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Using a focused He$^+$ beam for nanopatterning and writing of Josephson barriers we fabricated specially shaped Josephson junctions of in-line geometry in YBa$_2$Cu$_3$O$_7$ thin film microbridges with an asymmetry ratio of critical currents of opposite polarities (non-reciprocity ratio) $\approx 7$ at optimum magnetic field. Those Josephson diodes were subsequently used as ratchets to rectify an applied ac current into a dc voltage. We also demonstrate the operation of such a ratchet in the loaded regime, where it produces a nonzero dc output power and yields a thermodynamic efficiency of up to $75\,\mathrm{\%}$. The ratchet shows record figures of merit: an output dc voltage of up to $212\,\mathrm{\mu V}$ and an output power of up to $0.2\,\mathrm{nW}$. The device has an essential area $\approx 1\,\mathrm{\mu m^2}$. For rectification of quasistatic Gaussian noise, the figures of merit are more modest, however the efficiency can be as high as for the deterministic ac drives within some regimes. Since the device is based on YBa$_2$Cu$_3$O$_7$, it can operate at temperatures up to $\sim40\,\mathrm{K}$, where more noise is available for rectification.

Thin films of the superconductor YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) were modified by low-energy light-ion irradiation employing collimated or focused He$^+$ beams, and the long-term stability of irradiation-induced defects was investigated. For films irradiated with collimated beams, the resistance was measured in situ during and after irradiation and analyzed using a phenomenological model. The formation and stability of irradiation-induced defects are highly influenced by temperature. Thermal annealing experiments conducted in an Ar atmosphere at various temperatures demonstrated a decrease in resistivity and allowed us to determine diffusion coefficients and the activation energy $\Delta E = (0.31 \pm 0.03)$ eV for diffusive oxygen rearrangement within the YBCO unit cell basal plane. Additionally, thin YBCO films, nanostructured by focused He$^+$-beam irradiation into vortex pinning arrays, displayed significant commensurability effects in magnetic fields. Despite the strong modulation of defect densities in these pinning arrays, oxygen diffusion during room-temperature annealing over almost six years did not compromise the signatures of vortex matching, which remained precisely at their magnetic fields predicted by the pattern geometry. Moreover, the critical current increased substantially within the entire magnetic field range after long-term storage in dry air. These findings underscore the potential of ion irradiation in tailoring the superconducting properties of thin YBCO films., Comment: 16 pages, 8 figures

Suitably patterned single crystals made of the cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (BSCCO), intrinsically forming a stack of Josephson junctions, can generate electromagnetic radiation in the lower terahertz regime. Due to Joule heating the emission power of single stacks seems to be limited to values below 100 $\mu$W. To increase the radiation power, mutually synchronized arrays situated on the same BSCCO base crystal have been studied. Mutual electromagnetic interactions via a connecting BSCCO base crystal have been considered essential for synchronization, but the approach still suffers from Joule heating, preventing the synchronization of more than three stacks. In the present paper we show, on the basis of two emitting stacks, that mutual synchronization can also be achieved by stand-alone stacks contacted by gold layers and sharing only a common gold layer. Compared to BSCCO base crystals, the gold layers have a much higher thermal conductivity and their patterning is not very problematic. We analyze our results in detail, showing that the two oscillators exhibit phase correlations over a range of $\pm$0.4 GHz relative to their center frequencies, which we mainly studied between 745 GHz and 765 GHz. However, we also find that strong phase gradients in the beams radiated from both the mutually locked stacks and the unlocked ones play an important role and, presumably, diminish the detected emission power due to destructive interference. We speculate that the effect arises from higher-order cavity modes which are excited in the individual stacks. Our main message is that the mutual interaction provided by a common gold layer may open new possibilities for relaxing the Joule-heating-problem, allowing the synchronization of a higher number of stacks. Our findings may boost attempts to substantially increase the output power levels of the BSCCO terahertz oscillators.

We present a way to We present a way to fabricate bicrystal Josephson junctions of high-Tc cuprate superconductors that does not require bulk bicrystalline substrates. Based on vector substrate technology, this novel approach makes use of a few tens-of-nanometers-thick bicrystalline membranes transferred onto conventional substrates.We demonstrate 24{\deg} YBa2Cu3O7-x Josephson junctions fabricated on sapphire single crystals by utilizing 10-nm-thick bicrystalline membranes of SrTiO3. This technique allows one to manufacture bicrystalline Josephson junctions of high-Tc superconductors on a large variety of bulk substrate materials, providing novel degrees of freedom in designing the junctions and their electronic properties. It furthermore offers the capability to replace the fabrication of bulk bicrystalline substrates with thin-film growth methods

Controlled engineering of vortex pinning sites in copper-oxide superconductors is a critical issue in manufacturing devices based on magnetic flux quanta. To address this, we employed a focused He-ion beam (He-FIB) to irradiate thin YBa$_2$Cu$_3$O$_{7-\delta}$ films and create ultradense hexagonal arrays of defects with lattice spacings as small as 20 nm. Critical current and magnetoresistance measurements demonstrate efficient pinning by an unprecedentedly high matching field of 6 T visible in a huge temperature range from the critical temperature $T_c$ down to 2 K. These results show that He-FIB irradiation provides excellent opportunities for the development and application of superconducting fluxonic devices based on Abrikosov vortices. In particular, our findings suggest that such devices can operate at temperatures far below $T_c$, where superconductivity is robust., Comment: 12 pages, 7 figures

