One dimensional Josephson junction arrays have been fabricated and current-voltage characteristics (IVC) have been measured at cryogenic temperatures. The arrays were fabricated in a SQUID-geometry which allowed an in. situ tuning of thc Josephson energy by application of a magnetic field. The IVC of thc arrays shows a clear Coulomb blockade state. In the Coulomb blockade regime the IVC are hysteretic, The array is modeled using a Serial resistive-inductive-junction model which is able to qualitatively explain the IVC. In this model an inductance of the order of 0.1-10 mH per Junction is needed to account for the hysteresis. Kinetic inductance. stemming from the inertia of the Cooper pairs. gives the correct order of magnitude. The problem of self-heating is also discussed as an alternative explanation of the hysteresis.
The IV characteristics (IVC) of 1D-arrays of small capacitance Josephson junctions with E-C similar to E-J have been measured. The IVC show Coulomb blockade of Cooper pair tunneling and exhibit a pronounced hysteresis which appears to be dual to the well-known resistively shunted junction behavior of ordinary Josephson junctions. A dual serially resistive junction model is used to qualitatively explain the measured data.
Exploiting multiple modes in a quantum acoustic device could enable applications in quantum information in a hardware-efficient setup, including quantum simulation in a synthetic dimension and continuous-variable quantum computing with cluster states. We develop a multimode surface acoustic wave (SAW) resonator with a superconducting quantum interference device (SQUID) integrated in one of the Bragg reflectors. The interaction with the SQUID-shunted mirror gives rise to coupling between the more than 20 accessible resonator modes. We exploit this coupling to demonstrate two-mode squeezing of SAW phonons, as well as four-mode multipartite entanglement. Our results open avenues for continuous-variable quantum computing in a compact hybrid quantum system.
We have studied 1D-arrays of Josephson junctions with a gate capacitively coupled to the middle of the array. The SQUID shape of each junction enables tuning of the Josephson coupling energy, El. By adding a signal to the gate with a radio-frequency f we create a step in the I-V characteristics at the value I = 2ef: The step is clearly visible as a peak in the differential resistance dI/dV and can be seen in the whole frequency range studied (10-90 MHz).
A long one-dimensional array of small Josephson junctions exhibits Coulomb blockade of Cooper pair tunneling. This zero-current state exists up to a switching voltage, V-sw, where there is a sudden onset of current. In this paper we present histograms showing how V-sw changes with temperature for a long array and calculations of the corresponding escape rates. Our analysis of the problem is based on the existence of a voltage-dependent energy barrier and we do not make any assumptions about its shape. The data divide into two temperature regimes, the higher of which can be explained with the Kramers thermal escape model. At low temperatures the escape becomes independent of temperature.
The interface between two wide band-gap insulators, LaAlO3 and SrTiO3 (LAO/STO) offers a unique playground to study the interplay and competitions between different ordering phenomena in a strongly correlated two- dimensional electron gas. Recent studies of the LAO/STO interface reveal the inhomogeneous nature of the 2DEG that strongly influences electrical-transport properties. Nanowires needed in future applications may be adversely affected, and our aim is, thus, to produce a more homogeneous electron gas. In this work, we demonstrate that nanostructures fabricated in the quasi-2DEG at the LaAlO3/SrTiO3 interface, capped with a SrCuO2 layer, retain their electrical resistivity and mobility independent of the structure size, ranging from 100 nm to 30 mu m. This is in contrast to noncapped LAO/STO structures, where the room-temperature electrical resistivity significantly increases when the structure size becomes smaller than 1 mu m. High-resolution intermodulation electrostatic force microscopy reveals an inhomogeneous surface potential with "puddles" of a characteristic size of 130 nm in the noncapped samples and a more uniform surface potential with a larger characteristic size of the puddles in the capped samples. In addition, capped structures show superconductivity below 200 mK and nonlinear currentvoltage characteristics with a clear critical current observed up to 700 mK. Our findings shed light on the complicated nature of the 2DEG at the LAO/STO interface and may also be used for the design of electronic devices.
