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In this work we study the effect of engineered disorder on the local magnetic response of proximity coupled superconducting island arrays by comparing scanning Superconducting Quantum Interference Device (SQUID) susceptibility measurements to a model in which we treat the system as a network of one-dimensional (1D) superconductor-normal metal-superconductor (SNS) Josephson junctions, each with a Josephson coupling energy $E_J$ determined by the junction length or distance between islands. We find that the disordered arrays exhibit a spatially inhomogeneous diamagnetic response which, for low local applied magnetic fields, is well described by this junction network model, and we discuss these results as they relate to inhomogeneous two-dimensional (2D) superconductors. Our model of the static magnetic response of the arrays does not fully capture the onset of nonlinearity and dissipation with increasing applied field, as these effects are associated with vortex motion due to the dynamic nature of the scanning SQUID susceptometry measurement. This work demonstrates a model 2D superconducting system with engineered disorder and highlights the impact of dissipation on the local magnetic properties of 2D superconductors and Josephson junction arrays., Main text: 9 pages, 5 figures. Supplementary material: 11 pages, 12 figures. Accepted to Phys. Rev. B. The first two authors contributed equally

The spin-triplet superconductor UTe$_2$ shows spontaneous time-reversal symmetry breaking and multiple superconducting phases in some crystals, implying chiral superconductivity. Here we microscopically image the local magnetic fields and magnetic susceptibility near the surface of UTe$_2$, observing a homogeneous superfluid density $n_s$ and homogeneous pinned vortices. The temperature dependence of $n_s$ is consistent with an anisotropic gap and shows no evidence for an additional kink that would be expected at any second phase transition. Our findings are consistent with a dominant $B_{3u}$ superconducting order parameter in the case of a quasi-2D Fermi surface and provide no evidence for multiple phase transitions in $n_s(T)$ in UTe$_2$., Comment: 12 pages, 13 figures

Quantitative understanding of the spatial distribution of magnetic fields and Meissner screening currents in two-dimensional (2D) superconductors and mesoscopic thin film superconducting devices is critical to interpreting the results of magnetic measurements of such systems. Here, we introduce SuperScreen, an open-source Python package for simulating the response of 2D superconductors to trapped flux and applied time-independent or quasi-DC magnetic fields for any value of the effective magnetic penetration depth, $\Lambda$. Given an applied magnetic field, SuperScreen solves the 2D London equation using an efficient matrix inversion method to obtain the Meissner currents and magnetic fields in and around structures composed of one or more superconducting thin films of arbitrary geometry. SuperScreen can be used to model screening effects and calculate self- and mutual-inductance in thin film superconducting devices., Comment: 21 pages, 8 figures. This is the accepted version. GitHub repository: https://github.com/loganbvh/superscreen/ . Supplementary Jupyter notebooks: https://github.com/loganbvh/superscreen-paper

The heavy fermion superconductor $\mathrm{U}{\mathrm{Ru}}_{2}{\mathrm{Si}}_{2}$ is a candidate for chiral, time-reversal symmetry-breaking superconductivity with a nodal gap structure. Here, we microscopically visualized superconductivity and spatially inhomogeneous ferromagnetism in $\mathrm{U}{\mathrm{Ru}}_{2}{\mathrm{Si}}_{2}$. We observed linear-$T$ superfluid density, consistent with $d$-wave pairing symmetries including chiral $d$ wave, but did not observe the spontaneous magnetization expected for chiral $d$ wave. Local vortex pinning potentials had either four- or twofold rotational symmetries with various orientations at different locations. Taken together, these data support a nodal gap structure in $\mathrm{U}{\mathrm{Ru}}_{2}{\mathrm{Si}}_{2}$ and suggest that chirality either is not present or does not lead to detectable spontaneous magnetization.

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The tetragonal domain structure in SrTiO3 (STO) is known to modulate the normal-state carrier density in LaAlO3/SrTiO3 (LAO/STO) heterostructures, among other electronic properties, but the effect of STO domains on the superconductivity in LAO/STO has not been fully explored. Using a scanning SQUID susceptometer microscope to map the superconducting response as a function of temperature in LAO/STO, we find that the superconducting transition temperature is spatially inhomogeneous and modulated in a pattern that is characteristic of structural domains in the STO.

Specialized imaging methods are now available to measure the quantum properties of materials with high sensitivity and resolution. These techniques are key to the design, synthesis and understanding of materials with exotic functionalities.

