Tunneling Strength Research Articles

Interlayer pairings in the Josephson-coupled layered superconductors

The general expression of the effective pairing Hamiltonian is proposed to obtain the multicomponent Ginzburg–Landau free energy functional for strongly anisotropic layered superconductors. The effective Hamiltonian contains an intralayer pairing interaction as well as all possible interlayer pairing potentials. It is shown that the problem with many order parameters can be reduced to the problem with two order parameters which characterize the effective intralayer and effective interlayer pairings. The interlayer interaction Ṽ 0, which corresponds to the coherently hopping of pairs from one layer to the nearest neighboring layers, renormalizes the Josephson tunneling strength for an intralayer effective order parameter. Mixing of two order parameters is characterized by the Lifschitz invariant in the free energy functional. The Lifschitz invariant is enhanced due to the interlayer pairing potential V 01 which represents an interaction of two particles on the layer with scattering one of them into the nearest neighboring layers. The interlayer interaction V 01 also stabilizes the mixing of two-order parameters. Since in the absence of V 01 the Lifschitz invariant vanishes for a half-filled band of two-dimensional electrons in a layer. The transition temperature T c to the superconducting state and upper critical magnetic field H c 2 are calculated. Effects of all possible interlayer pairing interactions on T c and H c 2 are studied.

Images of interlayer josephson vortices in Tl2Ba2CuO6+delta

The strength of the interlayer Josephson tunneling in layered superconductors is an essential test of the interlayer tunneling model as a mechanism for superconductivity, as well as a useful phenomenological parameter. A scanning superconducting quantum interference device (SQUID) microscope was used to image interlayer Josephson vortices in Tl2Ba2CuO6+delta and to obtain a direct measure of the interlayer tunneling in a high-transition temperature superconductor with a single copper oxide plane per unit cell. The measured interlayer penetration depth, lambdac, is approximately 20 micrometers, about 20 times the penetration depth required by the interlayer tunneling model.

Charging ultrasmall tunnel junctions in an electromagnetic environment

We have investigated the quantum admittance of an ultrasmall tunnel junction with arbitrary tunneling strength under an electromagnetic environment. Using the functional integral approach a close analytical expression of the quantum admittance is derived for a general electromagnetic environment. We then consider a specific controllable environment where a resistance is connected in series with the tunneling junction, for which we derived the dc quantum conductance from the zero frequency limit of the imaginary part of the quantum admittance. For such electromagnetic environment the dc conductance has been investigated in recent experiments, and our numerical results agree quantitatively very well with the measurements. Our complete numerical results for the entire range of junction conductance and electromagnetic environmental conductance confirmed the few existing theoretical conclusions.

Magic numbers and optical-absorption spectrum in vertically coupled quantum dots in the fractional quantum Hall regime.

Exact diagonalization is used to study the quantum states of vertically coupled quantum dots in strong magnetic fields. We find that electron correlation in the double dot leads to angular momentum magic numbers that are distinct from those of a single dot. The double dot magic numbers occur at low angular momentum and the single dot magic numbers reappear at a critical angular momentum determined by the strength of the interdot electron tunneling. We also propose that the magic numbers can be investigated experimentally in vertically coupled dots. Because of the generalized Kohn theorem, the far-infrared optical absorption spectrum of a single dot is unaffected by correlation, but the theorem does not hold for two vertically coupled dots that have different confining potentials. We show that the absorption energy of the double dot should exhibit discontinuities at the magnetic fields where the total angular momentum changes from one magic number to another. \textcopyright{} 1996 The American Physical Society.

Dc Josephson current through a quantum dot coupled with superconducting leads.

The transport in a superconductor--quantum-dot--superconductor tunnel junction with a Coulomb repulsion in the dot was studied numerically. We calculated the dc Josephson current by noncrossing approximations varying the strength of the Coulomb repulsion. The critical current has a peak structure that is a function of the energy-level position in the dot, but the number of the peaks changes depending on the temperature, the strength of electron tunneling, and the Coulomb repulsion. It has been predicted previously that the junction behaves as a \ensuremath{\pi} junction for an infinitely strong Coulomb repulsion. We obtained the conditions for the strength of the Coulomb repulsion necessary for the \ensuremath{\pi} junction.

Gap-function anisotropy and collective modes in a bilayer superconductor with Cooper-pair tunneling

We study the gap-function anisotropy and collective mode spectrum (\ensuremath{\omega}\ensuremath{\le}2\ensuremath{\Delta}) of the Anderson-Chakravarty model for high-${\mathit{T}}_{\mathit{c}}$ oxides based on Cooper-pair tunneling in a bilayer (with strength ${\mathit{T}}_{\mathit{J}}$). For both s-wave and d-wave pairing in the layers, the shape of the gap around the Fermi surface is strongly dependent on ${\mathit{T}}_{\mathit{J}}$. Besides the usual Anderson-Bogoliubov phase and Littlewood-Varma amplitude modes, we find branches (optical phononlike modes) involving fluctuations of the relative phase and amplitude of the order parameters of the two layers. These modes are the dynamic signature of the Cooper-pair tunneling model since their energy and damping depends critically on the relative magnitudes of the Cooper-pair tunneling strength (${\mathit{T}}_{\mathit{J}}$) and the pairing interaction (g), but not significantly on the symmetry of the pairing. The generalization to a trilayer system (which can arise in Bi, Tl, and Hg copper oxides) is briefly discussed.