Superconducting circuits with nonlinear elements such as Josephson tunnel junctions or kinetic inductance nanowires are the workhorse for microwave quantum and superconducting sensing technologies. For devices, which can be operated at high temperatures and large magnetic fields, nano-constrictions as nonlinear elements are recently under intense investigation. Constrictions, however, are far less understood than conventional Josephson tunnel junctions, and their current-phase-relationships (CPRs) -- although highly important for device design -- are hard to predict. Here, we present a niobium microwave cavity with a monolithically integrated, neon-ion-beam patterned three-dimensional (3D) nano-constriction. By design, we obtain a DC-current-tunable microwave circuit and characterize how the bias-current-dependent constriction properties impact the cavity resonance. Based on the results of these experiments, we reconstruct the CPR of the nanoconstriction. Finally, we discuss the Kerr nonlinearity of the device, a parameter important for many high-dynamic-range applications and an experimental probe for the second and third derivatives of the CPR. Our platform provides a useful method to comprehensively characterize nonlinear elements integrated in microwave circuits and could be of interest for current sensors, hybrid quantum systems and parametric amplifiers. Our findings furthermore contribute to a better understanding of nano-fabricated 3D constrictions.

There is growing interest in strongly correlated insulator thin films because the intricate interplay of their intrinsic and extrinsic state variables causes memristive behavior that might be used for bio-mimetic devices in the emerging field of neuromorphic computing. In this study we find that laser irradiation tends to drive V$_2$O$_3$ from supercooled/superheated metastable states towards thermodynamic equilibrium, most likely in a non-thermal way. We study thin films of the prototypical Mott-insulator V$_2$O$_3$, which show spontaneous phase separation into metal-insulator herringbone domains during the Mott transition. Here, we use low-temperature microscopy to investigate how these metal-insulator domains can be modified by scanning a focused laser beam across the thin film surface. We find that the response depends on the thermal history: When the thin film is heated from below the Mott transition temperature, the laser beam predominantly induces metallic domains. On the contrary, when the thin film is cooled from a temperature above the transition, the laser beam predominantly induces insulating domains. Very likely, the V$_2$O$_3$ thin film is in a superheated or supercooled state, respectively, during the first-order phase transition, and the perturbation by a laser beam drives these metastable states into stable ones. This way, the thermal history is locally erased. Our findings are supported by a phenomenological model with a laser-induced lowering of the energy barrier between the metastable and equilibrium states., Comment: 14 pages, 10 figures

The shot noise in tunneling experiments reflects the Poissonian nature of the tunneling process. The shot noise power is proportional to both the magnitude of the current and the effective charge of the carrier. Shot noise spectroscopy thus enables, in principle, to determine the effective charge q of the charge carriers that tunnel. This can be used to detect electron pairing in superconductors: in the normal state, the noise corresponds to single electron tunneling (q = 1e), while in the paired state, the noise corresponds to q = 2e. Here, we use a newly developed amplifier to reveal that in typical mesoscopic superconducting junctions, the shot noise does not reflect the signatures of pairing and instead stays at a level corresponding to q = 1e. We show that transparency can control the shot noise and this q = 1e is due to the large number of tunneling channels with each having very low transparency. Our results indicate that in typical mesoscopic superconducting junctions one should expect q = 1e noise, and lead to design guidelines for junctions that allow the detection of electron pairing.

The focused ion beam (FIB) is a powerful tool for the fabrication, modification and characterization of materials down to the nanoscale. Starting with the gallium FIB, which was originally intended for photomask repair in the semiconductor industry, there are now many different types of FIB that are commercially available. These instruments use a range of ion species and are applied broadly in materials science, physics, chemistry, biology, medicine, and even archaeology. The goal of this roadmap is to provide an overview of FIB instrumentation, theory, techniques and applications. By viewing FIB developments through the lens of the various research communities, we aim to identify future pathways for ion source and instrumentation development as well as emerging applications, and the scope for improved understanding of the complex interplay of ion-solid interactions. We intend to provide a guide for all scientists in the field that identifies common research interests and will support future fruitful interactions connecting tool development, experiment and theory. While a comprehensive overview of the field is sought, it is not possible to cover all research related to FIB technologies in detail. We give examples of specific projects within the broader context, referencing original works and previous review articles throughout., Comment: This publication is based upon work from the COST Action FIT4NANO CA19140, supported by COST (European Cooperation in Science and Technology) https://www.cost.eu/. Financial support from COST Action CA19140 is acknowledged http://www.fit4nano.eu/ Version 3 has many text and language edits as well as layout tuning but no substantial new content

Nonlinear microwave circuits are key elements for many groundbreaking research directions and technologies, such as quantum computation and quantum sensing. The majority of microwave circuits with Josephson nonlinearities to date is based on aluminum thin films, and therefore they are severely restricted in their operation range regarding temperatures and external magnetic fields. Here, we present the realization of superconducting niobium microwave resonators with integrated, three-dimensional (3D) nanobridge-based superconducting quantum interference devices. The 3D nanobridges (constriction weak links) are monolithically patterned into pre-fabricated microwave LC circuits using neon ion beam milling, and the resulting quantum interference circuits show frequency tunabilities, flux responsivities and Kerr nonlinearities on par with comparable aluminum nanobridge devices, but with the perspective of a much larger operation parameter regime. Our results reveal great potential for application of these circuits in hybrid systems with e.g. magnons and spin ensembles or in flux-mediated optomechanics.