Scanning Superconducting Quantum Interference Device (SQUID) Susceptometry simultaneously images the local magnetic fields and susceptibilities above a sample with sub-micron spatial resolution. Further development of this technique requires a thorough understanding of the current, voltage, and flux ( I V &Phi, ) characteristics of scanning SQUID susceptometers. These sensors often have striking anomalies in their current&ndash, voltage characteristics, which we believe to be due to electromagnetic resonances. The effect of these resonances on the performance of these SQUIDs is unknown. To explore the origin and impact of the resonances, we develop a model that qualitatively reproduces the experimentally-determined I V &Phi, characteristics of our scanning SQUID susceptometers. We use this model to calculate the noise characteristics of SQUIDs of different designs. We find that the calculated ultimate flux noise is better in susceptometers with damping resistors that diminish the resonances than in susceptometers without damping resistors. Such calculations will enable the optimization of the signal-to-noise characteristics of scanning SQUID susceptometers.

The conducting interfaces between the insulators LaAlO${}_{3}$ and SrTiO${}_{3}$ generate a variety of phenomena that are entirely unexpected for insulators. These phenomena include two-dimensional superconductivity and ferromagnetism. A variety of models for mechanisms causing the ferromagnetism has been proposed. By applying a broad set of local and integral measurement techniques to series of samples fabricated to be virtually free of magnetic contaminations, authors' studies conclusively show that the LaAlO${}_{3}$-SrTiO${}_{3}$ interfaces do not intrinsically induce ferromagnetism. The magnetism is caused by defects such as oxygen vacancies generated at the interfaces.

Nanowires can serve as flexible substrates for hybrid epitaxial growth on selected facets, allowing for design of heterostructures with complex material combinations and geometries. In this work we report on hybrid epitaxy of semiconductor - ferromagnetic insulator - superconductor (InAs/EuS/Al) nanowire heterostructures. We study the crystal growth and complex epitaxial matching of wurtzite InAs / rock-salt EuS interfaces as well as rock-salt EuS / face-centered cubic Al interfaces. Because of the magnetic anisotropy originating from the nanowire shape, the magnetic structure of the EuS phase are easily tuned into single magnetic domains. This effect efficiently ejects the stray field lines along the nanowires. With tunnel spectroscopy measurements of the density of states, we show the material has a hard induced superconducting gap, and magnetic hysteretic evolution which indicates that the magnetic exchange fields are not negligible. These hybrid nanowires fulfil key material requirements for serving as a platform for spin-based quantum applications, such as scalable topological quantum computing., 15 pages, 5 figures

Gate-tunable semiconductor-superconductor nanowires with superconducting leads form exotic Josephson junctions that are a highly desirable platform for two types of qubits: those with topological superconductivity (Majorana qubits) and those based on tunable anharmonicity (gatemon qubits). Controlling their behavior, however, requires understanding their electrostatic environment and electronic structure. Here we study gated InAs nanowires with epitaxial aluminum shells. By measuring current-phase relations (CPR) and comparing them with analytical and numerical calculations, we show that we can tune the number of modes, determine the transparency of each mode, and tune into regimes in which electron-electron interactions are apparent, indicating the presence of a quantum dot. To take into account electrostatic and geometrical effects, we perform microscopic self-consistent Schrodinger-Poisson numerical simulations, revealing the energy spectrum of Andreev states in the junction as well as their spatial distribution. Our work systematically demonstrates the effect of device geometry, gate voltage and phase bias on mode behavior, providing new insights into ongoing experimental efforts and predictive device design., Comment: Main: 16 pages, 4 figures. Supplement: 8 pages, 4 figures

Strong vortex pinning in FeSe could be useful for technological applications and could provide clues about the coexistence of superconductivity and nematicity. To characterize the pinning of individual, isolated vortices, we simultaneously apply a local magnetic field and image the vortex motion with scanning SQUID susceptibility. We find that the pinning is highly anisotropic: the vortices move easily along directions that are parallel to the orientations of twin domain walls and pin strongly in a perpendicular direction. These results are consistent with a scenario in which the anisotropy arises from vortex pinning on domain walls and quantify the dynamics of individual vortex pinning in FeSe., 7 pages, 7 figures

We report on a study of epitaxially grown ultrathin Pb films that are only a few atoms thick and have parallel critical magnetic fields much higher than the expected limit set by the interaction of electron spins with a magnetic field, that is, the Clogston-Chandrasekhar limit. The epitaxial thin films are classified as dirty-limit superconductors because their mean-free paths, which are limited by surface scattering, are smaller than their superconducting coherence lengths. The uniformity of superconductivity in these thin films is established by comparing scanning tunneling spectroscopy, scanning superconducting quantum interference device (SQUID) magnetometry, double-coil mutual inductance, and magneto-transport, data that provide average superfluid rigidity on length scales covering the range from microscopic to macroscopic. We argue that the survival of superconductivity at Zeeman energies much larger than the superconducting gap can be understood only as the consequence of strong spin-orbit coupling that, together with substrate-induced inversion-symmetry breaking, produces spin splitting in the normal-state energy bands that is much larger than the superconductor's energy gap.