Unified scaling theory of the electron box for arbitrary tunneling strength.

Unified scaling theory of the electron box for arbitrary tunneling strength.

Tunneling in the electron box in the nonperturbative regime

We study charging effects and tunneling in the single electron box. Tunneling mixes different charge states and in the nonperturbative regime the charge in the island may be strongly screened. When charge states are nearly degenerate the screening of the charge is strong even in the week tunneling regime. Virtual tunneling processes reduce both the level splitting Δ and the tunneling strength α. The charge on the island and the decay rates are calculated. In the strong tunneling regime also nondegenerate states are affected by tunneling. Strong-coupling scaling renormalizes the effective capacitance, a result which we confirm by Monte Carlo simulations. The tunneling strength α scales to smaller values into the regime where the weak-coupling scaling applies. We propose a two-stage scaling procedure providing the unified picture for the problem. The scaling analysis is also extended to superconducting tunnel junctions with finite subgap conductance.

Corrections from Electron‐Electron Interaction to the One‐Particle Density of States in Strongly Anisotropic Two‐Dimensional Systems

AbstractA simple model is proposed for the description of the one‐particle density of states ν(ε) of the degenerate electron gas in the grain boundary (inversion layer) of a semiconductor bicrystal or in a surface superlattice. The electron–electron interaction effect is calculated renormalized by scattering on the disorder in diffusion approximation. In the case of small tilt angles, where the grain boundary may be considered as a planar array of edge dislocation tubes (chains), a crossing‐over is obtained for ν(ε) from one‐dimensional (∼1/|ε|1/2) to two‐dimensional (∼ In2|ε|) behaviour in the neighbourhood of εcross ∼ w⟂2|ε|/h. Here ε is the difference of the energy from the Fermi energy, τ is the relaxation time due to scattering on the disorder, w⟂ is the transverse overlap integral characterizing the strength of the electron tunneling between dislocation tubes.

Localization and tunneling effects in percolating systems.

Localization and tunneling effects in percolating systems are studied using the homomorphic-cluster and coherent-potential approximations. The localization behavior of the electron states and hence the mobility edges are analyzed by means of the localization functions L(E) and F(E). When tunneling is neglected, the problem at hand reduces to the ordinary quantum percolation model. As the tunneling strength is increased, the percolation threshold decreases and no localization transition occurs when the tunneling is sufficiently strong.

Localization in a system of N coupled chains

The behaviour of a quantum particle moving in a system of N coupled chains parallel to each other and packed into a bundle is investigated in the presence of weak disorder. This system may be thought of as a model of an anisotropic thin wire. The dependence of the localization length r loc on N and t ⊥ is studied (t ⊥ is the interchain exchange integral characterizing the strength of the interchain tunneling). For t ⊥ < t c ≅ h/τ the localization length r loc increases proportionally to lt ⊥/(t τ −t ⊥) attaining a plateau value of the order of Nl (τ is the relaxation time and 1 the mean free path for elastic scattering). Such a behaviour may be called a transition from the Mott localization regime to the Thouless localization regime. It may be considered as a precursor of the insulator-metal transition (r loc → ∞) occuring for t ⊥ → t c in the quasi-1d system (N → ∞).

Reply by Dr J. M. Edmond and Mr J. D. Graham

We would like to thank Dr Barton for his comments, which dealt principally with the material forming the Appendix to the paper. The basis for Dr Barton's hindsight ‘prediction’ for systematic support of 2.5 m long bolts at 1 m spacing plus 50 mm of reinforced shotcrete (with its similarity to the engineers' enquiry specification shown on pp. 291 and 292, and figs. 9 and 10) is interesting although inherently probably somewhat subjective. It must be emphasised that the NGI system was not available to us at the time of the tunnel investigation and was only briefly appended to the case study in order to try to compare it, albeit rather superficially, with the Bieniawski (1973) system. We tried however to be as objective as possible in applying it on the basis of the site investigation results only. The basic approach to design was that the rock, together with its primary support system, provided the main strength of the tunnel. Such primary system was a permanent part of the works. For a hydraulic tunnel such as this one a smooth circular concrete surface was required, Over the life of the structure the provision of this concrete lining, together with grouting measures, consolidates and completes the tunnel strength, durability and serviceability. From the results of the site investigation the recommended primary support for those lengths of the tunnel which were not highly weathered was based largely upon one of Bieniawski's