Vortex Tunneling Research Articles

Quantum tunneling of vortices in two-dimensional condensates

The tunneling rate t_v of a vortex between two pinning sites (of strength V separated by d) is computed using the Bogoliubov expansion of vortex wavefunctions overlap. For BCS vortices, tunneling is suppressed beyond a few Fermi wavelengths. For Bose condensates, t_v = V exp(- pi n_s d^2/2), where n_s is the boson density. The analogy between vortex hopping in a superconducting film and 2D electrons in a perpendicular magnetic field is exploited. We derive the variable range hopping temperature, below which vortex tunneling contributes to magneto-resistance. Using the 'Quantum Hall Insulator' analogy we argue that the -Hall conductivity- (rather than the inverse Hall resistivity) measures the effective carrier density in domains of mobile vortices. Details of vortex wavefunctions and overlap calculations, and a general derivation of the Magnus coefficient for any wavefunction on the sphere, are provided in appendices.

Quantum behaviors in high-TC systems: Macroscopic and vortex quantum tunneling

We describe the main ideas and some experimental outcomes of two experiments, both aimed to study quantum tunneling effects in high-TC structures. In the first experiment, macroscopic quantum tunneling is demonstrated in grain boundary YBaCuO Josephson junctions revealing dissipation levels lower than expected and opening novel perspectives for quantum circuitry. In the second, the low temperature dissipation is dominated by quantum tunneling of individual Pearl vortices in ultra-thin CaBaCuO systems characterized by extremely long Pearl lengths.

Two-dimensional vortex dynamics in decoupledYBa2Cu3O7/PrBa2Cu3O7superlattices

Two-dimensional (2D) vortex dynamics is studied in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}/{\mathrm{PrBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$ superlattices by measuring the current-voltage $(I\ensuremath{-}V)$ characteristics. In the high current limit, the 2D collective creep is observed with an activation energy $U(j)\ensuremath{\propto}{j}^{\ensuremath{-}\ensuremath{\mu}},$ with j the current density. The exponent $\ensuremath{\mu}$ is 0.8 at low temperatures and $\ensuremath{\mu}=0.2$ at high temperatures. A dislocation-mediated vortex melting occurs when the temperature is increased. In the low current limit, the exponential growth of the energy barrier for elastic motion is prohibited by the plastic deformation of vortices. The observed plateau in the resistive transition is attributed to the possible quantum tunneling of vortices.

Interaction of mesoscopic Josephson devices with non-classical microwaves

Mesoscopic Josephson devices, interacting with non-classical microwaves, are studied. The phase difference in Josephson's equations is a quantum mechanical operator, whose expectation value with respect to the density matrix describing the microwaves, determines the current. Dual phenomena with vortex condensates in Josephson array insulators are also considered. Dual Josephson junctions for vortices, made from two insulators separated by a weak link through which the vortices tunnel, are described by dual Josephson equations.

Vortices in Josephson arrays interacting with non-classical microwaves: The effect of dissipation

Vortices circulating in a ring made from a Josephson array in the insulating phase are studied. The ring contains a `dual Josephson junction' through which the vortices tunnel. External non-classical microwaves are coupled to the device. The time evolution of this two-mode fully quantum mechanical system is studied, taking into account the dissipation in the system. The effect of the quantum statistics of the photons on the quantum statistics of the vortices is discussed. Entropic calculations quantify the entanglement between the two systems. Quantum phenomena in the system are also studied through Wigner functions. After a certain time (which depends on the dissipation parameters) these quantum phenomena are destroyed due to dissipation.

Quantum tunneling of vortices in MgB2 superconductor

Magnetic relaxation in a MgB2 superconductor was measured. The temperature dependence of the normalized relaxation rate was determined for three different magnetic fields. By extrapolating these rates to T=0 K, we find that these extrapolations do not approach zero, indicating quantum tunneling of vortices in the superconductor. A quantum correction of the relaxation rate, followed by the correction of the magnetic moment, is proposed. Using the quantum correction, we find that U0 increases with decreasing temperature and approaches a maximum at T=0.