Topological superconductivity is of both fundamental and technological interest as a novel state of matter with potential applications in quantum information processing. Among the most promising materials for exhibiting intrinsic topological superconductivity is Sr${}_{2}$RuO${}_{4}$, which has shown evidence of triplet pairing and time-reversal symmetry breaking. Here, the authors use a scanning SQUID microscope to measure the local change in the critical temperature under application of anisotropic strain to test for a linear cusp at small strains, a key prediction of existing models for the superconducting state. The reported absence of such a cusp constrains future descriptions of this enigmatic material.

The diamagnetic susceptibility of a superconductor is directly related to its superfluid density. Mutual inductance is a highly sensitive method for characterizing thin films; however, in traditional mutual inductance measurements, the measured response is a non-trivial average over the area of the mutual inductance coils, which are typically of millimeter size. Here we image localized, isolated features in the diamagnetic susceptibility of {\delta}-doped SrTiO3, the 2-DES at the interface between LaAlO3 and SrTiO3, and Nb superconducting thin film systems using scanning superconducting quantum interference device susceptometry, with spatial resolution as fine as 0.7 {\mu}m. We show that these features can be modeled as locally suppressed superfluid density, with a single parameter that characterizes the strength of each feature. This method provides a systematic means of finding and quantifying submicron defects in two-dimensional superconductors., Comment: 11 pages, 10 figures

The high critical temperature superconductor Lanthanum Barium Copper Oxide (La2-xBaxCuO4 or LBCO) exhibits a strong anomaly in critical temperature at 1/8th doping, nematicity, and other interesting properties. We report here Scanning Superconducting Quantum Interference Device (SQUID) imaging of the magnetic fields and susceptibility in a number of thin film LBCO samples with doping in the vicinity of the 1/8th anomaly. Spatially resolved measurements of the critical temperatures of these samples do not show a pronounced depression at 1/8th doping. They do, however, exhibit strong, nearly linear modulations of the susceptibility ("straie") of multiple samples with surprisingly long periods of 1-4 microns. Counterintuitively, vortices trap in positions of largest diamagnetic susceptibility in these striae. Given the rich interplay of different orders in this material system and its known sensitivity to epitaxial strain, we propose phase separation as a possible origin of these features and discuss scenarios in which that might arise.