The competition between intrinsic disorder in superconducting YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ (YBCO) thin films and an ultradense triangular lattice of cylindrical pinning centers spaced at 30 nm intervals results in an ordered Bose glass phase of vortices. The samples were created by scanning the focused beam of a helium-ion microscope over the surface of the YBCO thin film to form columns of point defects where superconductivity was locally suppressed. The voltage-current isotherms reveal critical behavior and scale in the vicinity of the second-order glass transition. The latter exhibits a distinct peak in melting temperature ($T_g$) vs. applied magnetic field ($B_a$) at the magnetic commensurability field, along with a sharp rise in the lifetimes of glassy fluctuations. Angle-dependent magnetoresistance measurements in constant-Lorentz-force geometry unveil a strong increase in anisotropy compared to a pristine reference film where the density of vortices matches that of the columnar defects. The pinning is therefore, dominated by the magnetic-field component parallel to the columnar defects, exposing its one-dimensional character. These results support the idea of an ordered Bose glass phase., Comment: 9 pages, 4 figures

Some correlated materials display an insulator-to-metal transition as the temperature is increased. In most cases this transition can also be induced electrically, resulting in volatile resistive switching due to the formation of a conducting filament. While this phenomenon has attracted much attention due to potential applications, many fundamental questions remain unaddressed. One of them is its characteristic lengths: what sets the size of these filaments, and how does this impact resistive switching properties. Here we use a combination of wide-field and scattering-type scanning near-field optical microscopies to characterize filament formation in NdNiO3 and SmNiO3 thin films. We find a clear trend: smaller filaments increase the current density, yielding sharper switching and a larger resistive drop. With the aid of numerical simulations, we discuss the parameters controlling the filament width and, hence, the switching properties.

We report the levitation of a superconducting lead-tin sphere with 100 micrometer diameter (corresponding to a mass of 5.6 micrograms) in a static magnetic trap formed by two coils in an anti-Helmholtz configuration, with adjustable resonance frequencies up to 240 hertz. The center-of-mass motion of the sphere is monitored magnetically using a dc superconducting quantum interference device as well as optically and exhibits quality factors of up to 2.6e7. We also demonstrate 3D magnetic feedback control of the sphere's motion. The setup is housed in a dilution refrigerator operating at 15 millikelvin. By implementing a cryogenic vibration isolation system we can attenuate environmental vibrations at 200 hertz by approximately seven orders of magnitude. The combination of low temperature, large mass and high quality factor as well as adjustable resonance frequencies provides a promising platform for testing quantum physics in previously unexplored regimes with high mass and long coherence times., Comment: Updated to published version

The defect-rich morphology of YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ (YBCO) thin films leads to a glass-like arrangement of Abrikosov vortices which causes the resistance to disappear in vanishing current densities. This vortex glass consists of entangled vortex lines and is identified by a characteristic scaling of the voltage-current isotherms. Randomly distributed columnar defects stratify the vortex lines and lead to a Bose glass. Here, we report on the observation of an ordered Bose glass in a YBCO thin film with a hexagonal array of columnar defects with 30 nm spacings. The periodic pinning landscape was engineered by a focused beam of 30 keV He$^+$ ions in a helium-ion microscope., Comment: 10 pages, 4 figures

Hybrid quantum systems involving cold atoms and microwave resonators can enable cavity-mediated infinite-range interactions between atomic spin systems and realize atomic quantum memories and transducers for microwave to optical conversion. To achieve strong coupling of atoms to on-chip microwave resonators, it was suggested to use atomic Rydberg states with strong electric dipole transitions. Here we report on the realization of coherent coupling of a Rydberg transition of ultracold atoms trapped on an integrated superconducting atom chip to the microwave field of an on-chip coplanar waveguide resonator. We observe and characterize the cavity driven Rabi oscillations between a pair of Rydberg states of atoms in an inhomogeneous electric field near the chip surface. Our studies demonstrate the feasibility, but also reveal the challenges, of coherent state manipulation of Rydberg atoms interacting with superconducting circuits., Comment: 12 pages, 4 figures

We theoretically demonstrate that the high-critical-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (BSCCO) is a natural candidate for the recently envisioned classical space-time crystal. BSCCO intrinsically forms a stack of Josephson junctions. Under a periodic parametric modulation of the Josephson critical current density, the Josephson currents develop coupled space-time crystalline order, breaking the continuous translational symmetry in both space and time. The modulation frequency and amplitude span a (nonequilibrium) phase diagram for a so-defined spatiotemporal order parameter, which displays rigid pattern formation within a particular region of the phase diagram. Based on our calculations using representative material properties, we propose a laser-modulation experiment to realize the predicted space-time crystalline behavior. Our findings bring new insight into the nature of space-time crystals and, more generally, into nonequilibrium driven condensed matter systems., Comment: 12 pages, 7 figures