The best organic solar cells are limited by bimolecular recombination. Tools to study these losses are available; however, they are only developed for small area (laboratory-scale) devices and are not yet available for large area (production-scale) devices. Here we introduce the Intermodulation Light Beam-Induced Current (IMLBIC) technique, which allows simultaneous spatial mapping of both the amount of extracted photocurrent and the bimolecular recombination over the active area of a solar cell. We utilize the second-order non-linear dependence on the illumination intensity as a signature for bimolecular recombination. Using two lasers modulated with different frequencies, we record the photocurrent response at each modulation frequency and the bimolecular recombination in the second-order intermodulation response at the sum and difference of the two frequencies. Drift-diffusion simulations predict a unique response for different recombination mechanisms. We successfully verify our approach by studying solar cells known to have mainly bimolecular recombination and thus propose this method as a viable tool for lateral detection and characterization of the dominant recombination mechanisms in organic solar cells. We expect that IMLBIC will be an important future tool for characterization and detection of recombination losses in large area organic solar cells.
We have measured the Hall resistance in two-dimensional arrays of ultrasmall aluminium Josephson junctions. We found that the Hall resistance was periodical with respect to an external magnetic field applied perpendicular to the plane of the array. We also found that the Hall resistance was affected by an applied voltage to a nearby gate electrode, but not by a gate plane silting underneath the array.
We demonstrate an alternative to Kelvin Probe Force Microscopy for imaging surface potential. The open-loop, single-pass technique applies a low-frequency AC voltage to the atomic force microscopy tip while driving the cantilever near its resonance frequency. Frequency mixing due to the nonlinear capacitance gives intermodulation products of the two drive frequencies near the cantilever resonance, where they are measured with high signal to noise ratio. Analysis of this intermodulation response allows for quantitative reconstruction of the contact potential difference. We derive the theory of the method, validate it with numerical simulation and a control experiment, and we demonstrate its utility for fast imaging of the surface photo-voltage on an organic photovoltaic material.
Low noise measurement of small currents in nanometer-scale junctions is of central importance to the characterization of novel high-performance devices and materials for applications ranging from energy harvesting and energy conversion to topological materials for quantum computers. The high resistance of these junctions and the stray capacitance of their measurement leads impose speed limitations (tens of seconds) on the traditional methods of measuring their nonlinear conductance, making detailed investigations of change with external fields or maps of variation over a surface impractical, if not impossible. Here we demonstrate fast (milliseconds) reconstruction of nonlinear current-voltage characteristics from phase-coherent multifrequency lock-in data using the inverse Fourier transform. The measurement technique allows for separation of the galvanic and displacement currents in the junction and easy cancellation of parasitic displacement current due to the measurement leads. We use the method to reveal nanometer-scale variations in the electrical transport properties of organic photovoltaic and semiconducting thin films. The method has broad applicability and its wide-spread implementation promises advancement in high-speed and high-resolution characterization for nanotechnology.
We present an alternative approach to pump-probe spectroscopy for measuring fast charge dynamics with an atomic force microscope (AFM). Our approach is based on coherent multifrequency lock-in measurement of the intermodulation between a mechanical drive and an optical or electrical excitation. In response to the excitation, the charge dynamics of the sample is reconstructed by fitting a theoretical model to the measured frequency spectrum of the electrostatic force near resonance of the AFM cantilever. We discuss the time resolution, which in theory is limited only by the measurement time, but in practice is of order one nanosecond for standard cantilevers and imaging speeds. We verify the method with simulations and demonstrate it with a control experiment, achieving a time resolution of 20 ns in ambient conditions, limited by thermal noise.
We present an alternative approach to pump-probe spectroscopy for measuring fast charge dynamics with an atomic force microscope (AFM). Our approach is based on coherent multifrequency lock-in measurement of the intermodulation between a mechanical drive and an optical or electrical excitation. In response to the excitation, the charge dynamics of the sample is reconstructed by fitting a theoretical model to the measured frequency spectrum of the electrostatic force near resonance of the AFM cantilever. We discuss the time resolution, which in theory is limited only by the measurement time, but in practice is of order 1 ns for standard cantilevers and imaging speeds. We verify the method with simulations and demonstrate it with a control experiment, achieving a time resolution of 30 ns in ambient conditions, limited by thermal noise.