Thermally assisted quantum vortex tunneling in the Hall and dissipative regime

Quantum vortex tunneling is studied for the case where the Hall and the dissipative dynamics are simultaneously present. For a given temperature, the magnetization relaxation rate is calculated as a function of the external current and the quasiparticle scattering time. The relaxation rate is solved analytically at zero temperature and obtained numerically at finite temperatures by the variational method. In moderately clean samples, we have found that a minimum in the relaxation rate exists at zero temperature, which tends to disappear with an increase in the temperature.

Vortex tunneling spectra of high- Tc superconductors based on the t–J model

The local density of states and the c-axis tunneling spectrum around a vortex core and a nonmagnetic impurity in high- T c superconductors are studied using the two-dimensional t–J model and considering the anisotropy of the c-axis tunneling matrix elements. The order parameters are determined in a self-consistent way within the Gutzwiller approximation and the Bogoliubov–de Gennes theory. It is shown that neither the anisotropic matrix elements nor d+is state account for the recent STS data on the vortex core of Bi 2Sr 2CaCu 2O 8+ δ .

Exactly solvable model of dissipative vortex tunneling

I consider the problem of vortex tunneling in a two-dimensional superconductor. The vortex dynamics is governed by the Magnus force and the Ohmic friction force. Under-barrier motion in the vicinity of the saddle point of the pinning potential leads to a model with quadratic Hamiltonian which can be analytically diagonalized. I find the dependence of the tunneling probability on the normal state quasiparticle relaxation time $\tau$ with a minimum at $\omega_0\tau\sim 1$, where $\omega_0$ is the level spacing of the quasiparticle bound states inside the vortex core. The results agree qualitatively with the available experimental data.

Critical currents, flux-creep activation energy, and potential barriers for the vortex motion from flux-creep experiments

We present an experimental study of thermally activated flux creep in a superconducting ring-shaped epitaxial YBCO film as well as a new way of analyzing the experimental data. The measurements were made in a wide range of temperatures between 10 and 83 K. The upper temperature limit was dictated by our experimental technique and at low temperatures we were limited by a crossover to quantum tunneling of vortices. It is shown that the experimental data can very well be described by assuming a simple thermally activated hopping of vortices or vortex bundles over potential barriers, whereby the hopping flux objects remain the same for all currents and temperatures. The new procedure of data analysis also allows to establish the current and temperature dependencies of the flux-creep activation energy U, as well as the temperature dependence of the critical current Ic, from the flux-creep rates measured at different temperatures. The variation of the activation energy with current, U(I/Ic), is then used to reconstruct the profile of the potential barriers in real space.

Tunneling of vortices through a weak link in an insulating Josephson array

Tunneling of vortices through a weak link in an insulating Josephson array

Crossover from thermally activated flux creep to quantum tunneling of vortices in a YBa 2Cu 3O 7−x film

We present the results of a study of flux creep in a ring-shaped epitaxial superconducting YBa 2Cu 3O 7− x film at low temperatures. Measurements between 2 and 20 K have been made and it is confirmed that the flux creep is a thermally activated process at temperatures exceeding 10 K. The low-temperature data are analyzed by assuming a crossover to quantum tunneling of the vortex lines. Using the fact that the critical current in our sample is almost independent of temperature below 20 K, we establish the temperature dependence of the Euclidian action S directly from the experimental data without any a priori assumptions. Our results imply that at temperatures below 8.5 K S( T)= S(0)(1− T 2/ T qc 2), with approximately the same value of T qc≈15 K for the case of the remnant magnetization as well as in an external magnetic field of 1 kOe.

Absence of the zero bias peak in vortex tunneling spectra of high-temperature superconductors

The c-axis tunneling matrix of high-${T}_{c}$ superconductors is shown to depend strongly on the in-plane momentum of electrons and vanish along the four nodal lines of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave energy gap. This anisotropic tunneling matrix suppresses completely the contribution of the most extended quasiparticles in the vortex core to the c-axis tunneling current and leads to a spectrum similar to that of a nodeless superconductor. Our results give a natural explanation of the absence of the zero-bias peak as well as other features observed in the vortex tunneling spectra of high-${T}_{c}$ cuprates.