Resistive-switching -- the current-/voltage-induced electrical resistance change -- is at the core of memristive devices, which play an essential role in the emerging field of neuromorphic computing. This study is about resistive switching in a Mott-insulator, which undergoes a thermally driven metal-to-insulator transition. Two distinct switching mechanisms were reported for such a system: electric-field-driven resistive switching and electrothermal resistive switching. The latter results from an instability caused by Joule heating. Here, we present the visualization of the reversible resistive switching in a planar V$_2$O$_3$ thin-film device using high-resolution wide-field microscopy in combination with electric transport measurements. We investigate the interaction of the electrothermal instability with the strain-induced spontaneous phase-separation in the V$_2$O$_3$ thin film at the Mott-transition. The photomicrographs show the formation of a narrow metallic filament with a minimum width $\lesssim$ 500\,nm. Although the filament formation and the overall shape of the current-voltage characteristics (IVCs) are typical of an electrothermal breakdown, we also observe atypical effects like oblique filaments, filament splitting, and hysteretic IVCs with sawtooth-like jumps at high currents in the low-resistance regime. We were able to reproduce the experimental results in a numerical model based on a two-dimensional resistor network. This model demonstrates that resistive switching, in this case, is indeed electrothermal and that the intrinsic heterogeneity is responsible for the atypical effects. This heterogeneity is strongly influenced by strain, thereby establishing a link between switching dynamics and structural properties., Comment: (18 pages, 12 figures)

The angular dependence of magnetic-field commensurability effects in thin films of the cuprate high-critical-temperature superconductor YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ (YBCO) with an artificial pinning landscape is investigated. Columns of point defects are fabricated by two different methods of ion irradiation -- scanning the focused 30 keV ion beam in a helium ion microscope or employing the wide-field 75 keV He$^+$ beam of an ion implanter through a stencil mask. Simulations of the ion-target interactions and the resulting collision cascades reveal that with both methods square arrays of defect columns with sub-$\mu$m spacings can be created. They consist of dense point-defect clusters, which act as pinning centers for Abrikosov vortices. This is verified by the measurement of commensurable peaks of the critical current and related minima of the flux-flow resistance vs magnetic field at the matching fields. In oblique magnetic fields the matching features are exclusively governed by the component of the magnetic field parallel to the axes of the columnar defects, which confirms that the magnetic flux is penetrated along the defect columns. We demonstrate that the latter dominate the pinning landscape despite of the strong intrinsic pinning in thin YBCO films., Comment: 8 pages, 6 figures

Intrinsic Josephson junctions in high-temperature superconductor Bi2Sr2CaCu2O8 are known for their capability to emit high-power terahertz photons with widely tunable frequencies. Hotspots, as inhomogeneous temperature distributions across the junctions, are believed to play a critical role in synchronizing the gauge-invariant phase difference among the junctions, so as to achieve coherent strong emission. Previous optical imaging techniques have indirectly suggested that the hotspot temperature can go higher than the superconductor critical temperature. However, such optical approaches often disturb the local temperature profile and are too slow for device applications. In this paper, we demonstrate an on-chip in situ sensing technique that can precisely quantify the local temperature profile. This is achieved by fabricating a series of micro "sensor" junctions on top of an "emitter" junction and measuring the critical current on the sensors versus the bias current applied to the emitter. This fully electronic on-chip design could enable efficient close-loop control of hotspots in BSCCO junctions and significantly enhance the functionality of superconducting terahertz emitters., Comment: 6 pages, 5 figures

We present an experimental approach for cryogenic dielectric measurements on ultra-thin insulating films. Based on a coplanar microwave waveguide design we implement superconducting quarter-wave resonators with inductive coupling, which allows us to determine the real part $\varepsilon_1$ of the dielectric function at GHz frequencies and for sample thicknesses down to a few nm. We perform simulations to optimize resonator coupling and sensitivity, and we demonstrate the possibility to quantify $\varepsilon_1$ with a conformal mapping technique in a wide sample-thickness and $\varepsilon_1$-regime. Experimentally we determine $\varepsilon_1$ for various thin-film samples (photoresist, MgF$_2$, and SiO$_2$) in the thickness regime of nm up to $\mu m$. We find good correspondence with nominative values and we identify the precision of the film thickness as our predominant error source. Additionally we present a temperature-dependent measurement for a SrTiO$_3$ bulk sample, using an in-situ reference method to compensate for the temperature dependence of the superconducting resonator properties.

Magnetic fields penetrate a type-II superconductor as magnetic flux quanta, called vortices. In a clean superconductor they arrange in a hexagonal lattice, while by adding periodic artificial pinning centers many other arrangements can be realized. Using the focused beam of a helium ion microscope we have fabricated periodic patterns of dense pinning centers with spacings as small as 70 nm in thin films of the cuprate superconductor YBa$_{2}$Cu$_{3}$O$_{7-\delta}$. In these ultradense kagom\'e-like patterns, the voids lead to magnetic caging of vortices, resulting in unconventional commensurability effects that manifest themselves as peaks in the critical current and minima in the resistance versus applied magnetic field up to $\sim 0.4\,$T. The various vortex patterns at different magnetic fields are analyzed by molecular dynamics simulations of vortex motion, and the magnetic field dependence of the critical current is confirmed. These findings open the way for a controlled manipulation of vortices in cuprate superconductors by artificial sub-100 nm pinning landscapes., Comment: Minor additions

We demonstrate the operation of superconducting coplanar microwave resonators in a very large frequency range up to 50 GHz. The resonators are fabricated from niobium thin films on sapphire substrates and optimized for these high frequencies by small chip sizes. We study numerous harmonics of the resonators at temperatures between 1.5 K and 6 K, and we determine quality factors of up to 25000 at 1.5 K. As an example for spectroscopy applications of such resonators we detect the superconducting transition of a bulk tin sample at multiple probing frequencies., Comment: 6 pages, 3 figures