We describe a phase-coherent multifrequency lock-in measurement technique that uses the inverse Fourier transform to reconstruct the nonlinear current-voltage characteristic of a nanoscale junction. The method provides separation of the galvanic and displacement currents in the junction and easy cancellation of the parasitic displacement current from the measurement leads. These two features allow us to overcome traditional limitations imposed by the low conductance of the junction and the high capacitance of the leads, thus providing an increase in measurement speed of several orders of magnitude. We demonstrate the method in the context of conductive atomic force microscopy, acquiring current-voltage characteristics at every pixel while scanning at standard imaging speed.
We use a recently developed scanning probe technique to image with high spatial resolution the injection and extraction of charge around individual surface-modified aluminum oxide nanoparticles embedded in a low-density polyethylene (LDPE) matrix. We find that the experimental results are consistent with a simple band structure model where localized electronic states are available in the band gap (trap states) in the vicinity of the nanoparticles. This work offers experimental support to a previously proposed mechanism for enhanced insulating properties of nanocomposite LDPE and provides a powerful experimental tool to further investigate such properties.
Background forces are linear long-range interactions of the cantilever body with its surroundings that must be compensated for in order to reveal tip-surface force, the quantity of interest for determining material properties in atomic force microscopy. We provide a mathematical derivation of a method to compensate for background forces, apply it to experimental data, and discuss how to include background forces in simulation. Our method, based on linear-response theory in the frequency domain, provides a general way of measuring and compensating for any background force and it can be readily applied to different force reconstruction methods in dynamic AFM.
We present a theoretical framework for the dynamic calibration of the higher eigenmode parameters (stiffness and optical lever inverse responsivity) of a cantilever. The method is based on the tip-surface force reconstruction technique and does not require any prior knowledge of the eigenmode shape or the particular form of the tip-surface interaction. The calibration method proposed requires a single-point force measurement by using a multimodal drive and its accuracy is independent of the unknown physical amplitude of a higher eigenmode.
We propose a theoretical framework for reconstructing tip-surface interactions using the intermodulation technique when more than one eigenmode is required to describe the cantilever motion. Two particular cases of bimodal motion are studied numerically: one bending and one torsional mode, and two bending modes. We demonstrate the possibility of accurate reconstruction of a two-dimensional conservative force field for the former case, while dissipative forces are studied for the latter.
Surface science, which spans the fields of chemistry, physics, biology and materials science, requires information to be obtained on the local properties and property variations across a surface. This has resulted in the development of different scanning probe methods that allow the measurement of local chemical composition and local electrical and mechanical properties. These techniques have led to rapid advancement in fundamental science with applications in areas such as composite materials, corrosion protection and wear resistance. In this perspective article, we focussed on the branch of scanning probe methods that allows the determination of surface nanomechanical properties. We discussed some different AFM-based modes that were used for these measurements and provided illustrative examples of the type of information that could be obtained. We also discussed some of the difficulties encountered during such studies.
We report an experimental study on the effect of high impedance environment on a Cooper pair transistor (CPT). The CPT consists of two small capacitance Josephson tunnel junctions in series with a gate electrode coupled through a capacitance Cg to a central island. In small-capacitance CPT the charging energy EC = e2/2C, where C ∼ 2CJ+Cg is the total capacitance of the island, becomes relevant at low temperature, and charging effects influence the transport properties.
We have measured the current-voltage characteristics of a single Josephson junction placed in a high impedance environment. The transfer of Cooper pairs through the junction is governed by overdamped quasicharge dynamics, leading to Coulomb blockade and Bloch oscillations. Exact duality exists to the standard overdamped phase dynamics of a Josephson junction, resulting in a dual shape of the current-voltage characteristic, with current and voltage changing roles. We demonstrate this duality with experiments which allow for a quantitative comparison with a theory that includes the effect of fluctuations due to the finite temperature of the electromagnetic environment.
