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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.

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.

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.

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

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.

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 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.

We have used a high-resolution scanning SQUID microscope to directly image conventional ( $h/2e$) Josephson vortices trapped in grain boundaries, and half-integer ( $h/4e$) Josephson vortices trapped at the tricrystal point, of the high- ${T}_{c}$ superconductor ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ grown on tricrystal substrates of SrTi${\mathrm{O}}_{3}$. Our observation of the half-integer vortex at the tricrystal point is the first direct demonstration of the positive paramagnetic Meissner effect in a polycrystalline high- ${T}_{c}$ film. In addition, our images provide the first direct measurement of the Josephson penetration depth.

The total specific heat of YBa2Cu3O6.95 single crystals includes contributions from phonons and spin-1/2 particles, as well as electronic contributions. The electronic specific heat is described by a quadratic term αT2 in zero field and a linear term [γ(0)+γ⊥(H)]T which is increased when a magnetic field H is applied perpendicular to the CuO2 planes. In agreement with d-wave superconductivity, we find that α≈γn/Tc and γ⊥(H)≈γn(H/Hc2)1/2, where γn is the coefficient of the normal-state linear term. The H1/2 dependence of the density of states at the Fermi level was predicted by G. Volovik for lines of nodes in the gap: the quasiparticles which contribute to this density of states are close to the nodes in momentum space and are located outside the vortex core.

In the past, magnetic images acquired using scanning Superconducting Quantum Interference Device (SQUID) microscopy have been interpreted using simple models for the sensor point spread function. However, more complicated modeling is needed when the characteristic dimensions of the field sensitive areas in these sensors become comparable to the London penetration depth. In this paper we calculate the response of SQUIDs with deep sub-micron pickup loops to different sources of magnetic fields by solving coupled London's and Maxwell's equations using the full sensor geometry. Tests of these calculations using various field sources are in reasonable agreement with experiments. These calculations allow us to more accurately interpret sub-micron spatial resolution data obtained using scanning SQUID microscopy., 15 pages, 9 figures

We describe a simple method to study vortex dynamics that can determine or set an upper limit on the vortex mass. The specific heat of the vortex lattice in layered superconductors has a classical limit of 1 kB per pancake vortex if the vortex mass is zero. If the vortex mass mv is finite, a new Einstein branch of normal modes will appear with a crossover temperature ΘE ∝ mv−1, and the specific heat will saturate at a new classical limit of 2 kB per pancake vortex.

Superconducting QUantum Interference Device (SQUID) microscopy has excellent magnetic field sensitivity, but suffers from modest spatial resolution when compared with other scanning probes. This spatial resolution is determined by both the size of the field sensitive area and the spacing between this area and the sample surface. In this paper we describe scanning SQUID susceptometers that achieve sub-micron spatial resolution while retaining a white noise floor flux sensitivity of $\approx 2\mu\Phi_0/Hz^{1/2}$. This high spatial resolution is accomplished by deep sub-micron feature sizes, well shielded pickup loops fabricated using a planarized process, and a deep etch step that minimizes the spacing between the sample surface and the SQUID pickup loop. We describe the design, modeling, fabrication, and testing of these sensors. Although sub-micron spatial resolution has been achieved previously in scanning SQUID sensors, our sensors not only achieve high spatial resolution, but also have integrated modulation coils for flux feedback, integrated field coils for susceptibility measurements, and batch processing. They are therefore a generally applicable tool for imaging sample magnetization, currents, and susceptibilities with higher spatial resolution than previous susceptometers., Comment: 13 figures

We present depth resolved X-ray micro-Laue diffraction experiments on the low temperature domain structure of SrTiO3. At 80 K, monochromatic X-ray diffraction shows an elongated out-of-plane unit cell axis within a matrix of in-plane oriented tetragonal unit cells. Full deviatoric strain mappings from white beam diffraction show a dominance of two tetragonal domain orientations (x- and z-axes) over a large area of sample surface. This information sets an upper bound on domain wall widths and offers a method for studying 3D domain structure at low temperatures.

The interface between the insulating oxides LaAlO${}_{3}$ and SrTiO${}_{3}$ exhibits a superconducting two-dimensional electron system that can be modulated by a gate voltage. While the conductivity has been probed extensively and gating of the superconducting critical temperature has been demonstrated, the question as to whether, and if so how, the gate tunes the superfluid density and superconducting order parameter needs to be answered. We present local magnetic susceptibility, related to the superfluid density, as a function of temperature, gate voltage, and location. We show that the temperature dependence of the superfluid density at different gate voltages collapses to a single curve that is characteristic of a full superconducting gap. Further, we show that the dipole moments observed in this system are not modulated by the gate voltage.