We have fabricated and investigated a stacked two-chip device, consisting of a lumped element resonator on one chip, which is side-coupled to a coplanar waveguide transmission line on a second chip. We present a full model to predict the behavior of the device dependent on the position of the lumped element resonator with respect to the transmission line. We identify different regimes, in which the device can be operated. One of them can be used to tune the coupling between the two subsystems. Another regime enables frequency tunability of the device, without leaving the over-coupled limit for internal quality factors of about $10^4$, while in the last regime the resonator properties are insensitive against small variations of the position. Finally, we have measured the transmission characteristics of the resonator for different positions, demonstrating a good agreement with the model., Comment: 8 pages, 4 figures plus supplemental material (5 pages, 4 figures)

Polarized light microscopy, as a contrast-enhancing technique for optically anisotropic materials, is a method well suited for the investigation of a wide variety of effects in solid-state physics, as for example birefringence in crystals or the magneto-optical Kerr effect (MOKE). We present a microscopy setup that combines a widefield microscope and a confocal scanning laser microscope with polarization-sensitive detectors. By using a high numerical aperture objective, a spatial resolution of about 240 nm at a wavelength of 405 nm is achieved. The sample is mounted on a $^4$He continuous flow cryostat providing a temperature range between 4 K and 300 K, and electromagnets are used to apply magnetic fields of up to 800 mT with variable in-plane orientation and 20 mT with out-of-plane orientation. Typical applications of the polarizing microscope are the imaging of the in-plane and out-of-plane magnetization via the longitudinal and polar MOKE, imaging of magnetic flux structures in superconductors covered with a magneto-optical indicator film via Faraday effect or imaging of structural features, such as twin-walls in tetragonal SrTiO$_3$. The scanning laser microscope furthermore offers the possibility to gain local information on electric transport properties of a sample by detecting the beam-induced voltage change across a current-biased sample. This combination of magnetic, structural and electric imaging capabilities makes the microscope a viable tool for research in the fields of oxide electronics, spintronics, magnetism and superconductivity., Comment: 14 pages, 11 figures. The following article has been accepted by Review of Scientific Instruments. After it is published, it will be found at http://aip.scitation.org/journal/rsi

We experimentally investigate superconducting coplanar waveguide resonators in external magnetic fields and present two strategies to reduce field-induced dissipation channels and resonance frequency shifts. One of our approaches is to significantly reduce the superconducting ground-plane areas, which leads to reduced magnetic field-focussing and thus to lower effective magnetic fields inside the waveguide cavity. By this measure, the field-induced losses can be reduced by more than one order of magnitude in mT out-of-plane magnetic fields. When these resonators are additionally coupled inductively instead of capacitively to the microwave feedlines, an intrinsic closed superconducting loop is effectively shielding the heart of the resonator from magnetic fields by means of flux conservation. In total, we achieve a reduction of the field-induced resonance frequency shift by up to two orders of magnitude. We combine systematic parameter variations on the experimental side with numerical magnetic field calculations to explain the effects of our approaches and to support our conclusions. The presented results are relevant for all areas, where high-performance superconducting resonators need to be operated in magnetic fields, e.g. for quantum hybrid devices with superconducting circuits or electron spin resonance detectors based on coplanar waveguide cavities.

The current-phase relation (CPR) of a Josephson junction (JJ) determines how the supercurrent evolves with the superconducting phase difference across the junction. Knowledge of the CPR is essential in order to understand the response of a JJ to various external parameters. Despite the rising interest in ultra-clean encapsulated graphene JJs, the CPR of such junctions remains unknown. Here, we use a fully gate-tunable graphene superconducting quantum intereference device (SQUID) to determine the CPR of ballistic graphene JJs. Each of the two JJs in the SQUID is made with graphene encapsulated in hexagonal boron nitride. By independently controlling the critical current of the JJs, we can operate the SQUID either in a symmetric or asymmetric configuration. The highly asymmetric SQUID allows us to phase-bias one of the JJs and thereby directly obtain its CPR. The CPR is found to be skewed, deviating significantly from a sinusoidal form. The skewness can be tuned with the gate voltage and oscillates in anti-phase with Fabry-P\'{e}rot resistance oscillations of the ballistic graphene cavity. We compare our experiments with tight-binding calculations which include realistic graphene-superconductor interfaces and find a good qualitative agreement., Comment: Supplementary information added; some references modified

Metallic coplanar microwave resonators are widely employed at room temperature, but their low-temperature performance has received little attention so far. We characterize compact copper coplanar resonators with multiple modes from 2.5 to 20 GHz at temperatures as low as 5 K. We investigate the influence of center conductor width (20 to 100 {\mu}m) and coupling gap size (10 to 50 {\mu}m), and we observe a strong increase of quality factor (Q) for wider center conductors, reaching values up to 470. The magnetic-field dependence of the resonators is weak, with a maximum change in Q of 3.5% for an applied field of 7 T. This makes these metallic resonators well suitable for magnetic resonance studies, as we document with electron spin resonance (ESR) measurements at multiple resonance frequencies., Comment: 6 pages, 5 figures

We used 2D coupled sine-Gordon equations combined with 3D heat diffusion equations to numerically investigate the thermal and electromagnetic properties of a $250 \times 70\,\mu\mathrm{m}^2$ intrinsic Josephson junction stack. The 700 junctions are grouped to 20 segments; we assume that in a segment all junctions behave identically. At large input power a hot spot forms in the stack. Resonant electromagnetic modes, oscillating either along the length ((0, $n$) modes) or the width (($m$, 0) modes) of the stack or having a more complex structure, can be excited both with and without a hot spot. At fixed bath temperature and bias current several cavity modes can coexist in the absence of a magnetic field. The (1, 0) mode, considered to be the most favorable mode for THz emission, can be stabilized by applying a small magnetic field along the length of the stack. A strong field-induced enhancement of the emission power is also found in experiment, for an applied field around 5.9 mT., Comment: 8 pages, 4 figures