We have measured the Cooper pair transistor (CPT) in a tunable electromagnetic environment consisting of four one-dimensional superconducting quantum interference device arrays. The transport properties of the CPT in the high impedance limit, Z(env)> R-Q similar or equal to 6.45 k Omega, are studied for different ratios of the Josephson coupling energy to the charging energy. As the impedance of the environment is increased, the current-voltage characteristic (IVC) of the CPT develops a Coulomb blockade of Cooper pair tunneling and the measured IVCs agree qualitatively with a theory based on quasicharge dynamics for a CPT. Increasing the impedance of the environment induces a transition in the modulation of the IVC with the gate charge from e-periodic to 2e-periodic.
We perform a comparative study of dynamic force measurements using an Atomic Force Microscope (AFM) on the same soft polymer blend samples in both air and liquid environments. Our quantitative analysis starts with calibration of the same cantilever in both environments. Intermodulation AFM (ImAFM) is used to measure dynamic force quadratures on the same sample. We validate the accuracy of the reconstructed dynamic force quadratures by numerical simulation of a realistic model of the cantilever in liquid. In spite of the very low quality factor of this resonance, we find excellent agreement between experiment and simulation. A recently developed moving surface model explains the measured force quadrature curves on the soft polymer, in both air and liquid.
We studied quantum phase-slip (QPS) phenomena in long one-dimensional Josephson junction series arrays with tunable Josephson coupling. These chains were fabricated with as many as 2888 junctions, where one sample had a separately tunable link in the middle of the chain. Measurements were made of the zero-bias resistance, R-0, as well as current-voltage characteristics (IVC). The finite R-0 is explained by QPS and shows an exponential dependence on root E-J/E-C with a distinct change in the exponent at R-0 = R-Q = h/4e(2). When R-0 > R-Q, the IVC clearly shows a remnant of the Coulomb blockade, which evolves to a zero-current state with a sharp critical voltage as E-J is tuned to a smaller value. The zero-current state below the critical voltage is due to coherent QPSs and we show that these are enhanced when the central link is weaker than all other links. Above the critical voltage, a negative, differential resistance is observed, which nearly restores the zero-current state.
We studied current-voltage characteristics of long one-dimensional Josephson junction chains with Josephson energy much larger than charging energy, E-J >> E-C. In this regime, typical I-V curves of the samples consist of a supercurrent-like branch at low-bias voltages followed by a voltage-independent chain current branch, I-chain at high bias. Our experiments showed that I-chain is not only voltage-independent but it is also practically temperature-independent up to T = 0.7T(C). We have successfully model the transport properties in these chains using a capacitively shunted junction model with nonlinear damping.
The Josephson effect, tunnelling of a supercurrent through a thin insulator layer between two superconducting islands, is a phenomena characterized by a spatially distributed phase of the superconducting condensate. In recent years, there has been a growing focus on Josephson junction devices particularly for the applications of quantum metrology and superconducting qubits. In this study, we report the development of Josephson junction circuit formed by serially connecting many Superconducting Quantum Interference Devices, SQUIDs. We present experimental measurements as well as numerical simulations of a phase-slip center, a SQUID with weaker junctions, embedded in a Josephson junction chain. The DC transport properties of the chain are the result of phase slips which we simulate using a classical model that includes linear external damping, terminating impedance, as well as internal nonlinear quasiparticle damping. We find good agreement between the simulated and the experimental current voltage characteristics. The simulations allow us to examine the spatial and temporal distribution of phase-slip events occurring across the chains and also the existence of travelling voltage pulses which reflect at the chain edges.
Conventional dynamic atomic force microscopy (AFM) can be extended to bimodal and multimodal AFM in which the cantilever is simultaneously excited at two or more resonance frequencies. Such excitation schemes result in one additional amplitude and phase images for each driven resonance, and potentially convey more information about the surface under investigation. Here we present a theoretical basis for using this information to approximate the parameters of a tip-surface interaction model. The theory is verified by simulations with added noise corresponding to room-temperature measurements.
