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It is a well known phenomenon in optics that spectroscopic resolution of a diffraction grating is much better compared to an interference device having just two slits, as in the Young's famous double-slit experiment. On the other hand, it is well known that a classical superconducting quantum interference device (SQUID) is analogous to the optical double-slit experiment. Here we report experiments and present a model describing a superconducting analogue to the diffraction grating, namely an array of superconducting islands positioned on a topological insulator (TI) film Bi0.8Sb1.2Te3. In the limit of extremely weak field, of the order of one vortex per the entire array, such devices exhibit a critical current peak that is much sharper than the analogous peak of an ordinary SQUID. Because of this, such arrays can be used as sensitive absolute magnetic field sensors. An important finding is that, due to the inherent asymmetry of such arrays, the device also acts as a superconducting diode., Comment: 8 pages, 6 figures

Microseismicity in subsurface geologic environments, such as sandstone gas reservoirs, is expected in the presence of liquid or gas injection. Although difficult to predict, the potential for microseismic events is important to field-scale projects, such as geologic storage of CO2 whereby the gas is injected into natural sandstone formations. We conjecture that a primary factor causing microseismicity is the existence of metastable states in granular porous medium and provide experimental evidence for its validity. External perturbation trigger abrupt relaxation events, which, with a certain probability, can grow into macroscopic microseismic events. Here the triggering perturbation is produced by cooling to a cryogenic temperature. As the "sensor" for the abrupt relaxation events we use thin Al films deposited on the sandstone surface. We show that as the temperature is varied, the films' resistance exhibits sharp jumps, which we attribute to mechanical restructuring or microfractures in the fabric of the sandstone. We checked the superconducting characteristics of the Al thin films on the sandstone and found microwave-induced Shapiro steps on the voltage-current diagrams. Such quantized steps provide indicates that the film is made of a network of nanobridges, which makes it ever more sensitive to abrupt relaxation events occurring in the substrate, i.e., in the underlying sandstone.

Sandstone mechanical stability is of key concern in projects involving injections of CO2 in sandstone geological reservoirs, for the purpose of long-term storage. We developed a method to measure nanometer-scale deformations of sandstones in real time. We demonstrate that Berea sandstone, when hydrated, changes dimensions with a relative deformation of the order of 10^(-4). If the moisture content increases, sandstone samples exhibit an extension and if the moisture content decreases then the samples shrink. We also discover that, immediately after exposure to water, the sandstone temporarily shrinks, just for a few seconds, after which a slow extension begins, and continues until about half of the fluid evaporates. Such shrinkage followed by an extension has been observed also when the sample was exposed to acetone, Mineral Spirits or Vacuum Oil. The results are obtained using a high-resolution nano-positioner technique and, in independent experiments, confirmed using the technique of coda wave interferometry., Comment: 18 pages, 8 figures

We fabricate nanolayer alumina capacitor and apply high electric fields, close to 1 GV/m, to inject charges in the dielectric. Asymmetric charge distributions have been achieved due to the selectivity of the quantum tunneling process. Namely, the electrons cannot tunnel to a region near cathode, where the total energy would be less than the potential energy. This mechanism exhibits a strong tendency to populate charge traps located near the anode, i.e., the regions where their potential energy is the lowest. This charge injection allows a permanent storage of the bulk charge even if the capacitor plates are short-circuited, provided that the temperature is sufficiently low so that the conductivity of the dielectric is negligible. In our experiments, the total charge stored in the dielectric was up to seven and a half times higher than the charge stored on the capacitor plates. Also, measurements of the breakdown voltage show that the breakdown electric field, i.e., the dielectric strength, is independent of the thickness of the dielectric., Comment: 11 pages, 6 figures

We report superconducting kinetic inductance memory (SKIM) element, which can be controlled exclusively by the bias supercurrent, without involving magnetic fields and heating elements. The SKIM is non-volatile memory. The device is made of Nb and it can operate reliable up to 2.8 K. The achieved error rate is as low as one in 100000 operations., Comment: 9 pages, 6 figures