The two-dimensional superconductor formed at the interface between the complex oxides, lanthanum aluminate (LAO) and strontium titanate (STO) has several intriguing properties that set it apart from conventional superconductors. Most notably, an electric field can be used to tune its critical temperature (T$_c$), revealing a dome-shaped phase diagram reminiscent of high T$_c$ superconductors. So far, experiments with oxide interfaces have measured quantities which probe only the magnitude of the superconducting order parameter and are not sensitive to its phase. Here, we perform phase-sensitive measurements by realizing the first superconducting quantum interference devices (SQUIDs) at the LAO/STO interface. Furthermore, we develop a new paradigm for the creation of superconducting circuit elements, where local gates enable in-situ creation and control of Josephson junctions. These gate-defined SQUIDs are unique in that the entire device is made from a single superconductor with purely electrostatic interfaces between the superconducting reservoir and the weak link. We complement our experiments with numerical simulations and show that the low superfluid density of this interfacial superconductor results in a large, gate-controllable kinetic inductance of the SQUID. Our observation of robust quantum interference opens up a new pathway to understand the nature of superconductivity at oxide interfaces., Comment: Version prior to peer review. Final version published in Nature Nanotechnology

Microscopic studies of superconductors and their vortices play a pivotal role in our understanding of the mechanisms underlying superconductivity. Local measurements of penetration depths or magnetic stray-fields enable access to fundamental aspects of superconductors such as nanoscale variations of superfluid densities or the symmetry of their order parameter. However, experimental tools, which offer quantitative, nanoscale magnetometry and operate over the large range of temperature and magnetic fields relevant to address many outstanding questions in superconductivity, are still missing. Here, we demonstrate quantitative, nanoscale magnetic imaging of Pearl vortices in the cuprate superconductor YBCO, using a scanning quantum sensor in form of a single Nitrogen-Vacancy (NV) electronic spin in diamond. The sensor-to-sample distance of ~10nm we achieve allows us to observe striking deviations from the prevalent monopole approximation in our vortex stray-field images, while we find excellent quantitative agreement with Pearl's analytic model. Our experiments yield a non-invasive and unambiguous determination of the system's local London penetration depth, and are readily extended to higher temperatures and magnetic fields. These results demonstrate the potential of quantitative quantum sensors in benchmarking microscopic models of complex electronic systems and open the door for further exploration of strongly correlated electron physics using scanning NV magnetometry., Comment: Main text (5 pages, 4 figures) plus supplementary material (5 pages, 6 figures). Comments welcome. Further information under http://www.quantum-sensing.ch

We describe a fully broadband approach for electron spin resonance (ESR) experiments where it is possible to not only tune the magnetic field but also the frequency continuously over wide ranges. Here a metallic coplanar transmission line acts as compact and versatile microwave probe that can easily be implemented in different cryogenic setups. We perform ESR measurements at frequencies between 0.1 and 67 GHz and at temperatures between 50 mK and room temperature. Three different types of samples (Cr3+ ions in ruby, organic radicals of the nitronyl-nitroxide family, and the doped semiconductor Si:P) represent different possible fields of application for the technique. We demonstrate that an extremely large phase space in temperature, magnetic field, and frequency for ESR measurements, substantially exceeding the range of conventional ESR setups, is accessible with metallic coplanar lines., Comment: 6 pages, 5 figures

We fabricated YBa$_2$Cu$_3$O$_7$ (YBCO) direct current (dc) nano superconducting quantum interference devices (nanoSQUIDs) based on grain boundary Josephson junctions by focused ion beam patterning. Characterization of electric transport and noise properties at 4.2$\,$K in magnetically shielded environment yields a very small inductance $L$ of a few pH for an optimized device geometry. This in turn results in very low values of flux noise $<50\,{\rm n}\Phi_0/{\rm Hz}^{1/2}$ in the thermal white noise limit, which yields spin sensitivities of a few $\mu_{\rm B}/{\rm Hz}^{1/2}$ ($\Phi_0$ is the magnetic flux quantum and $\mu_{\rm B}$ is the Bohr magneton). We observe frequency-dependent excess noise up to 7$\,$MHz, which can only partially be eliminated by bias reversal readout. This indicates the presence of fluctuators of unknown origin, possibly related to defect-induced spins in the SrTiO$_3$ substrate. We demonstrate the potential of using YBCO nanoSQUIDs for the investigation of small spin systems, by placing a 39$\,$nm diameter Fe nanowire, encapsulated in a carbon nanotube, on top of a non-optimized YBCO nanoSQUID and by measuring the magnetization reversal of the Fe nanowire via the change of magnetic flux coupled to the nanoSQUID. The measured flux signals upon magnetization reversal of the Fe nanowire are in very good agreement with estimated values, and the determined switching fields indicate magnetization reversal of the nanowire via curling mode., Comment: 10 pages, 5 figure and supplemental material (4 pages)