Atomic force microscopy has recently been extented to bimodal operation, where increased image contrast is achieved through excitation and measurement of two cantilever eigenmodes. This enhanced material contrast is advantageous in analysis of complex heterogeneous materials with phase separation on the micro or nanometre scale. Here we show that much greater image contrast results from analysis of nonlinear response to the bimodal drive, at harmonics and mixing frequencies. The amplitude and phase of up to 17 frequencies are simultaneously measured in a single scan. Using a machine-learning algorithm we demonstrate almost threefold improvement in the ability to separate material components of a polymer blend when including this nonlinear response. Beyond the statistical analysis performed here, analysis of nonlinear response could be used to obtain quantitative material properties at high speeds and with enhanced resolution.
We present a method to reconstruct the nonlinear tip-surface force and extract material properties from a multifrequency atomic force microscopy (AFM) measurement with a high-quality-factor cantilever resonance. In a measurement time of similar to 2 ms, we are able to accurately reconstruct the tip-surface force-displacement curve, allowing simultaneous high-resolution imaging of both topography and material properties at typical AFM scan rates. We verify the method using numerical simulations, apply it to experimental data, and use it to image mechanical properties of a polymer blend. We further discuss the limitations of the method and identify suitable operating conditions for AFM experiments.
We demonstrate quantitative force imaging of long-range magnetic forces simultaneously with near-surface van-der-Waals and contact-mechanics forces using intermodulation atomic force microscopy. Magnetic forces at the 200 pN level are separated from near-surface forces at the 30 nN level. Imaging of these forces is performed in both the contact and non-contact regimes of near-surface interactions.
We discuss the physical origin and measurement of force between an atomic force microscope tip and a soft material surface. Quasi-static and dynamic measurements are contrasted and similarities are revealed by analyzing the dynamics in the frequency domain. Various dynamic methods using single and multiple excitation frequencies are described. Tuned multifrequency lockin detection with one reference oscillation gives a great deal of information from which one can reconstruct the tip–surface interaction. Intermodulation in a weakly perturbed high Q resonance enables the measurement of a new type of dynamic force curve, offering a physically intuitive way to visualize both elastic and viscous forces.
Experiments on one-dimensional small capacitance Josephson Junction arrays are described. The arrays have a junction capacitance that is much larger than the stray capacitance of the electrodes, which we argue is important for observation of Coulomb blockade. The Josephson energy can be tuned in situ and an evolution from Josephson-like to Coulomb blockade behavior is observed. This evolution can be described as a superconducting to insulating, quantum phase transition. In the Coulomb blockade state, hysteretic current-voltage characteristics are described by a dynamic model which is dual to the resistively shunted junction model of classical Josephson junctions.
We describe experiments on one-dimensional arrays of small capacitance Josephson junctions which show how the Coulomb blockade of Cooper pair tunneling is influenced by changing the Josephson coupling energy in situ with an externally applied magnetic flux. We show how the zero bias resistance of the array is affected by the length of the array, and we use the length scaling of this resistance to infer that a quantum phase transition occurs as the Josephson coupling energy is changed. The data are qualitatively analyzed in terms of a theoretical model of the quantum phase transition which uses a mapping to the two-dimensional XY model.
One-dimensional arrays of small capacitance SQUIDs have been studied experimentally. The effective Josephson coupling between neighboring electrodes is tunable in situ. The arrays can be tuned from a Josephson-like state, with low resistance and sharp critical current, to a Coulomb blockade state, with infinite resistance and sharp threshold voltage. A quantum phase transition occurs at the crossover between these two types of behavior, which is evident from an analysis of the temperature dependence of the zero bias resistance.
We study the interaction between an AFM tip and a soft viscoelastic surface. Using a multifrequency method we measure the amplitude-dependence of the cantilever dynamic force quadratures, which clearly show the effect of finite relaxation time of the viscoelastic surface. A model is introduced which treats the tip and surface as a two-body dynamic problem with a nonlinear interaction depending on their separation. We find good agreement between simulations of this model and experimental data on polymer blend samples for a variety of materials and measurement conditions.