The main mechanism of energy loss in capacitors with nanoscale dielectric films is leakage currents. Using the example of Al-Al2O3-Al, we show that there are two main contributions, namely the cold field emission effect and the hopping conductivity through the dielectric. Our main finding is that an application of a high electric field, ~0.6-0.7 GV/m, causes electrons to penetrate the dielectric. If the temperature is sufficiently low, such electrons become permanently trapped in the dielectric. To achieve a strong charging of the dielectric, the voltage needs to be high enough, so that a field emission occurs from the cathode into the dielectric. Such a strongly charged dielectric layer generates a Coulomb barrier and leads to a suppression of the leakage current. Thus, after the dielectric nanolayer of the capacitor is charged, the field emission and the hopping conductivity are both suppressed, and the hysteresis of the I-V curve disappears. The phenomenon is observed at temperatures up to ~225 K. It would be advantageous to identify insulators in which the phenomenon of the Coulomb barriers persists even up to the room temperature, but at this time it is not known whether such dielectrics exist and/or can be designed., Comment: 16 pages, 6 figures

We study one dimensional chains of superconducting islands with a particular emphasis on the regime in which every second island is switched into its normal state, thus forming a superconductor-insulator-normal metal (S-I-N) repetition pattern. As is known since Giaever tunneling experiments, tunneling charge transport between a superconductor and a normal metal becomes exponentially suppressed, and zero-bias resistance diverges, as the temperature is reduced and the energy gap of the superconductor grows larger than the thermal energy. Here we demonstrate that this physical phenomenon strongly impacts transport properties of inhomogeneous superconductors made of weakly coupled islands with fluctuating values of the critical temperature. We observe a non-monotonous dependence of the chain resistance on both temperature and magnetic field, with a pronounced resistance peak at temperatures at which some but not all islands are superconducting. We explain this phenomenon by the inhomogeneity of the chains, in which neighboring superconducting islands have slightly different critical temperatures. We argue that the Giaever's resistance divergence can also occur in the zero-temperature limit. Such quantum transition can occur if the magnetic field is tuned such that it suppresses superconductivity in the islands with the weaker critical field, while the islands with stronger energy gap remain superconducting. In such a field, the system acts as a chain of S-I-N junctions., Comment: 12 pages, 8 figures

The demand for low-dissipation nanoscale memory devices is as strong as ever. As Moore's Law is staggering, and the demand for a low-power-consuming supercomputer is high, the goal of making information processing circuits out of superconductors is one of the central goals of modern technology and physics. So far, digital superconducting circuits could not demonstrate their immense potential. One important reason for this is that a dense superconducting memory technology is not yet available. Miniaturization of traditional superconducting quantum interference devices is difficult below a few micrometers because their operation relies on the geometric inductance of the superconducting loop. Magnetic memories do allow nanometer-scale miniaturization, but they are not purely superconducting (Baek et al 2014 Nat. Commun. 5 3888). Our approach is to make nanometer scale memory cells based on the kinetic inductance (and not geometric inductance) of superconducting nanowire loops, which have already shown many fascinating properties (Aprili 2006 Nat. Nanotechnol. 1 15; Hopkins et al 2005 Science 308 1762). This allows much smaller devices and naturally eliminates magnetic-field cross-talk. We demonstrate that the vorticity, i.e., the winding number of the order parameter, of a closed superconducting loop can be used for realizing a nanoscale nonvolatile memory device. We demonstrate how to alter the vorticity in a controlled fashion by applying calibrated current pulses. A reliable read-out of the memory is also demonstrated. We present arguments that such memory can be developed to operate without energy dissipation.

We study nanodevices based on ultrathin superconducting nanowires connected in parallel to form nanowire SQUIDs. The function of the critical current versus magnetic field, $I_{C}(B)$, is multivalued, asymmetric and its maxima and minima are shifted from the usual integer and half integer flux quantum points. The nanowire interference device is qualitatively distinct from conventional SQUIDs because nanowires do not obey the same current-phase relationship (CPR) as Josephson junctions. We demonstrate that the results can be explained assuming that (i) the CPR is linear and (ii) that each wire is characterized by a sample-specific critical phase, which is usually much larger than $\pi/2$. Our proposed model offers accurate fits to $I_{C}(B)$. It explains the single-valuedness regions where only one vorticity (i.e., the order parameter winding number) is stable as well as regions where multiple vorticity values are allowed for the SQUIDs. We also observe and explain regions in which the standard deviation of the switching current is independent of the magnetic field. We develop a technique that allows a reliable detection of hidden phase-slips. Using this technique we find that our model correctly predicts the boundaries of vorticity regions, even at low currents where $I_C(B)$ is not directly measurable.