La$_{0.7}$Ce$_{0.3}$MnO$_3$ thin films of different thicknesses, degrees of CeO$_2$-phase segregation and oxygen deficiency, grown on SrTiO$_3$ single crystal substrates, were comparatively investigated with respect to both their spectral and temperature-dependent photoconductivity (PC) and their magnetoresistance (MR) behaviour under photoexcitation. While as-grown films were insensitive to optical excitation, oxygen reduction appeared to be an effective way to decrease the film resistance, but the film thickness was found to play a minor role. However, from the evaluation of the spectral behaviour of the PC and the comparison of the MR of the LCeMO/substrate-samples with a bare substrate under illumination we find that the photoconductivity data reflects not only contributions from (i) photogenerated charge carriers in the film and (ii) carriers injected from the photoconductive substrate (as concluded from earlier works), but also (iii) a decisive parallel photoconduction in the SrTiO$_3$ substrate. Furthermore -- also by analyzing the MR characteristics -- the unexpected occurence of a strong electroresistive effect in the sample with the highest degree of CeO$_2$ segregation and oxygen deficiency could be attributed to the electroresistance of the SrTiO$_3$ substrate as well. The results suggest a critical reconsideration and possibly a reinterpretation of several previous photoconductivity and electroresistance investigations of manganite thin films on SrTiO$_3$., Comment: 11 pages, 11 figures

Microwave spectroscopy is a powerful experimental tool to reveal information on the intrinsic properties of superconductors. Superconducting stripline resonators, where the material under study constitutes one of the ground planes, offer a high sensitivity to investigate superconducting bulk samples. In order to improve this measurement technique, we have studied stripline resonators made of niobium, and we compare the results to lead stripline resonators. With this technique we are able to determine the temperature dependence of the complex conductivity of niobium and the energy gap $\Delta(0)=2.1$ meV. Finally we show measurements at the superconducting transition of a tantalum bulk sample using niobium stripline resonators.

Presently, cerium-doped LaMnO$_3$ is vividly discussed as an electron-doped counterpart prototype to the well-established hole-doped mixed-valence manganites. Here, La$_{0.7}$Ce$_{0.3}$MnO$_3$ thin films of different thicknesses, degrees of CeO$_2$ phase segregation, and oxygen deficiency, grown on SrTiO$_3$ single crystal substrates, are compared with respect to their resistance-vs.-temperature (R vs. T) behavior from 300~K down to 90~K. While the variation of the film thickness (and thus the degree of epitaxial strain) in the range between 10~nm and 100~nm has only a weak impact on the electrical transport, the degree of oxygen deficiency as well as the existence of CeO$_2$ clusters can completely change the type of hopping mechanism. This is shown by fitting the respective \textit{R-T} curves with three different transport models (adiabatic polaron hopping, Mott variable-range hopping, Efros-Shklovskii variable-range hopping), which are commonly used for the mixed-valence manganites. Several characteristic transport parameters, such as the hopping energies, the carrier localization lengths, as well as the Mn valences are derived from the fitting procedures., Comment: 9 pages, 3 figures

We present an optimization study of the spin sensitivity of nanoSQUIDs based on resistively shunted grain boundary Josephson junctions. In addition the dc SQUIDs contain a narrow constriction onto which a small magnetic particle can be placed (with its magnetic moment in the plane of the SQUID loop and perpendicular to the grain boundary) for efficient coupling of its stray magnetic field to the SQUID loop. The separation of the location of optimum coupling from the junctions allows for an independent optimization of the coupling factor $\phi_\mu$ and junction properties. We present different methods for calculating $\phi_\mu$ (for a magnetic nanoparticle placed 10\,nm above the constriction) as a function of device geometry and show that those yield consistent results. Furthermore, by numerical simulations we obtain a general expression for the dependence of the SQUID inductance on geometrical parameters of our devices, which allows to estimate their impact on the spectral density of flux noise $S_\Phi$ of the SQUIDs in the thermal white noise regime. Our analysis of the dependence of $S_\Phi$ and $\phi_\mu$ on the geometric parameters of the SQUID layout yields a spin sensitivity $S_\mu^{1/2}=S_\Phi^{1/2}/\phi_\mu$ of a few $\mu_{\rm{B}}/\rm{Hz^{1/2}}$ ($\mu_B$ is the Bohr magneton) for optimized parameters, respecting technological constraints. However, by comparison with experimentally realized devices we find significantly larger values for the measured white flux noise, as compared to our theoretical predictions. Still, a spin sensitivity on the order of $10\,\mu_{\rm B}/\rm{Hz^{1/2}}$ for optimized devices seems to be realistic., Comment: 10 pages, 5 figures, Superconductor Science and Technology (submitted). arXiv admin note: text overlap with arXiv:1301.1189 The paper has been withdrawn due to a wrong article number assignment. The article 1406.1402 was intended to be a replacement of 1301.1189

Films of cerium-doped LaMnO$_3$, which has been intensively discussed as an electron-doped counterpart to hole-doped mixed-valence lanthanum manganites during the past decade, were analyzed by x-ray photoemission spectroscopy with respect to their manganese valence under photoexcitation. The comparative analysis of the Mn 3s exchange splitting of La$_{0.7}$Ce$_{0.3}$MnO$_3$ (LCeMO) films in the dark and under illumination clearly shows that both oxygen reduction and illumination are able to decrease the Mn valence towards a mixed 2$+$/3$+$ state, independently of the film thickness and the degree of CeO$_2$ segregation. Charge injection from the photoconductive SrTiO$_3$ substrate into the Mn e$_g$ band with carrier lifetimes in the range of tens of seconds and intrinsic generation of electron-hole pairs within the films are discussed as two possible sources of the Mn valence shift and the subsequent electron doping., Comment: 6 pages, 2 figures