We have designed and characterized a micro-SQUID with dispersive readout for use in low temperature scanning probe microscopy systems. The design features a capacitively shunted RF SQUID with a tunable resonance frequency from 5 to 12 GHz, micrometer spatial resolution, and integrated superconducting coils for local application of magnetic fields. The SQUID is operated as a nonlinear oscillator with a flux- and power-dependent resonance frequency. Measurements for device characterization and noise benchmarking were carried out at 4 K. The measured flux noise above 10 kHz at 4 K is 80 nΦ0 Hz−1∕2 at a bandwidth of 200 MHz. Estimations suggest that one can benefit from parametric gain based on inherent nonlinearity of the Josephson junction and reduce the flux noise to 30 nΦ0Hz–1∕2 at 100 mK, which corresponds to 10.6 μBHz–1∕2 for a magnetic moment located at the center of the pickup loop.Measuring the magnetic response of mesoscopic samples or mapping it vs. position for extended systems is effective methods for revealing the fundamental quantum properties of condensed matter systems. Over the past few decades, many advanced magnetic imaging schemes have been developed, including magnetic force microscopy,1 scanning Hall probe microscopy,2 superconducting interference devices (SQUIDs),3,4 and NV center based magnetometry.5 The high sensitivity, low back action, and low power dissipation of SQUIDs make them attractive for many types of low temperature experiments. One classic example is the central role of scanning SQUID microscopy in tests of pairing symmetry of high-Tc cuprate superconductors.6 Other prominent applications are the thermodynamic characteristics of persistent currents in normal metal rings7 and proof of edge states in topological insulators in the quantum spin Hall regime.8A key performance for a SQUID is its flux sensitivity. Parametric amplification has been harnessed in nano-SQUIDs based on aluminum junctions9,10 in order to reduce the flux noise down to 30 nΦ0Hz–1∕2 with a bandwidth exceeding 60 MHz.10 Recent studies on parametric amplifiers and dispersive readout of superconducting qubits also harness the nonlinearity of the Josephson junction to boost sensitivity.11–13In scanning SQUID microscopy, signal sources often behave dipole-like, such as superconducting vortices in mesoscopic dots or currents in mesoscopic rings. Smaller SQUIDs provide better coupling to smaller samples which leads to higher spin sensitivity3,14 as the magnetic field of a dipole decreases with 1/r3. Various approaches have been pursued to reduce the size. The smallest nano-SQUID to date has been fabricated by evaporating Nb or Pb15 onto the apex of a sharp quartz tip reaching a loop diameter of below nm and a spin sensitivity of 0.38 μBHz−1/2 at tens of kHz bandwidth. Compared to such size-optimized devices, micro-SQUIDs fabricated using a standard Nb technique have the advantage of on-chip field coils and modulation coils,14 and can be operated at 4 K allowing for a wide range of applications. However, these come at the cost of larger pick-up loops of a few microns and a resulting poorer spin sensitivity of 200 μBHz−1/2 for a magnetic moment located at the center of the pickup loop.The limitation of large pickup loops was previously only overcome by devices with pickup loops defined by the focused-ion-beam,16 but has recently also been achieved by improvements in lithography and shown to offer better spatial resolution as well.17 Here, we present a scanning micro-SQUID which is based on the same fabrication technology incorporating another major advancement. Our design exploits the parametric amplification based on nonlinearities of the SQUID to boost sensitivity. The combination of a smaller pickup loop and parametric amplification of the signal leads to better spin sensitivity (10.6 μBHz−1/2) and higher bandwidth (200 MHz) compared to traditional DC micro-SQUIDs in which the flux sensitivity is mainly limited by internal dissipation.Our devices were fabricated at Hypres Inc. using planarized Nb/AlOx/Nb trilayer Josephson junction technology, including two planarized Nb layers with approximately 0.8 μm minimum feature size. The SQUID consists of a superconducting ring shunted by one Josephson junction with a designed critical current of 20 μA [Fig. 1(a)]. With this geometry, the SQUID is gradiometric, i.e., the effect of any homogeneous background magnetic field approximately cancels out. The smallest pickup loops implemented have an inner (outer) diameter of 1 μm (2 μm). The superconducting loop is shunted by an on-chip parallel-plate capacitor with amorphous silicon dioxide as dielectric which was designed to have a capacitance of 80 pF. The superconducting loop and the capacitor form a resonator with a flux dependent resonance frequency from 5 to 12 GHz. The pickup loops are placed on opposite corners of the parallel-plate capacitor at a distance of about 450 μm so that one loop can be located in close proximity to the sample while the other is kept far away from it. External fields can be applied to the sample by local single-turn field coils situated around each pickup loop. The field coils are fully integrated into the chip layout and can also be used to bias the SQUID at its most sensitive point. Compared to using additional modulation coils,14 this approach has the advantage of reducing the total device inductance, which leads to a higher sensitivity.18 In a scanning microscope, the field coil at the rear end (away from the sample) can be used to bias the SQUID or operate it in flux feedback such that resulting stray fields will not act on the sample, apart from a weak screening current through the pickup loop. The effective diameter of each coil is 7.5 μm, resulting in a mutual inductance of about 0.34 Φ0/mA (for the smallest pickup loop). The SQUID resonator is connected by an on-chip Z0 = 50 Ω coplanar waveguide (CPW) transmission line to the bonding pads. The two field coils are connected by two smaller CPWs to the bottom edge bonding pads [Fig. 1(c)], ending in two parallel-stripline waveguides running alongside the edges of the capacitor towards the respective field coils. Based on estimations, it should thus be possible to apply high frequency signals of at least several GHz to SQUID and sample.

Magnetizing a topological insulator Inducing magnetism in a topological insulator can lead to exotic effects. The usual experimental route is to introduce magnetic dopants into the material, but that approach is intricate and creates unwanted disorder. Wang et al. used a simpler technique: They fabricated a bilayer consisting of Bi 2 Se 3 , a topological insulator, and EuS, a magnet. The physical proximity of EuS induced magnetism on the surface of Bi 2 Se 3 . This approach allowed for the creation of magnetic domains at will and the detection of characteristic current flowing along the domains' edges. Science , this issue p. 948

The combination of ferromagnets with topological superconductors or insulators allows for new phases of matter that support excitations such as chiral edge modes and Majorana fermions. EuS, a wide-band-gap ferromagnetic insulator with a Curie temperature around 16 K, and SrTiO$_3$ (STO), an important substrate for engineering heterostructures, may support these phases. We present scanning superconducting quantum interference device (SQUID) measurements of EuS grown epitaxially on STO that reveal micron-scale variations in ferromagnetism and paramagnetism. These variations are oriented along the STO crystal axes and only change their configuration upon thermal cycling above the STO cubic-to-tetragonal structural transition temperature at 105 K, indicating that the observed magnetic features are due to coupling between EuS and the STO tetragonal structure. We speculate that the STO tetragonal distortions may strain the EuS, altering the magnetic anisotropy on a micron-scale. This result demonstrates that local variation in the induced magnetic order from EuS grown on STO needs to be considered when engineering new phases of matter that require spatially homogeneous exchange.