We present a new type of transmon split-junction qubit which can be tuned by Meissner screening currents in the adjacent superconducting film electrodes. The best detected relaxation time ($T_1$) was of the order of 50 $\mu$s and the dephasing time ($T_2$) about 40 $\mu$s. The achieved period of oscillation with magnetic field was much smaller than in usual SQUID-based transmon qubits, thus a strong effective field amplification has been realized. This Meissner qubit allows an efficient coupling to superconducting vortices. We present a quantitative analysis of the radiation-free energy relaxation in qubits coupled to Abrikosov vortices. The observation of coherent quantum oscillations provides strong evidence that vortices can exist in coherent quantum superpositions of different position states. According to our suggested model, the wave function collapse is defined by Caldeira-Leggett dissipation associated with viscous motion of the vortex cores., Comment: 13 pages and 9 figures; added references in the introduction section

Macroscopic quantum tunneling (MQT) is a fundamental phenomenon of quantum mechanics related to the actively debated topic of quantum-to-classical transition. The ability to realize MQT affects implementation of qubit-based quantum computing schemes and their protection against decoherence. Decoherence in qubits can be reduced by means of topological protection, e.g. by exploiting various parity effects. In particular, paired phase slips can provide such protection for superconducting qubits. Here, we report on the direct observation of quantum paired phase slips in thin-wire superconducting loops. We show that in addition to conventional single phase slips that change superconducting order parameter phase by $2\pi$, there are quantum transitions changing the phase by $4\pi$. Quantum paired phase slips represent a synchronized occurrence of two macroscopic quantum tunneling events, i.e. cotunneling. We demonstrate the existence of a remarkable regime in which paired phase slips are exponentially more probable than single ones.

We present measurements of the superconducting coherence length \xi\ in thin (d < 100 \AA) films of MoGe alloy and Nb using a combination of linear and nonlinear mutual inductance techniques. As the alternating current in the drive coil is increased at fixed temperature, we see a crossover from linear to nonlinear coupling to the pickup coil, consistent with the unbinding of vortex-antivortex pairs as the peak pair momentum nears \hbar\/\xi\ and the unbinding barrier vanishes. We compare measurements of \xi\ made by this mutual inductance technique to values determined from the films' upper critical fields, thereby confirming the applicability of a recent calculation of the upper limit on a vortex-free state in our experiment., Comment: 5 pages, 7 figures

We present the first study of superconducting nanowires shunted with an external resistor, geared towards understanding and controlling coherence and dissipation in nanowires. The dynamics is probed by measuring the evolution of the V-I characteristics and the distributions of switching and retrapping currents upon varying the shunt resistor and temperature. Theoretical analysis of the experiments indicates that as the value of the shunt resistance is decreased, the dynamics turns more coherent presumably due to stabilization of phase-slip centers in the wire and furthermore the switching current approaches the Bardeen's prediction for equilibrium depairing current. By a detailed comparison between theory and experimental, we make headway into identifying regimes in which the quasi-one-dimensional wire can effectively be described by a zero-dimensional circuit model analogous to the RCSJ (resistively and capacitively shunted Josephson junction) model of Stewart and McCumber. Besides its fundamental significance, our study has implications for a range of promising technological applications., Comment: 15 pages, 14 figures

