Stabilizing superconductivity in nanowires by coupling to dissipative environments

We present a theory for a finite-length superconducting nanowire coupled to an environment. We show that in the absence of dissipation quantum phase slips always destroy superconductivity, even at zero temperature. Dissipation stabilizes the superconducting phase. We apply this theory to explain the "antiproximity effect" recently seen by Tian et al. in zinc nanowires.     

Superconducting fluctuation induced conductance corrections near a pair-breaking quantum phase transition in doubly connected ultrathin cylinders of Al

We report measurements on ultrathin,doubly connected superconducting cylinders of Al that exhibit a destructive regime,which refers to the loss of superconductivity in a doubly connected superconductor near applied half flux quanta due to the sample topology and the small size of the sample.A depairing quantum phase transition(QPT)between a superconducting and metallic state tuned by the magnetic flux enclosed in the quasi one-dimensional(1D)cylinder was found at the onset of the destructive regime.Results on magnetic flux and temperature dependent sample resistance as well as current-voltage characteristics revealed the presence of both thermally activated and quantum phase slips near the depairing QPT.On the superconducting side of the QPT,thermally activated phase slips as described by the Langer-Ambegaokar and McCumber-Halperin(LAMH)theory were found to describe the sample resistance as the system was pushed towards the QPT by a magnetic field applied along the cylinder axis.However,deviation from this behavior was found at low temperatures,signaling the presence of the quantum phase slips.Most importantly,we observed a highly unusual negative slope in the resistance versus temperature curves on the metallic side of the QPT as predicted by the diagrammatic calculation of the dc conductivities in a 1D system near a depairing QPT.Our work suggests that fluctuations from both the phase and the amplitude of the superconducting order parameter are important for the superconductor-to-metal depairing QPT.     

Evidence for macroscopic quantum tunneling of phase slips in long one-dimensional superconducting Al wires

Quantum phase slips have received much attention due to their relevance to superfluids in reduced dimensions and to models of cosmic string production in the early universe. Their establishment in one-dimensional superconductors has remained controversial. Here we study the nonlinear current-voltage characteristics and linear resistance in long superconducting Al wires with lateral dimensions approximately 5 nm. We find that, in a magnetic field and at temperatures well below the superconducting transition, the observed behaviors can be described by the nonclassical, macroscopic quantum tunneling of phase slips, and are inconsistent with the thermal activation of phase slips.     

Quantum phase slips in the presence of finite-range disorder

To study the effect of disorder on quantum phase slips (QPSs) in superconducting wires, we consider the plasmon-only model where disorder can be incorporated into a first-principles instanton calculation. We consider weak but general finite-range disorder and compute the form factor in the QPS rate associated with momentum transfer. We find that the system maps onto dissipative quantum mechanics, with the dissipative coefficient controlled by the wave (plasmon) impedance Z of the wire and with a superconductor-insulator transition at Z = 6.5 k. We speculate that the system will remain in this universality class after resistive effects at the QPS core are taken into account.     

Possibility of persistent voltage observation in a system of asymmetric superconducting rings

The possibility of observing persistent voltage in superconducting rings of different arm widths is experimentally investigated. It was previously found that switching of the arms between superconducting and normal states by an AC current induces DC voltage oscillation in the magnetic field with a period corresponding to the flux quantum inside the ring. We used systems with a large number of asymmetric rings connected in series to investigate the possibility of observing this quantum phenomenon near the superconducting transition, where thermal fluctuations lead to switching of ring segments without an external influence and the persistent current is much smaller than in the superconducting state.     

Sharp superconductor-insulator transition in short wires

Recent experiments on short MoGe nanowires show a sharp superconducting-insulating transition at the universal resistance R(Q)=h/(4e(2)), contrary to the expectation of a smooth temperature dependence of the resistance for such Josephson-like systems. We present a self-consistent renormalization-group treatment of interacting quantum phase slips in short superconducting wires, which reproduces this sharp universal transition. Our method should also apply to other systems in the sine-Gordon universality class, in the previously inaccessible intermediate-coupling regime.     

