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.     

Quasiparticle scattering by quantum phase slips in one-dimensional superfluids

Quantum phase slips (QPS) in narrow superfluid channels generate momentum by unwinding the supercurrent. In a uniform Bose gas, this momentum needs to be absorbed by quasiparticles (phonons). We show that this requirement results in an additional exponential suppression of the QPS rate (compared to the rate of QPS induced by a sharply localized perturbation). In BCS-paired fluids, momentum can be transferred to fermionic quasiparticles, and we find an interesting interplay between quasiparticle scattering on QPS and on disorder.     

Quantum phase slips in superconducting wires with weak inhomogeneities

Quantum phase slips are traditionally considered in diffusive superconducting wires which are assumed homogeneous. We present a definite estimate for the amplitude of phase slips that occur at a weak inhomogeneity in the wire where local resistivity is slightly increased. We model such a weak link as a general coherent conductor and show that the amplitude is dominated by the topological part of the action. We argue that such weak links occur naturally in apparently homogeneous wires and adjust the estimate to that case. The fabrication of an artificial weak link would localize phase slips and facilitate a better control of the phase-slip amplitude.     

Flow of a single magnetic vortex in a submicron-size superconducting Al disk controlled by radio-frequency currents

We report the first observation of a single-vortex flow in a mesoscopic superconductor. A flow of a single vortex is successfully controlled by an rf current superimposed on a dc current, evidence of which is provided by voltage steps in current-voltage (I-V) characteristics. Irrespective of the number of vortices confined to the disk, we unambiguously observe that when a single vortex inside the disk is driven out of the disk, another vortex enters the disk similarly to two balls colliding in billiards: only one vortex passes through the Al disk at the same time in mesoscopic systems.     

Microscopic theory of thermal phase slips in clean narrow superconducting wires

We consider the structure of a thermal phase-slip center for a simple microscopic model of a clean one-dimensional superconductor in which superconductivity occurs only within one conducting channel or several identical channels. Surprisingly, the Eilenberger equations describing the saddle-point configuration allow for an exact analytical solution in the whole temperature and current range. This solution allows us to derive a closed expression for the free-energy barrier, which we use to compute its temperature and current dependences.     

Two-step synthesis of one-dimensional single crystalline GaN nanowires

Straight and smooth GaN nanowires were synthesized on quartz substrates through the direct reaction of Ga₂O₃ thin films with flowing ammonia in a horizontal oven without using a template or catalyst. X-ray diffraction (XRD), scanning electron microscopy (SEM), energy-dispersive X-ray (EDX), transmission electron microscopy (TEM) and photoluminescence (PL) were used to characterize the samples. The straight and smooth cylindrical nanostructures are high quality single crystalline hexagonal wurtzite GaN nanowires with diameters ranging from 5 to 30 nm and lengths up to 20 μm. The near-band-edge emission peak located at 367 nm was observed at room temperature.     

Phase slips in a one-dimensional superconducting wire: Crossover from quantum tunneling to thermal hopping

We carry out quantum Monte Carlo simulations for the finite temperature behavior of a chain of coupled superconducting grains, whose T = 0 characteristics have been presented by Matveev et al. [K.A. Matveev, A.I. Larkin, L.I. Glazman, Phys. Rev. Lett. 89 (2002) 096802]. Quantum phase slips at low temperatures and the crossover to thermal hopping at elevated temperatures are observed. The effect of phase slips on persistent currents is numerically demonstrated.     

Influence of high magnetic fields on the superconducting transition of one-dimensional Nb and MoGe nanowires

The effects of a strong magnetic field on superconducting Nb and MoGe nanowires with diameter approximately 10 nm have been studied. We have found that the Langer-Ambegaokar-McCumber-Halperin (LAMH) theory of thermally activated phase slips is applicable in a wide range of magnetic fields and describes well the temperature dependence of the wire resistance, over 11 orders of magnitude. The field dependence of the critical temperature, T(c), extracted from the LAMH fits is in good quantitative agreement with the theory of pair-breaking perturbations that takes into account both spin and orbital contributions. The extracted spin-orbit scattering time agrees with an estimate tau(s.o.) approximately tau(variant Planck's over 2pic/Ze(2))(4), where tau is the elastic scattering time and Z is the atomic number.     