Semiconductor nanowires with superconducting leads are considered promising for quantum computation. The current–phase relation is systematically explored in gate-tunable InAs Josephson junctions, and is shown to provide a clean handle for characterizing the transport properties of these structures. Gate-tunable semiconductor nanowires with superconducting leads have great potential for quantum computation1,2,3 and as model systems for mesoscopic Josephson junctions4,5. The supercurrent, I, versus the phase, φ, across the junction is called the current–phase relation (CPR). It can reveal not only the amplitude of the critical current, but also the number of modes and their transmission. We measured the CPR of many individual InAs nanowire Josephson junctions, one junction at a time. Both the amplitude and shape of the CPR varied between junctions, with small critical currents and skewed CPRs indicating few-mode junctions with high transmissions. In a gate-tunable junction, we found that the CPR varied with gate voltage: near the onset of supercurrent, we observed behaviour consistent with resonant tunnelling through a single, highly transmitting mode. The gate dependence is consistent with modelled subband structure that includes an effective tunnelling barrier due to an abrupt change in the Fermi level at the boundary of the gate-tuned region. These measurements of skewed, tunable, few-mode CPRs are promising both for applications that require anharmonic junctions6,7 and for Majorana readout proposals8.

Scanning Superconducting QUantum Interference Device (SQUID) microscopy is a powerful tool for imaging local magnetic properties of materials and devices, but it requires a low-vibration cryogenic environment, traditionally achieved by thermal contact with a bath of liquid helium or the mixing chamber of a "wet" dilution refrigerator. We mount a SQUID microscope on the 3 K plate of a Bluefors cryocooler and characterize its vibration spectrum by measuring SQUID noise in a region of sharp flux gradient. By implementing passive vibration isolation, we reduce relative sensor-sample vibrations to 20 nm in-plane and 15 nm out-of-plane. A variable-temperature sample stage that is thermally isolated from the SQUID sensor enables measurement at sample temperatures from 2.8 K to 110 K. We demonstrate these advances by imaging inhomogeneous diamagnetic susceptibility and vortex pinning in optimally-doped YBCO above 90 K., 7 pages, 8 figures

Proximity to a superconductor is predicted to induce exotic quantum phases in topological insulators. Here, scanning superconducting quantum interference device (SQUID) microscopy reveals that aluminum superconducting rings with topologically insulating Bi2Se3 junctions exhibit a conventional, nearly sinusoidal 2π-periodic current-phase relations. Pearl vortices occur in longer junctions, indicating suppressed superconductivity in aluminum, probably due to a proximity effect. Our observations establish scanning SQUID as a general tool for characterizing proximity effects and for measuring current-phase relations in new materials systems.

We demonstrate a design for a scanning superconducting quantum interference device(SQUID) microscope in which the sample temperature can be varied over a large range. In this design, both sample and SQUID are in the same vacuum space, separated by a few microns. By firmly anchoring the SQUID to a low-temperature bath, the sample temperature can be changed while the SQUID remains superconducting. This allows magnetic imaging at varying sample temperatures with micron-scale spatial resolution and the sensitivity of a low- T c SQUID. We demonstrate this approach by imaging the temperature dependence of Abrikosov vortices in thin films of the high-temperature superconductor YBa 2 Cu 3 O 7−δ . We extract the in-plane penetration depth λ ab (T) in our samples from these measurements.

Strontium titanate is a low-temperature, non-Bardeen-Cooper-Schrieffer superconductor that superconducts to carrier concentrations lower than in any other system and exhibits avoided ferroelectricity at low temperatures. Neither the mechanism of superconductivity in strontium titanate nor the importance of the structure and dielectric properties for the superconductivity are well understood. We studied the effects of twin structure on superconductivity in a 5.5-nm-thick layer of niobium-doped SrTiO$_{3}$ embedded in undoped SrTiO$_{3}$. We used a scanning superconducting quantum interference device susceptometer to image the local diamagnetic response of the sample as a function of temperature. We observed regions that exhibited a superconducting transition temperature $T_{c}$ $\gtrsim$ 10% higher than the temperature at which the sample was fully superconducting. The pattern of these regions varied spatially in a manner characteristic of structural twin domains. Our results emphasize that the anisotropic dielectric properties of SrTiO$_{3}$ are important for its superconductivity, and need to be considered in any theory of the mechanism of the superconductivity., 14 pages, 11 figures, Supplemental Information available at http://stanford.edu/group/moler/papers/Noad_STOsuperconductivity_SI.pdf

Manipulation of magnetism is a longstanding goal of research in exotic materials. In this work, we demonstrate that the small ferromagnetic patches in LaAlO(3)/SrTiO(3) heterostructures can be dramatically changed by in situ contact of a scanning probe. Our results provide a platform for manipulation of small magnets through either a strong magneto-elastic coupling or sensitivity to surface modification. The ability to locally control magnetism is particularly interesting due to the presence of superconductivity with strong spin-orbit coupling in LaAlO(3)/SrTiO(3).

