material to form the Josephson junctions, we have been able to fabricate such sensors with SIS cross-type Josephson tunnel junctions in an Nb/AlOx/Nb trilayer process. The small junction size and vanishing idle region of our cross-type junctions and a therefore very low capacitance lead to a high sensitivity of the resulting SQUIDs. First results on fabricated miniature SQUID magnetometer within this technology are shown. We found, that even with SQUID loop dimensions of about 10×10μm2 very low flux noise levels could be achieved, which clearly demonstrate the high potential of our approach. Furthermore we estimate the required SQUID parameter which may allow the detection of single electron spin-flips with such devices in the future.

First-Order 0-π Quantum Phase Transition in the Kondo Regime of a Superconducting Carbon-Nanotube Quantum Dot

We study a carbon nanotube quantum dot embedded into a SQUID loop in order to investigate the competition of strong electron correlations with proximity effect. Depending whether local pairing or local magnetism prevails, a superconducting quantum dot will respectively exhibit positive or negative supercurrent, referred to as a 0 or $\pi$ Josephson junction. In the regime of strong Coulomb blockade, the 0 to $\pi$ transition is typically controlled by a change in the discrete charge state of the dot, from even to odd. In contrast, at larger tunneling amplitude the Kondo effect develops for an odd charge (magnetic) dot in the normal state, and quenches magnetism. In this situation, we find that a first order 0 to $\pi$ quantum phase transition can be triggered at fixed valence when superconductivity is brought in, due to the competition of the superconducting gap and the Kondo temperature. The SQUID geometry together with the tunability of our device allows the exploration of the associated phase diagram predicted by recent theories. We also report on the observation of anharmonic behavior of the current-phase relation in the transition regime, that we associate with the two different accessible superconducting states. Our results ultimately reveal the spin singlet nature of the Kondo ground state, which is the key process in allowing the stability of the 0-phase far from the mixed valence regime.