Modulation theory of quantum tunneling into a Calogero-Sutherland fluid

We consider quantum slips of phase at a round hole punctured in a thin superconducting film and show that virtual vortex pairs provide an efficient pathway for these processes. Specifically, in the limit when the normalstate resistivity of the film is large, the presence of the film causes at most a logarithmic interaction between phase slips. This is in contrast to the nearly linear confining interaction (and the consequent nearly activated behavior of the resistance) obtained when vortices are neglected. The text was submitted by the author in English. An erratum to this article is available at .     

Tuning an rf-SQUID flux qubit system＇s potential with magnetic flux bias

At an extremely low temperature of 20 mK, we measured the loop current in a tunable rf superconducting quantum interference device (SQUID) with a dc-SQUID. By adjusting the magnetic flux applied to the rf-SQUID loop (Φ f ) and the small dc-SQUID (Φ cjj f ), respectively, the potential shape of the system can be fully controlled in situ. Variation in the transition step and overlap size in the switching current with a barrier flux bias are analyzed, from which we can obtain some relevant device parameters and build a model to explain the experimental phenomenon.     

Switching currents limited by single phase slips in one-dimensional superconducting Al nanowires

An aluminum nanowire switches from superconducting to normal as the current is increased in an upsweep. The switching current (I(s)) averaged over upsweeps approximately follows the depairing critical current (I(c)) but falls below it. Fluctuations in I(s) exhibit three distinct regions of behaviors and are nonmonotonic in temperature: saturation well below the critical temperature T(c), an increase as T(2/3) at intermediate temperatures, and a rapid decrease close to T(c). Heat dissipation analysis indicates that a single phase slip is able to trigger switching at low and intermediate temperatures, whereby the T(2/3) dependence arises from the thermal activation of a phase slip, while saturation at low temperatures provides striking evidence that the phase slips by macroscopic quantum tunneling.     

Universal conductance of nanowires near the superconductor-metal quantum transition

We consider wires near a zero temperature transition between superconducting and metallic states. The critical theory obeys hyperscaling, which leads to a universal frequency, temperature, and length dependence of the conductance; quantum and thermal phase slips are contained within this critical theory. Normal, superconducting, and mixed (SN) leads on the wire determine distinct universality classes. For the SN case, wires near the critical point have a universal dc conductance which is independent of the length of the wire at low temperatures.     

Analytical results of the Fokker-Planck equation derived for one superconducting nanowire quantum interference device and for DC SQUIDs-asymmetric devices

We consider an asymmetric two-junction superconducting quantum interference device, whose junctions are assumed to be overdamped, and regard Sin Fourier series for their current-phase relations. We take into account the effects of thermal fluctuations by forming a two-dimensional Fokker-Planck equation for the distribution function. We judge a series expansion of first order with respect to the components of the reduced inductance for distribution function and obtain current-voltage relation. We consider the measured resistance of the superconducting nanowire quantum interference device with mesoscopic leads that Hopkins et al. reported in Hopkins et al. [D.S. Hopkins, D. Pekker, P.M. Goldbart, A. Bezryadin, Science 308 (2005) 1762] and analyzed in Pekker et al. [D. Pekker, A. Bezryadin, D.S. Hopkins, P.M. Goldbart, Phys. Rev. B 72 (2005) 104517], by defining loop inductance, and by considering appropriate relations for resistance of nanowires. In fact we extend Chesca formulation [B. Chesca, J. Low Temp. Phys. 112 (1998) 165] simultaneously in three aspects and give a unified theory for nanowire two-junction devices, low T_c and high T_c DC SQUIDs, in restricted conditions.     

Persistent current in superconducting nanorings

The superconductivity in very thin rings is suppressed by quantum phase slips. As a result, the amplitude of the persistent current oscillations with flux becomes exponentially small, and their shape changes from sawtooth to a sinusoidal one. We reduce the problem of low-energy properties of a superconducting nanoring to that of a quantum particle in a sinusoidal potential and show that the dependence of the current on the flux belongs to a one-parameter family of functions obtained by solving the respective Schr?dinger equation with twisted boundary conditions.     