The order parameter of the recently-discovered ferric arsenide family of superconductors remains uncertain. Some early experiments on polycrystalline samples suggested line nodes in the order parameter, however later experiments on single crystals have strongly supported fully-gapped superconductivity. An absence of nodes does not rule out unconventional order: {pi} phase shifts between the separate Fermi sheets and time-reversal symmetry-breaking components in the order parameter remain possibilities. One test for unconventional order is scanning magnetic microscopy on well-coupled polycrystalline samples: d- or p-wave order would result in orbital frustration, leading to spontaneous currents and magnetization in the superconducting state. We have performed scanning SQUID microscopy on SmFeAsO{sub 0.85} and NdFeAsO{sub 0.94}F{sub 0.06}, and in neither material do we find spontaneous orbital currents, ruling out p- or d-wave order.

We report the Meissner effect studies on an FeSe thin film grown on Nb doped SrTiO3 substrate by molecular beam epitaxy. Two-coil mutual inductance measurement clearly demonstrates the onset of diamagnetic screening at 65 K, which is consistent with the gap opening temperature determined by previous angle resolved photoemission spectroscopy results. The applied magnetic field causes a broadening of the superconducting transition near the onset temperature, which is the typical behavior for quasi-two-dimensional superconductors. Our results provide direct evidence that FeSe thin film grown on Nb doped SrTiO3 substrate has an onset TC ~ 65 K, which is the highest among all iron based superconductors discovered so far., 9 pages, 3 figures, updated reference list

We use superconducting quantum interference device microscopy to characterize the current-phase relation (CPR) of Josephson junctions from the three-dimensional topological insulator HgTe (3D HgTe). We find clear skewness in the CPRs of HgTe junctions ranging in length from 200 to 600 nm. The skewness indicates that the Josephson current is predominantly carried by Andreev bound states with high transmittance, and the fact that the skewness persists in junctions that are longer than the mean free path suggests that the effect may be related to the helical nature of the Andreev bound states in the surface of HgTe. These experimental results suggest that the topological properties of the normal state can be inherited by the induced superconducting state, and that 3D HgTe is a promising material for realizing the many exciting proposals that require a topological superconductor.

We present transport and scanning SQUID measurements on InAs/GaSb double quantum wells, a system predicted to be a two-dimensional topological insulator. Top and back gates allow independent control of density and band offset, allowing tuning from the trivial to the topological regime. In the trivial regime, bulk conductivity is quenched but transport persists along the edges, superficially resembling the predicted helical edge-channels in the topological regime. We characterize edge conduction in the trivial regime in a wide variety of sample geometries and measurement configurations, as a function of temperature, magnetic field, and edge length. Despite similarities to studies claiming measurements of helical edge channels, our characterization points to a non-topological origin for these observations.

Recent measurements of the superconducting penetration depth in Ba(Fe 1− x Co x ) 2 As 2 appeared to disagree on the magnitude and curvature of Δ λ ab ( T ), even near optimal doping. These measurements were carried out on different samples grown by different groups. To understand the discrepancy, we use scanning SQUID susceptometry and a tunnel diode resonator to measure the penetration depth in a single sample. The penetration depth observed by the two techniques is identical with no adjustments. We conclude that any discrepancies arise from differences between samples, either in growth or crystal preparation.

High-purity and homogeneous YBa2Cu3Oy single crystals with carrier doping level near the AFM-SC boundary have been obtained in the oxygen content range between y = 6.340 and 6.370. The crystals are ortho-II phase at room temperature and undergo the orthorhombic to tetragonal transition at about 140_Degree_C. They show sharp superconducting transitions, with Tc between 4 and 20 K. Tc changes by 0.8 K when the oxygen content y is changed by 0.001, and is also sensitive to annealing conditions near room temperature, due to the dependence of doping on oxygen ordering correlation lengths. Crystals with oxygen content y lower than 6.345 are non-superconducting., Comment: 6 pages

Scanning Superconducting QUantum Interference Device (SQUID) microscopy provides valuable information about magnetic properties of materials and devices. The magnetic flux response of the SQUID is often linearized with a flux-locked feedback loop, which limits the response time to microseconds or longer. In this work, we present the design, fabrication, and characterization of a novel scanning SQUID sampler with a 40-ps time resolution and linearized response to periodically triggered signals. Other design features include a micron-scale pickup loop for the detection of local magnetic flux, a field coil to apply a local magnetic field to the sample, and a modulation coil to operate the SQUID sampler in a flux-locked loop to linearize the flux response. The entire sampler device is fabricated on a 2 mm × 2 mm chip and can be scanned over macroscopic planar samples. The flux noise at 4.2 K with 100 kHz repetition rate and 1 s of averaging is of order 1 mΦ0. This SQUID sampler will be useful for imaging dynamics in magnetic and superconducting materials and devices.