In LaAlO(3)/SrTiO(3) heterointerfaces, charge carriers migrate from the LaAlO(3) to the interface in an electronic reconstruction. Magnetism has been observed in LaAlO(3)/SrTiO(3), but its relationship to the interface conductivity is unknown. Here we show that reconstruction is necessary, but not sufficient, for the formation of magnetism. Using scanning superconducting quantum interference device microscopy we find that magnetism appears only above a critical LaAlO(3) thickness, similar to the conductivity. We observe no change in ferromagnetism with gate voltage, and detect ferromagnetism in a non-conducting p-type sample. These observations indicate that the carriers at the interface do not need to be itinerant to generate magnetism. The ferromagnetism appears in isolated patches whose density varies greatly between samples. This inhomogeneity strongly suggests that disorder or local strain generates magnetism in a population of the interface carriers.

Scanning SQUID susceptometry images the local magnetization and susceptibility of a sample. By accurately modeling the SQUID signal we can determine the physical properties such as the penetration depth and permeability of superconducting samples. We calculate the scanning SQUID susceptometry signal for a superconducting slab of arbitrary thickness with isotropic London penetration depth, on a non-superconducting substrate, where both slab and substrate can have a paramagnetic response that is linear in the applied field. We derive analytical approximations to our general expression in a number of limits. Using our results, we fit experimental susceptibility data as a function of the sample-sensor spacing for three samples: 1) delta-doped SrTiO3, which has a predominantly diamagnetic response, 2) a thin film of LaNiO3, which has a predominantly paramagnetic response, and 3) a two-dimensional electron layer (2-DEL) at a SrTiO3/AlAlO3 interface, which exhibits both types of response. These formulas will allow the determination of the concentrations of paramagnetic spins and superconducting carriers from fits to scanning SQUID susceptibility measurements., Comment: 11 pages, 13 figures

In heterostructures of LaAlO3 (LAO) and SrTiO3 (STO), two nonmagnetic insulators, various forms of magnetism have been observed [1-7], which may [8, 9] or may not [10] arise from interface charge carriers that migrate from the LAO to the interface in an electronic reconstruction [11]. We image the magnetic landscape [5] in a series of n-type samples of varying LAO thickness. We find ferromagnetic patches that appear only above a critical thickness, similar to that for conductivity [12]. Consequently we conclude that an interface reconstruction is necessary for the formation of magnetism. We observe no change in ferromagnetism with gate voltage, and detect ferromagnetism in a non-conducting p-type sample, indicating that the carriers at the interface do not need to be itinerant to generate magnetism. The fact that the ferromagnetism appears in isolated patches whose density varies greatly between samples strongly suggests that disorder or local strain induce magnetism in a population of the interface carriers.

The magnetic field dependence of the electronic density of states at the Fermi level, $N({E}_{F},H)$, is determined in single-crystal Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6.95}$ by specific heat measurements. The total specific heat is best described by including two predictions for the electronic specific heat of $d$-wave superconductivity: a ${T}^{2}$ term in zero field and an increased linear term in a magnetic field applied perpendicular to the Cu${\mathrm{O}}_{2}$ planes. The additional linear term, which implies a finite $N({E}_{F},H)$, obeys $N({E}_{F},H)\ensuremath{\propto}{(\frac{H}{{H}_{c2}})}^{\frac{1}{2}}$ as predicted by Volovik for superconductivity with lines of nodes in the gap.

We demonstrate the controlled, reversible manipulation of individual vortices in a superconductor with a locally applied magnetic field. The local field is supplied by a field coil on a superconducting quantum interference device (SQUID). The SQUID is used to image the vortices before and after moving. This device can be used both to push individual vortices and to create individual vortex–antivortex pairs. We calculate the force applied on a rigid vortex and find that ∼0.5 pN is necessary to move vortices in underdoped single crystals of YBa2Cu3O6.354 with Tc∼ 12 K.

Rings are a model system for studying phase coherence in one dimension. Superconducting rings have states with uniform phase windings that are integer multiples of 2$\pi$ called fluxoid states. When the energy difference between these fluxoid states is of order the temperature so that phase slips are energetically accessible, several states contribute to the ring's magnetic response to a flux threading the ring in thermal equilibrium and cause a suppression or downturn in the ring's magnetic susceptibility as a function of temperature. We review the theoretical framework for superconducting fluctuations in rings including a model developed by Koshnick$^1$ which includes only fluctuations in the ring's phase winding number called fluxoid fluctuations and a complete model by von Oppen and Riedel$^2$ that includes all thermal fluctuations in the Ginzburg-Landau framework. We show that for sufficiently narrow and dirty rings the two models predict a similar susceptibility response with a slightly shifted Tc indicating that fluxoid fluctuations are dominant. Finally we present magnetic susceptibility data for rings with different physical parameters which demonstrate the applicability of our models. The susceptibility data spans a region in temperature where the ring transitions from a hysteretic to a non hysteretic response to a periodic applied magnetic field. The magnetic susceptibility data, taken where transitions between fluxoid states are slow compared to the measurement time scale and the ring response was hysteretic, decreases linearly with increasing temperature resembling a mean field response with no fluctuations. At higher temperatures where fluctuations begin to play a larger role a crossover occurs and the non-hysteretic data shows a fluxoid fluctuation induced suppression of diamagnetism below the mean field response that agrees well with the models.