Microwave Fabry-Perot resonators containing nonlinear mesoscopic elements (such as superconducting nanowires) can be used to explore many-body circuit QED. Here, we report on observations of a superconductor-normal pulsing regime in microwave (GHz) coplanar waveguide resonators consisting of superconducting MoGe films interrupted by a gap that is bridged by one or more suspended superconducting nanowires. This regime, which involve MHz-frequency oscillations in the amplitude of the supercurrent in the resonator, are achieved when the steady-state amplitude of the current in the driven resonator exceeds the critical current of the nanowires. Thus we are able to determine the temperature dependence of the critical current, which agrees well with the corresponding Bardeen formula. The pulsing regime manifests itself as an apparent "crater" on top of the fundamental Lorentzian peak of the resonator. Once the pulsing regime is achieved at a fixed drive power, however, it remains stable for a range of drive frequencies corresponding to subcritical steady state currents in the resonator. We develop a phenomenological model of resonator-nanowire systems, from which we are able to obtain a quantitative description of the amplitude oscillations and also, inter alia, to investigate thermal relaxation processes in superconducting nanowires. For the case of resonators comprising two parallel nanowires and subject to an external magnetic field, we find field-driven oscillations of the onset power for the amplitude oscillations, as well as the occurrence (for values of the magnetic field that strongly frustrate the nanowires) of a distinct steady state in which the pulsing is replaced by stochastic amplitude-fluctuations. We conclude by giving a brief discussion of how circuit-QED-based systems have the potential to facilitate understanding of quantum phase-slips in superconducting nanowires., Comment: 40 pages, 20 figures

We report microwave transmission measurements of superconducting Fabry-Perot resonators (SFPR), having a superconducting nanowire placed at a supercurrent antinode. As the plasma oscillation is excited, the supercurrent is forced to flow through the nanowire. The microwave transmission of the resonator-nanowire device shows a nonlinear resonance behavior, significantly dependent on the amplitude of the supercurrent oscillation. We show that such amplitude-dependent response is due to the nonlinearity of the current-phase relationship (CPR) of the nanowire. The results are explained within a nonlinear oscillator model of the Duffing oscillator, in which the nanowire acts as a purely inductive element, in the limit of low temperatures and low amplitudes. The low quality factor sample exhibits a "crater" at the resonance peak at higher driving power, which is due to dissipation. We observe a hysteretic bifurcation behavior of the transmission response to frequency sweep in a sample with a higher quality factor. The Duffing model is used to explain the Duffing bistability diagram. We also propose a concept of a nanowire-based qubit that relies on the current dependence of the kinetic inductance of a superconducting nanowire., Comment: 28 pages, 7 figures

We present a method for in-situ tuning the critical current (or switching current) and critical temperature of a superconducting nanowire using high bias voltage pulses. Our main finding is that as the pulse voltage is increased, the nanowires demonstrate a reduction, a minimum and then an enhancement of the switching current and critical temperature. Using controlled pulsing, the switching current of a superconducting nanowire can be set exactly to a desired value. These results correlate with in-situ transmission electron microscope imaging where an initially amorphous nanowire transforms into a single crystal nanowire by high bias voltage pulses., Comment: 8 pages, 3 figures with 9 pages, 3 figures supplemental information

We report measurements of magnetoresistance in single-layer graphene as a function of gate voltage (carrier density) at 250 mK. By examining signatures of weak localization (WL) and universal conductance fluctuations (UCF), we find a consistent picture of phase coherence loss due to electron-electron interactions. The gate-dependence of the elastic scattering terms suggests that the effect of trigonal warping, i.e., the non-linearity of the dispersion curves, may be strong at high carrier densities, while intra-valley scattering may dominate close to the Dirac point. In addition, a decrease in UCF amplitude with decreasing carrier density can be explained by a corresponding loss of phase coherence.

We report measurements of magnetoresistance in bilayer graphene as a function of gate voltage (carrier density) and temperature. We examine multiple contributions to the magnetoresistance, including those of weak localization (WL), universal conductance fluctuations (UCF), and inhomogeneous charge transport. A clear WL signal is evident at all measured gate voltages (in the hole doped regime) and temperature ranges (from 0.25 K to 4.3 K), and the phase coherence length extracted from WL data does not saturate at low temperatures. The WL data is fit to demonstrate that electron-electron Nyquist scattering is the major source of phase decoherence. A decrease in UCF amplitude with increasing gate voltage and temperature is shown to be consistent with a corresponding decrease in the phase coherence length. In addition, a weak positive magnetoresistance at higher magnetic fields is observed, and attributed to inhomogeneous charge transport.