Model of a proposed superconducting phase slip oscillator: a method for obtaining few-photon nonlinearities

We theoretically investigate a driven oscillator with the superconducting inductance subject to quantum phase slips (QPS). We find uncommon nonlinearities in the proposed device: they oscillate as a function of the number of photons N with a local period of the order of √N. We prove that such nonlinearities result in multiple metastable states encompassing few photons and study oscillatory dependence of various responses of the oscillator. Such nonlinearities enable new possibilities for quantum manipulation of photon states and very sensitive measurements to confirm the coherence of phase slips.     

Tuning rf-SQUID flux qubit system's potential with magnetic flux bias

At an extremely low temperature of 20 mK, we measured loop current in a tunable rf superconducting quantum interference device (SQUID) with a dc-SQUID. By adjusting the magnetic flux applied to the rf-SQUID loop (Φ_f) and the small dc-SQUID (Φ_f^cjj), respectively, the potential shape of the system can be fully controlled in situ. Variations of transition step and overlap size in switching current with the barrier flux bias are analyzed, from which we can obtain some relevant device parameters and built up a model to explain the experimental phenomenon.     

General transport properties of superconducting quantum point contacts: a Green functions approach

We discuss the general transport properties of superconducting quantum point contacts. We show how these properties can be obtained from a microscopic model using nonequilibrium Green’s function techniques. For the case of a one-channel contact we analyze the response under different biasing conditions: constant applied voltage, current bias and microwave-induced transport. Current fluctuations are also analyzed with particular emphasis on thermal and shot-noise. Finally, the case of superconducting transport through a resonant level is discussed. The calculated properties show a remarkable agreement with the available experimental data from atomic-size contacts measurements. We suggest the possibility of extending this comparison to several other predictions of the theory.     

Coulomb effects in a ballistic one-channel S-S-S device

We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy E _C ≪Δ. We consider a small superconducting grain with finite capacitance connected to two superconducting leads by nearly ballistic single-channel quantum point contacts. The temperature is assumed to be very low, so there are no single-particle excitations on the grain. Then the behavior of the system can be described in terms of the quantum mechanics of the superconducting phase on the island. The Josephson energy as a function of this phase has two minima that become degenerate when the phase difference on the leads equals to π, the tunneling amplitude between them being controlled by the gate voltage on the grain. We find the Josephson current and its low-frequency fluctuations, and predict their periodic dependence with period 2e on the induced charge Q _x =CV _g . Zh. éksp. Teor. Fiz. 114, 640–653 (August 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor     

Macroscopic coherent rectification in Andreev interferometers

We investigate nonlinear transport through quantum coherent metallic conductors contacted to superconducting components. We find that in certain geometries, the presence of superconductivity generates a large, finite-average rectification effect. Specializing to Andreev interferometers, we show that the direction and magnitude of rectification can be controlled by a magnetic flux tuning the superconducting phase difference at two contacts. In particular, this results in the breakdown of an Onsager reciprocity relation at finite bias. The rectification current is macroscopic in that it scales with the linear conductance, and we find that it exceeds 5% of the linear current at sub-gap biases of a few tens of microelectronvolts.     

Gate-tuned high frequency response of carbon nanotube Josephson junctions

Carbon nanotube Josephson junctions in the open quantum dot limit are fabricated using Pd/Al bilayer electrodes, and exhibit gate-controlled superconducting switching currents. Shapiro voltage steps can be observed under radio frequency current excitations, with a damping of the phase dynamics that strongly depends on the gate voltage. These measurements are described by a standard resistively and capacitively shunted junction model showing that the switching currents from the superconducting to the normal state are close to the critical current of the junction. The effective dynamical capacitance of the nanotube junction is found to be strongly gate dependent, suggesting a diffusive contact of the nanotube.