A crucial point in the experimental implementation of hybrid quantum systems consisting of superconducting circuits and atomic ensembles is bringing the two partners close enough to each other that a strong quantum coherent coupling can be established. Here, we propose to use the metallization structures of a half wavelength superconducting coplanar waveguide resonator as a persistent current trap for ultracold paramagnetic atoms. Trapping atoms with the resonator structure itself is provided by using short-ended and inductively coupled resonators instead of capacitively coupled ones as customary in circuit quantum electrodynamics.We analyze the external quality factor of short-ended coplanar waveguide resonators and show that it can be easily designed for the desired regime of quantum circuits. The magnetic field configuration at the resonator is calculated by means of numerical three-dimensional simulations of the London equations. We present a way to transport an atomic ensemble into the coplanar resonator gap where the magnetic field of the cavity mode is maximum. The configuration allows stable trapping by persistent currents and paves the route towards strong coupling between atomic clouds and the cavity mode which is required for cooperative effects and gives the interface between atoms and circuit quantum electrodynamics.

We investigate electric transport and noise properties of microstrip-type submicron direct current superconducting quantum interference devices (dc SQUIDs) based on Nb thin films and overdamped Josephson junctions with a HfTi barrier. The SQUIDs were designed for optimal spin sensitivity $S_\mu^{1/2}$ upon operation in intermediate magnetic fields $B$ (tens of mT), applied perpendicular to the substrate plane. Our so far best SQUID can be continuously operated in fields up to $B\approx\pm50\,\rm{mT}$ with rms flux noise $S_{\Phi,\rm w}^{1/2}\leq250\,\rm{n\Phi_0/Hz^{1/2}}$ in the white noise regime and spin sensitivity $S_{\mu}^{1/2}\leq29\,\rm{\mu_B/Hz^{1/2}}$. Furthermore, we demonstrate operation in $B=0.5\,\rm{T}$ with high sensitivity in flux $S_{\Phi,\rm w}^{1/2}\approx680\,\rm{n\Phi_0/Hz^{1/2}}$ and in electron spin $S_{\mu}^{1/2}\approx79\,\rm{\mu_B/Hz^{1/2}}$. We discuss strategies to further improve the nanoSQUID performance., Comment: to appear in Apl. Phys. Lett

We present an optimization study of the spin sensitivity of nanoSQUIDs based on resistively shunted grain boundary Josephson junctions. In addition the dc SQUIDs contain a narrow constriction onto which a small magnetic particle can be placed (with its magnetic moment in the plane of the SQUID loop and perpendicular to the grain boundary) for efficient coupling of its stray magnetic field to the SQUID loop. The separation of the location of optimum coupling from the junctions allows for an independent optimization of the coupling factor $\phi_\mu$ and junction properties. We present different methods for calculating $\phi_\mu$ (for a magnetic nanoparticle placed 10\,nm above the constriction) as a function of device geometry and show that those yield consistent results. Furthermore, by numerical simulations we obtain a general expression for the dependence of the SQUID inductance on geometrical parameters of our devices, which allows to estimate their impact on the spectral density of flux noise $S_\Phi$ of the SQUIDs in the thermal white noise regime. Our analysis of the dependence of $S_\Phi$ and $\phi_\mu$ on the geometric parameters of the SQUID layout yields a spin sensitivity $S_\mu^{1/2}=S_\Phi^{1/2}/\phi_\mu$ of a few $\mu_{\rm{B}}/\rm{Hz^{1/2}}$ ($\mu_B$ is the Bohr magneton) for optimized parameters, respecting technological constraints. However, by comparison with experimentally realized devices we find significantly larger values for the measured white flux noise, as compared to our theoretical predictions. Still, a spin sensitivity on the order of $10\,\mu_{\rm B}/\rm{Hz^{1/2}}$ for optimized devices seems to be realistic., Comment: 10 pages, 5 figures, Superconductor Science and Technology (submitted)

The experimental investigation of the $I_c(B)$--$T_c(B)$ phase boundary of superconducting niobium films with large area quasihexagonal hole arrays is reported. The hole arrays were patterned with microsphere photolithography. We investigate the perforated niobium films by means of electrical directed current transport measurements close to the transition temperature $T_c$ in perpendicularly applied magnetic fields. We find pronounced modulations of the critcal current with applied magnetic field, which we interpret as a consequence of commensurable states between the Abrikosov vortex lattice and the quasihexagonal pinning array. Furthermore, we observe Little-Parks oscillations in the critical temperature vs magnetic field.

We performed transmission spectroscopy experiments on coplanar half wavelength niobium resonators at a temperature T=4.2 K. We observe not only a strong dependence of the quality factor Q and the resonance frequency f_res on an externally applied magnetic field but also on the magnetic history of our resonators, i.e. on the spatial distribution of trapped Abrikosov vortices in the device. We find these results to be valid for a broad range of frequencies and angles between the resonator plane and the magnetic field direction as well as for resonators with and without antidots near the edges of the center conductor and the ground planes. In a detailed analysis we show, that characteristic features of the experimental data can only be reproduced in calculations, if a highly inhomogeneous rf-current density and a flux density gradient with maxima at the edges of the superconductor is assumed. We furthermore demonstrate, that the hysteretic behaviour of the resonator properties can be used to considerably reduce the vortex induced losses and to fine-tune the resonance frequency by the proper way of cycling to a desired magnetic field.