Quantum spin Hall devices with edges much longer than several microns do not display ballistic transport: that is, their measured conductances are much less than $e^2/h$ per edge. We imaged edge currents in InAs/GaSb quantum wells with long edges and determined an effective edge resistance. Surprisingly, although the effective edge resistance is much greater than $h/e^2$, it is independent of temperature up to 30 K within experimental resolution. Known candidate scattering mechanisms do not explain our observation of an effective edge resistance that is large yet temperature-independent., Comment: Version accepted to Physical Review Letters (http://prl.aps.org/). 12 pages, 3 figures. Supplementary Online Materials available at http://stanford.edu/group/moler/papers/Spanton_InAsGaSb_imaging_SI_v2.pdf

We report on a scanning superconducting quantum interference device microscope operating at temperatures down to 20 mK in a dilution refrigerator. The instrument is designed for studying quantum mechanical coherence effects in mesoscopic systems and investigating magnetic effects on a mesoscopic length scale in novel materials. We have demonstrated the low-temperature operating capabilities of the instrument by studying superconducting tin disks and the superconducting transition of a thin-film tungsten sample and vortices in the same film. Looking forward, we discuss the applicability of the instrument to measurements of persistent currents in normal-metal rings.

We report a scanning superconducting quantum interference device (SQUID) microsusceptometer with a spatial resolution of 8 μm, tested by measuring the susceptibility of individual 3 μm diam tin disks. Images of the disks agree well with numerical modeling based on the known geometry of the SQUID microsusceptometers. The low-field spin sensitivity between 1.5 and 6 K is 1×105 μB/Hz while scanning.

Vibrations can cause noise in scanning probe microscopies. Relative vibrations between the scanning sensor and the sample are important but can be more difficult to determine than absolute vibrations or vibrations relative to the laboratory. We measure the noise spectral density in a scanning SQUID microscope as a function of position near a localized source of magnetic field, and show that we can determine the spectra of all three components of the relative sensor-sample vibrations. This method is a powerful tool for diagnosing vibrational noise in scanning microscopies., 4 pages, 3 figures

The interlayer penetration depth in layered superconductors may be determined from scanning Superconducting QUantum Interference Device (SQUID) microscope images of interlayer Josephson vortices. The authors compare their findings at 4 K for single crystals of the organic superconductor {kappa}-(BEDT-TTF){sub 2}Cu(NCS){sub 2} and three near-optimally doped cuprate superconductors: La{sub 2{minus}x}Sr{sub x}CuO{sub 4}, (Hg, Cu)Ba{sub 2}CuO{sub 4+{delta}}, and Tl{sub 2}Ba{sub 2}CuO{sub 6+{delta}}.

In a layered superconductor, the interlayer coupling strength determines the spatial variation of the magnetic fields parallel to the layers. Scanning SQUID microscope images of an edge of a single crystal of the layered organic superconductor show regions of inhomogeneous coupling as well as trapped interlayer Josephson vortices. Quantitative modelling of individual isolated vortices indicates an interlayer penetration depth . Previous bulk measurements that indicated a weaker interlayer coupling may have been dominated by inhomogeneities.

The strength of the interlayer Josephson tunneling in layered superconductors is an essential test of the interlayer tunneling model as a mechanism for superconductivity, as well as a useful phenomenological parameter. A scanning superconducting quantum interference device (SQUID) microscope was used to image interlayer Josephson vortices in Tl 2 Ba 2 CuO 6+ δ and to obtain a direct measure of the interlayer tunneling in a high–transition temperature superconductor with a single copper oxide plane per unit cell. The measured interlayer penetration depth, λ c , is ∼20 micrometers, about 20 times the penetration depth required by the interlayer tunneling model.

Grain boundary junctions in high-T/sub c/ thin films generally consist of facets with typical dimensions below 100 nm. In combination with a d(x/sup 2/-y/sup 2/) symmetry component of the order parameter, this faceting gives rise to an inhomogeneous critical current density J/sub c/ along the grain boundary. The inhomogeneity is most prominent for asymmetric 45/spl deg/ [001] tilt grain boundaries. For a large fraction of the facets in these boundaries the order parameter orientation gives rise to an additional /spl pi/ phase difference, and therefore to a 'negative' critical current density. This leads to highly anomalous magnetic field dependences of the critical current. Direct imaging with scanning SQUID microscopy provides evidence that magnetic flux is generated spontaneously in these boundaries. These observations have several significant implications, both for understanding the properties of grain boundaries in high-T/sub c/ superconductors and for their applications.

We present measurements of the specific heat of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ single crystals from 2 to 10 K and from 0 to 10 T, including both twinned and untwinned crystals with various oxygen doping (7-\ensuremath{\delta}=6.95, 6.97, and 6.99). The zero-field specific heat includes a linear-T term which is small compared to other ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ samples, but large compared to the ${\mathrm{T}}^{2}$ electronic specific heat predicted for a superconductor with clean lines of nodes in the gap function. This zero-field linear-T term is found to decrease with decreasing concentration of twin boundaries and oxygen vacancies \ensuremath{\delta}. The specific heat increases in a magnetic field and has a strong dependence on field orientation. Several possible field-dependent contributions are compared to the data, including a Schottky anomaly, vortex-vortex interactions, a traditional mixed-state HT term associated with vortex cores, and a $\sqrt{H}$T term predicted by G. Volovik for the mixed state in superconductors with lines of nodes in the gap function. The field dependence of the specific heat, according to a comparison of fits based on these possibilities, supports the existence of lines of nodes and suggests the presence of quasiparticle excitations outside the vortex core.