The mechanical properties of polymeric nanocomposites are strongly affected by the nature of the interphase between filler and matrix, which can be controlled by means of surface chemistry. In this report, we utilize intermodulation atomic force microscopy (ImAFM) to probe local mechanical response with nanometer-scale resolution of poly(dimethylsiloxane) (PDMS) coatings with and without 20 wt% of hydrophobic silica nanoparticles. The data evaluation is carried out without inferring any contact mechanics model, and is thus model-independent. ImAFM imaging reveals a small but readily measurable inhomogeneous mechanical response of the pure PDMS surface layer. The analysis of energy dissipation measured with ImAFM showed a lowering of the viscous response due to the presence of the hydrophobic silica nanoparticles in the polymer matrix. An enhanced elastic response was also evident from the in-phase stiffness of the matrix, which was found to increase by a factor of 1.5 in presence of the nanoparticles. Analysis of dissipation energy and stiffness in the immediate vicinity of the nanoparticles provides an estimate of the interphase thickness. Because the local stiffness varies significantly near the nanoparticle, AFM height images contain artifacts that must be corrected in order to reveal the true surface topography. Without such a correction the AFM height images erroneously show that the stiff particles protrude from the surface, whereas corrected images show that they are actually embedded in the matrix and likely covered with a thin layer of polymer.
Local surface mechanical properties of polymeric nanocomposites play a significant role in theirperformance. Atomic Force Microscopy (AFM) can be used to perform measurements of suchproperties with high lateral resolution. The interphase between filler and matrix, and how it can becontrolled by means of surface chemistry is of particular interest. In this work we compare threeoperating modes of AFM: Tapping mode, PeakForce QNM (Quantitative Nanomechanical Mapping)and Intermodulation AFM (ImAFM), for their ability to capture the tip-surface force and to extractlocal mechanical properties by applying different contact mechanics models. Layers ofpoly(dimethylsiloxane) (PDMS) with and without 20 wt.% of hydrophobic silica nanoparticles werestudied employing these AFM modes. We show that tapping mode AFM can provide qualitativeinformation, but it is insufficient to accurately and quantitatively discriminate surface propertiessince this mode does not allow extraction of the tip-surface force. Quantitative mapping ofmechanical properties is possible with both PeakForce QNM and ImAFM. However, it remained achallenge to evaluate the data for soft PDMS layers with PeakForce QNM. Local surface mechanicalproperties could be more reproducibly assessed via ImAFM. We show that the Tapping modeimages for pure PDMS report a relatively homogeneous surface, but as we utilize PeakForce QNMand ImAFM more details appear and the inhomogeneous nature of the surface layer becomesapparent. Incorporation of silica particles in the PDMS layer results in a significant increase in theapparent stiffness of the matrix. All imaging modes allow visualization of the hard particles in thesoft matrix. However, we were most successful with imaging the interphase using ImAFM.
We describe a method of analysis which allows for reconstructing the nonlinear disturbance of a high Q harmonic oscillator. When the oscillator is driven with two or more frequencies, the nonlinearity causes intermodulation of the drives, resulting in a complicated spectral response. Analysis of this spectrum allows one to approximate the nonlinearity. The method, which is generally applicable to measurements based on resonant detection, increases the information content of the measurement without requiring large detection bandwidth, and optimally uses the enhanced sensitivity near resonance to extract information and minimize error due to detector noise.
We investigate one-dimensional Josephson junction arrays with generalized unit cells, beyond a single junction or SQUID, as a circuit approach to engineer band gaps. Within a specific frequency range, of the order of the single junction plasma frequency, the dispersion relation becomes gapped and the impedance becomes purely imaginary. We derive the parameter dependence of this gap and suggest designs to lower it to microwave frequencies. The gap can be tuned in a wide frequency range by applying external flux, and persists in the presence of small imperfections. These arrays, which can be thought of as tunable artificial crystals, may find use in applications ranging filters to the protection of quantum bits.