Shape and motion of vortex cores inBi2Sr2CaCu2O8+δ

We present a detailed study on the behaviour of vortex cores in Bi_2Sr_2CaCu_2O_{8+\delta} using scanning tunneling spectroscopy. The very irregular distribution and shape of the vortex cores imply a strong pinning of the vortices by defects and inhomogeneities. The observed vortex cores seem to consist of two or more randomly distributed smaller elements. Even more striking is the observation of vortex motion where the vortex cores are divided between two positions before totally moving from one position to the other. Both effects can be explained by quantum tunneling of vortices between different pinning centers.

Quantum tunneling of vortices in Bi-2212 with randomly oriented columnar defects

Vortex pinning in textured Bi-2212/Ag superconducting tapes was enhanced by randomly oriented columnar defects, formed by GeV proton-induced fission of Bi-nuclei. Studies of J versus time in the range 2–40 K shows that thermally activated current decay decreased greatly. However, temperature-independent quantum tunneling of vortices considerably limits J and its temporal stability for a significant fraction of the finite- J c region.

Current decay from quantum tunneling of vortices in Bi-2212 superconductors

We have created randomly oriented columnar defects in textured Bi 2Sr 2CaCu 2O x /Ag superconducting tapes and Tl-2212 materials, using a fission process driven by irradiation with 0.8 GeV protons. Vortex pinning was significantly improved, leading to increased persistent current density J. The thermally activated decay of current with time was greatly decreased, compared with unirradiated materials. Nonetheless, temperature-independent vortex motion from quantum tunneling limits J and its stability in time. Analysis of the time-dependent studies provides estimates for the elementary vortex attempt time τ, for both as-formed and ion-processed materials.

Quantum constraints on technological superconductors

Vortex pinning in textured Bi2Sr2CaCu2Ox/Ag superconducting tapes was enhanced by irradiation with 0.8 GeV protons, creating randomly oriented columnar defects. Measurements of the current density J versus time show that thermally-activated current decay was greatly decreased, compared with unirradiated tapes. However, temperature-independent quantum tunneling of vortices considerably limits J and its temporal stability, for a significant fraction of the finite-Jc region.

Hall Tunneling of Vortices in Superclean Superconductors

We discuss the main features of Hall tunneling of pancake vortices in superclean high-T c superconductors. The general formalism for the calculation of the lifetime of a vortex pinned in a metastable configuration is described. The results are applied to the problem of quantum tunneling of a pancake vortex from a columnar defect in the limit of a small driving current.

Vortex quantum micleation and tunneling in superconducting thin films: Role of dissipation and periodic pinning

We investigate the phenomenon of decay of a supercurrent in a superconducting thin film in the absence of an applied magnetic field. The resulting zero-temperature resistance derives from two equally possible mechanisms: 1) quantum tunneling of vortices from the edges of the sample; and 2) homogeneous quantum nucleation of vortex-antivortex pairs in the bulk of the sample, arising from the instability of the Magnus field's ``vacuum''. We study both situations in the case where quantum dissipation dominates over the inertia of the vortices. We find that the vortex tunneling and nucleation rates have a very rapid dependence on the current density driven through the sample. Accordingly, whilst normally the superconductor is essentially resistance-free, for the high current densities that can be reached in high-$T_c$ films a measurable resistance might develop. We show that edge-tunneling appears favoured, but the presence of pinning centres and of thermal fluctuations leads to an enhancement of the nucleation rates. In the case where a periodic pinning potential is artificially introduced in the sample, we show that current-oscillations will develop indicating an effect specific to the nucleation mechanism where the vortex pair-production rate, thus the resistance, becomes sensitive to the corrugation of the pinning substrate. In all situations, we give estimates for the observability of the studied phenomena.

Comment on vortex mass and quantum tunneling of vortices

Vortex mass in Fermi superfluids and superconductors and its influence on quantum tunneling of vortices are discussed. The vortex mass is essentially enhanced due to the fermion zero modes in the core of the vortex: the bound states of the Bogoliubov quasiparticles localized in the core. These bound states form the normal component, which is nonzero even in the low-temperature limit. In the collisionless regime ω 0 τ≫1 the normal component trapped by the vortex is unbound from the normal component in a bulk superfluid/superconductor and adds to the inertial mass of the moving vortex. In a d-wave superconductor the vortex mass has an additional factor of (B c2/B)1/2 due to the gap nodes.