NMR experiments are ideally carried out in well-controlled magnetic fields. When samples of natural porous materials are studied, the situation can be complicated if the sample itself contains magnetic components, giving rise to internal magnetic fields in the pore space that modulate the externally applied fields. If not properly accounted for, the internal fields can lead to misinterpretation of relaxation, diffusion, or imaging data. To predict the potential effect of internal fields, and develop effective mitigation strategies, it is important to develop a quantitative understanding of the magnitude and distribution of internal fields occurring in natural porous media. To develop such understanding, we employ scanning SQUID microscopy, a technique that can detect magnetic field variations very accurately at high spatial resolution (∼3 μm). We prepared samples from natural unconsolidated aquifer material, and scanned areas of about 200 × 200 μm in a very low background magnetic field of ∼2 μT. We found large amplitude variations with a magnitude of about 2 mT, across a relatively long spatial scale of about 200 μm, that are associated with a large magnetic grain (>50 μm radius) with a strong magnetic remanence. We also detected substantial variations exceeding 60 μT on small spatial scales of about ∼10 μm. We attribute these small-scale variations to very fine-grained magnetic material. Because we made our measurements at very low background field, the observed variations are not induced by the background field but due to magnetic remanence. Consequently, the observed internal fields will affect even low-field NMR experiments.

As part of a joint Stanford/IBM effort to build a scanning SQUID microscopy user facility at Stanford, we have designed and fabricated three types of scanning SQUID microscope sensors. The first is a SQUID susceptometer, with a symmetric, gradiometric design, pickup loops with 0.1 micrometer minimum feature size integrated into the SQUID body through coaxially shielded leads, integrated flux modulation coils, and counterwound one-turn field coils. The second is a SQUID sampler, in which a picosecond current pulse generated on chip is inductively coupled into a hysteric scanning SQUID sensor. The feedback flux to keep the average SQUID voltage at a constant value is proportional to the flux through the sensor pickup loop at a fixed time delay. JSPICE simulations indicate that time resolutions below 10 picosec can be obtained. The third type is a dispersive SQUID, in which the capacitance and Josephson inductance of a one-junction SQUID are chosen so it has an LC resonance in the GHz range. The Josephson inductance depends on the magnetic flux through the SQUID. The magnetic flux is sensed through phase shifts in the reflected microwave signals at resonance. Calculations indicate spin sensitivities better than 1 Bohr magneton per root Hz for a 0.3 micrometer pickup loop diameter, with bandwidths of about 100 MHz possible.

The quantum spin Hall (QSH) state is a genuinely new state of matter characterized by a non-trivial topology of its band structure. Its key feature is conducting edge channels whose spin polarization has potential for spintronic and quantum information applications. The QSH state was predicted and experimentally demonstrated to exist in HgTe quantum wells. The existence of the edge channels has been inferred from the fact that local and non-local conductance values in sufficiently small devices are close to the quantized values expected for ideal edge channels and from signatures of the spin polarization. The robustness of the edge channels in larger devices and the interplay between the edge channels and a conducting bulk are relatively unexplored experimentally, and are difficult to assess via transport measurements. Here we image the current in large Hallbars made from HgTe quantum wells by probing the magnetic field generated by the current using a scanning superconducting quantum interference device (SQUID). We observe that the current flows along the edge of the device in the QSH regime, and furthermore that an identifiable edge channel exists even in the presence of disorder and considerable bulk conduction as the device is gated or its temperature is raised. Our results represent a versatile method for the characterization of new quantum spin Hall materials systems, and confirm both the existence and the robustness of the predicted edge channels., Comment: 11 pages, 4 figures; v2: link to supplementary information added, see http://www.stanford.edu/group/moler/publications.html

The ability to control materials properties through interface engineering is demonstrated by the appearance of conductivity at the interface of certain insulators, most famously the {001} interface of the band insulators LaAlO$_{3}$ and TiO$_{2}$-terminated SrTiO$_{3}$ (STO). Transport and other measurements in this system show a plethora of diverse physical phenomena. To better understand the interface conductivity, we used scanning superconducting quantum interference device microscopy to image the magnetic field locally generated by current in an interface. At low temperature, we found that the current flowed in conductive narrow paths oriented along the crystallographic axes, embedded in a less conductive background. The configuration of these paths changed on thermal cycling above the STO cubic-to-tetragonal structural transition temperature, implying that the local conductivity is strongly modified by the STO tetragonal domain structure. The interplay between substrate domains and the interface provides an additional mechanism for understanding and controlling the behaviour of heterostructures.