Asymmetric double-tunnel barriers with the center electrode being a metal cluster in the quantum regime are studied. The zero dimensionality of the clusters used and the associated quantized energy spectra are manifest in well-defined steps in the current-voltage characteristic. Record high current rectification ratios of similar to 10(4) for tunneling through such clusters are demonstrated at room temperature. We are able to account for all of the experimentally observed features by modeling our double-barrier structures using a combination of discrete states and charging effects for tunneling through quantum dots.
Double tunnel barrier structures were obtained by using a scanning tunneling microscope and samples composed of metallic nanoparticles deposited onto an oxidized bottom electrode. The nanoparticles were formed by evaporating subpercolation thin metallic layers. Due to the small size of the particles their energy spectrum is discrete, which is evidenced by the measured quantized current-voltage characteristics. Current rectification ratios of 100-1000 for tunneling through such quantum dots are demonstrated at room temperature.
Scanning tunneling microscopy (STM) is used to study transport in magnetic double tunnel junctions (DTJs) formed using a fixed transparency barrier of a patterned tunnel junction (TJ), and a variable tunnel barrier between the top electrode of the patterned junction and the STM tip. A sufficiently thin top electrode has been predicted to result in a rectification of charge current through a DTJ when the two barriers have different transparency. Our measurements indeed show a high current rectification ratio for 3-nm-thick, continuous film top electrodes, which is observed for junctions with asymmetric tunnel barriers.
We investigate the electrical transport properties of narrow titanium (Ti) wires which are thinned by anodic oxidation. At temperatures below 1 K the current-voltage (IV) characteristics of the resulting Ti/TiOx nanostructures exhibit a zero current state due to the occurrence of Coulomb blockade. An indium gate electrode is placed on top of the anodised region, and the modulation of the conductance as a function of the gate voltage is investigated.
We have numerically studied the behavior of one-dimensional tunnel junction arrays when random background charges are included using the orthodox theory of single-electron tunneling. Random background charge distributions are varied in both amplitude and density. The use of a uniform array as a transistor is discussed both with and without random background charges. An analytic expression for the gain near zero gate voltage in a uniform array with no background charges is derived. The gate modulation with background charges present is simulated.
Spin dependent transport in a ferromagnet-superconductor single-electron transistor is studied theoretically taking into account spin accumulation, spin relaxation, gap suppression, and charging effects. A strong dependence of the gap on the magnetic state of the electrodes is found, which gives rise to a magnetoresistance of up to 100%. We predict that fluctuations of the spin accumulation can play such an important role as to cause the island to fluctuate between the superconducting and normal states. Furthermore, the device exhibits a nearly complete gate-controlled spin-valve effect.
Transport properties of ferromagnetic/nonmagnetic/ferromagnetic single electron transistors are investigated as a function of external magnetic-field, temperature, bias, and gate voltage. By designing the magnetic electrodes to have different switching fields, a two-mode device is realized having two stable magnetization states, with the electrodes aligned in parallel and antiparallel. Magnetoresistance of approximately 100% is measured in Co/AlOX/Al/AlOX/Co double tunnel junction spin valves at low bias, with the Al spacer in the superconducting state. The effect is substantially reduced at high bias and temperatures above the T-C of the Al. The experimental results are interpreted as due to spin imbalance of charge carriers resulting in suppression of the superconducting gap of the Al island.
A lateral array of ferromagnetic tunnel junctions is used to inject and detect nonequilibrium quasiparticle spin distribution in a superconducting strip made of Al. The strip width and thickness are kept below the quasiparticle spin diffusion length in Al. Nonlocal measurements in multiple parallel and antiparallel magnetic states of the detectors are used to in situ determine the quasiparticle spin diffusion length. A very large increase in the spin accumulation in the superconducting state compared to that in the normal state is observed and is attributed to a diminishing of the quasiparticle population by the opening of the gap below the transition temperature.