Quantum phase slippage (QPS) in a superconducting nanowire is a new candidate for developing a quantum bit. It has also been theoretically predicted that the occurrence of QPS significantly changes the current-phase relationship (CPR) of the wire due to the tunneling between topologically different metastable states. We present studies on the microwave response of the superconducting nanowires to reveal their CPRs. First, we demonstrate a simple nanowire fabrication technique, based on commercially available adhesive tapes, which allows making thin superconducting wire from different metals. We compare the resistance vs. temperature curves of Mo$_{76}$Ge$_{24}$ and Al nanowires to the classical and quantum models of phase slips. In order to describe the experimentally observed microwave responses of these nanowires, we use the McCumber-Stewart model, which is generalized to include either classical or quantum CPR., Comment: to be published in Nano Letters

Superconducting nanowires fabricated via carbon-nanotube-templating can be used to realize and study quasi-one-dimensional superconductors. However, measurement of the linear resistance of these nanowires have been inconclusive in determining the low-temperature behavior of phase-slip fluctuations, both quantal and thermal. Thus, we are motivated to study the nonlinear current-voltage characteristics in current-biased nanowires and the stochastic dynamics of superconductive-resistive switching, as a way of probing phase-slip events. In particular, we address the question: Can a single phase-slip event occurring somewhere along the wire--during which the order-parameter fluctuates to zero--induce switching, via the local heating it causes? We explore this and related issues by constructing a stochastic model for the time-evolution of the temperature in a nanowire whose ends are maintained at a fixed temperature. We derive the corresponding master equation as tool for evaluating and analyzing the mean switching time at a given value of current. The model indicates that although, in general, several phase-slip events are necessary to induce switching via a thermal runaway, there is indeed a regime of temperatures and currents in which a single event is sufficient. We carry out a detailed comparison of the results of the model with experimental measurements of the distribution of switching currents, and provide an explanation for the counter-intuitive broadening of the distribution width that is observed upon lowering the temperature. Moreover, we identify a regime in which the experiments are probing individual phase-slip events, and thus offer a way for exploring the physics of nanoscale quantum tunneling of the superconducting order parameter., Comment: 21 pages, 15 figures

We expose superconducting nanowires to microwave radiation in order to study phase lock-in effects in quasi one dimensional superconductors. For sufficiently high microwave powers a resistive branch with Shapiro steps appears in the voltage-current characteristics. At frequencies in the range of 0.9-4 GHz these steps are of integer order only. At higher frequencies steps of 1/2, 1/3, 1/4 and even 1/6 order appear. We numerically model this behavior using a multi-valued current-phase relationship (CPR) for nanowires., Comment: 8 Pages plus 3 Figures and references. To appear in App. Phys. Lett

Phase slips are topological fluctuation events that carry the superconducting order-parameter field between distinct current carrying states. Owing to these phase slips low-dimensional superconductors acquire electrical resistance. In quasi-one-dimensional nanowires it is well known that at higher temperatures phase slips occur via the process of thermal barrier-crossing by the order-parameter field. At low temperatures, the general expectation is that phase slips should proceed via quantum tunnelling events, which are known as quantum phase slips (QPS). Here we report strong evidence for individual quantum tunnelling events undergone by the superconducting order-parameter field in homogeneous nanowires.We accomplish this via measurements of the distribution of switching currents-the high-bias currents at which superconductivity gives way to resistive behaviour-whose width exhibits a rather counter-intuitive, monotonic increase with decreasing temperature. We outline a stochastic model of phase slip kinetics which relates the basic phase slip rates to switching rates. Comparison with this model indicates that the phase predominantly slips via thermal activation at high temperatures but at sufficiently low temperatures switching is caused by individual topological tunnelling events of the order-parameter field, i.e., QPS. Importantly, measurements on several wires show that quantum fluctuations tend to dominate over thermal fluctuations at larger temperatures in wires having larger critical currents. This fact provides strong supports the view that the anomalously high switching rates observed at low temperatures are indeed due to QPS, and not consequences of extraneous noise or hidden inhomogeneity of the wire., Comment: 39 pages: added more experimental data and analysis

We have developed a superconducting phase gradiometer consisting of two parallel DNA-templated nanowires connecting two thin-film leads. We have ramped the cross current flowing perpendicular to the nanowires, and observed oscillations in the lead-to-lead resistance due to cross-current-induced phase differences. By using this gradiometer we have measured the temperature and magnetic field dependence of the superfluid density and observed an amplification of phase gradients caused by elastic vortex displacements. We examine our data in light of Miller-Bardeen theory of dirty superconductors and a microscale version of Campbell's model of field penetration., Comment: 5 pages, 6 figures