Coherent single photon transport in a one-dimensional waveguide coupled with superconducting quantum bits

A recent theoretical analysis and experimental results show that interesting transport properties of a single microwave photon emerge when a quantum bit in a cavity is coupled to a one-dimensional waveguide. Here we adopt a real-space model Hamiltonian to give a unified approach which accounts for the experimental results, and make new predictions on the properties of single photon transport, such as the general Fano line shape, symmetric vacuum Rabi splitting for a leaky cavity at resonance, and a one-photon switching capability.     

New Andreev-type states in superconducting nanowires

Superconducting nanowires can exhibit a spatially inhomogeneous pair condensate that leads to the formation of new Andreev-type states. Such states are mainly located beyond the regions where the order parameter is enhanced, and no normal-superconducting contact or external magnetic field is needed for their formation. Our numerical self-consistent solutions of the Bogoliubov-de Gennes equations for cylindrical nanowires, in the clean limit, demonstrate that these new Andreev-type states decrease the ratio of the energy gap to the critical temperature as compared to its bulk value. The low-lying excitations in a clean superconducting nanowire are these new Andreev-type states induced by quantum confinement of the electrons in the transverse direction.     

Aharanov-Bohm currents in thin superconducting cylinders

The Aharanov-Bohm effect is the influence of classically inaccessible electromagnetic fields on quantum wave functions. In this paper we consider the Ginsburg-Landau (GL) equations for the stationary states of a thin, superconducting cylinder in the presence of a curl-free, static electromagnetic potential corresponding to zero fields. We solve the GL equations explicitly to obtain self-consistent solutions for the current density, the induced field and the free energy in a well-defined and accessible approximation. The analysis makes quantitative predictions which can, in principle, be experimentally tested to provide a clear and convincing demonstration of the Aharanov-Bohm effect.     

Fluctuation conductivity of thin films and nanowires near a parallel-field-tuned superconducting quantum phase transition

We calculate the fluctuation correction to the normal state conductivity in the vicinity of a quantum phase transition from a superconducting to a normal state, induced by applying a magnetic field parallel to a dirty thin film or a nanowire with thickness smaller than the superconducting coherence length. We find that at zero temperature, where the correction comes purely from quantum fluctuations, the positive "Aslamazov-Larkin" contribution, the negative "density of states" contribution, and the "Maki-Thompson" interference contribution are all of the same order and the total correction is negative. Further, we show that, based on how the quantum critical point is approached, there are three regimes that show different temperature and field dependencies which should be experimentally accessible.     

Persistent currents in superconducting quantum interference devices

Starting from the reduced dynamical model of a two-junction quantum interference device, it shown that a quantum analog of the system can be exhibited. This quantum model extends the well-known properties of the device when its characteristic dimensions are of the order of mesoscopic length scales. By finding eigenvalues of the corresponding Hamiltonian operator, the persistent currents flowing in the ring have been obtained. The resulting quantum analog of the overdamped two-junction quantum interference device can be seen as a supercurrent qubit operating in the limit of negligible capacitance and finite inductance.     

Persistent currents in one-dimensional aperiodic mesoscopic rings

In the tight-binding approximation, we have investigated the behaviour of persistent currents in a one-dimensional Thue-Morse mesoscopic ring threaded by a magnetic flux. By applying a transfer-matrix technique, the energy spectra and the persistent currents in the system have been numerically calculated. It is shown that the flux-dependent eigenenergies form “band” structures and the energy gaps will enlarge if the site energy increases. Actually, the site energy and the filling-up number of electrons are two important factors which have much influence upon the persistent current. Increment of the site energy in the system will lead to a dramatic suppression of the currents. When the highest-occupied energy level is on the top of the band, the total current is limited; otherwise, the persistent current increases by several orders of magnitude. Generally, this kind of large scale change in the magnitude of the current can easily be observed in the vicinity of band gaps. The parity effect in the Thue-Morse ring is also discussed. Received 22 January 2001 and Received in final form 25 October 2001     

Precursor diamagnetism in superconducting Al films

The precursor diamagnetism is studied in a stack of Al films whose thickness is much smaller than the coherence length. The magnetization shows the (T ? T_c)^?1 behavior in a finite range of temperature above T_c. At T_c, in low magnetic fields constant magnetization independent of the field strength is observed. The results are in agreement with the theories of the two-dimensional superconductor.