Magnetic fields and magnetic impurities are each known to suppress superconductivity. However, as the field quenches (i.e. polarizes) the impurities, rich consequences, including field-enhanced superconductivity, can emerge when both effects are present. For the case of superconducting wires and thin films, this field-spin interplay is investigated via the Eilenberger-Usadel scheme. Non-monotonic dependence of the critical current on the field (and therefore field-enhanced superconductivity) is found to be possible, even in parameter regimes in which the critical temperature decreases monotonically with increasing field. The present work complements that of Kharitonov and Feigel'man, which predicts non-monotonic behavior of the critical temperature., Comment: 8 pages, 2 figures, EPL format

A theory describing the operation of a superconducting nanowire quantum interference device (NQUID) is presented. The device consists of a pair of thin-film superconducting leads connected by a pair of topologically parallel ultra-narrow superconducting wires. It exhibits intrinsic electrical resistance, due to thermally-activated dissipative fluctuations of the superconducting order parameter. Attention is given to the dependence of this resistance on the strength of an externally applied magnetic field aligned perpendicular to the leads, for lead dimensions such that there is essentially complete and uniform penetration of the leads by the magnetic field. This regime, in which at least one of the lead dimensions lies between the superconducting coherence and penetration lengths, is referred to as the mesoscopic regime. The magnetic field causes a pronounced oscillation of the device resistance, with a period not dominated by the Aharonov-Bohm effect through the area enclosed by the wires and the film edges but, rather, in terms of the geometry of the leads, in contrast to the well-known Little-Parks resistance of thin-walled superconducting cylinders. A theory, encompassing this phenomenology, is developed through extensions, to the setting of parallel superconducting wires, of the Ivanchenko-Zil'berman-Ambegaokar-Halperin theory for the case of short wires and the Langer-Ambegaokar-McCumber-Halperin theory for the case of longer wires. It is demonstrated that the NQUID acts as a probe of spatial variations in the superconducting order parameter., Comment: 20 pages, 18 figures

The electronic properties of multi-wall carbon nanotubes (MWNTs) have attracted much attention because they could lead to nano-sized electronic devices. Using chemical vapor deposition (CVD), MWNTs are produced in large quantities at a low cost. CVD-produced MWNTs, however, generally contain a considerable amount of structural defects due to their low temperature synthesis. Since these defects act as scattering centers in electron transport and thus limit the electronic mean free path (EMFP), high-temperature annealing should lengthen the EMFP. This is based on the previous experiments in which annealing eliminated structural defects in various carbon materials including nanotubes. In this study, we investigate how high-temperature annealing affects the transport properties, especially EMFP, of CVD-grown MWNTs. To measure the EMFP of a nanotube, we submerged samples into liquid mercury (Hg) and measured the variation in conductance. We found that the EMFP is much longer in nanotubes annealed at 2700oC compared with that of as-produced ones. The annealed nanotubes show quasi-ballistic electronic transport with the EMFP reaching a few microns, even at room temperature.

Room-temperature quasi-ballistic electron transport in double-wall carbon nanotubes (DWNT) is demonstrated. Conductance dependence on the length was measured by submerging DWNTs into liquid mercury. The conductance plots show plateaus, indicating weak dependence of the electrode-tube-electrode electrical resistance on the length of the connecting nanotube. We infer a mean free path between 0.6 and 10 micron meters for around 80% of the DWNTs, which is in good agreement with calculations based on the electron scattering by acoustic phonons and by disorder.

Continuous Nb wires, 7-15 nm in diameter, have been fabricated by sputter-coating single fluorinated carbon nanotubes. Transmission electron microscopy revealed that the wires are polycrystalline, having grain sizes of about 5 nm. The critical current of wires thicker than ~12 nm is very high (10^7 A/cm^2) and comparable to the expected depairing current. The resistance versus temperature curves measured down to 0.3 K are well described by the Langer-Ambegaokar-McCumber-Halperin (LAMH) theory of thermally activated phase slips. Quantum phase slips are suppressed., Comment: 11 pages, 4 figures. Accepted for publication in Appl. Phys. Lett