Jorge Berger

Connectivity and Superconductivity

In the Memory of Shlomo Alexander.- Topological Considerations in Superconductivity.- The de Gennes-Alexander Theory of Superconducting Micronetworks.- Nodal Sets, Multiplicity and Superconductivity in Non-simply Connected Domains.- Connectivity and Flux Confinement Phenomena in Nanostructured Superconductors.- Zero Set of the Order Parameter, Especially in Rings.- Persistent Currents in Ginzburg-Landau Models.- On the Normal/Superconducting Phase Transition in the Presence of Large Magnetic Fields.- On the Numerical Solution of the Time-Dependent Ginzburg-Landau Equations in Multiply Connected Domains.- Formation of Vortex-Antivortex Pairs.- The Order Parameter as a Macroscopic Quantum Wavefunction.- The Ehrenberg-Siday-Aharonov-Bohm Effect.- Connectivity and Superconductivity in Inhomogeneous Structures.

CLASSIFICATION SCHEME FOR TOROIDAL MOLECULES

A class of planar periodic tilings, which correspond to toroidal arrangements of trivalent atoms, with pentagonal, hexagonal and heptagonal rings, has been constructed. Each tiling is characterized by a set of four integers and defines a toroidal molecule. The tiling rules are motivated by geometric considerations and the tiling patterns are rich enough to describe a wide class of toroidal carbon molecules, with a broad range of shapes and numbers of atoms. The molecular dimensions are simply related to the integers that determine the tiling. The configurational energy and the delocalisation energy of several molecules obtained in this way were computed for Tersoff and Huckel models. The results indicate that many of these molecules are not strained, and may be expected to be stable. The influence of size on the Huckel spectrum bears both similarities and differences compared with the case of tubules.

Dynamic measurement of oxygen diffusion in indium-tin oxide

Abstract The diffusion of oxygen through an impervious ITO layer has been determined by measuring admittances in the range 5×10 −5 -5 s −1 . The results can be fit by a model which assumes simultaneous oxygen diffusion and generation. The diffusion coefficient does not depend noticeably on the oxygen pressure and has an activation energy comparable to that found for In 2 O 3 .

Bifurcation analysis for phase transitions in superconducting rings with nonuniform thickness

We perform an analytic study of the problem of transitions between normal and superconducting phases for a sample which encloses a magnetic flux, as in the classic Little--Parks experiment. For a sample of uniform thickness the order parameter is uniform, but even infinitesimal deviations from uniform thickness give rise to a mixed state which avoids enclosing the magnetic field. The stability domain of this mixed state is a line segment in the magnetic field-temperature plane, delimited by two critical points. The phase diagram contains several bifurcation lines, which are systematically analyzed.

Noise rectification by a superconducting loop with two weak links

We consider a superconducting loop with two weak links that encloses a magnetic flux. The weak links are unequal and are treated as Josephson junctions with non-sinusoidal phase dependence. We devise a model that takes into account the fluctuation of the critical currents, due to the fluctuations of the order parameter in the weak links. These fluctuations are important near the onset of superconductivity; in this regime they may significantly weaken and eventually disconnect the superconducting loop. As a consequence of these fluctuations and of the resistive noise in the junctions, the average dc voltage does not vanish. Our model can be easily extended to provide a qualitative description of a recent experiment.

Flux-induced vortex in mesoscopic superconducting loops

We predict the existence of a quantum vortex for an unusual situation. We study the order parameter in doubly connected superconducting samples embedded in a uniform magnetic field. For samples with perfect cylindrical symmetry, the order parameter has been known for a long time and no vortices are present in the linear regime. However, if the sample is not symmetric, there exist ranges of the field for which the order parameter vanishes along a line, parallel to the field. In many respects, the behavior of this line is qualitatively different from that of the vortices encountered in type-II superconductivity. For samples with mirror symmetry, this flux-induced vortex appears at the thin side for small fluxes and at the opposite side for large fluxes. We propose direct and indirect experimental methods which could test our predictions.

Personal computer as an inexpensive lock‐in analyzer operating at very low frequencies

We describe inexpensive equipment and present a simple basic program which permits one to utilize a personal computer as a lock‐in analyzer for frequencies below ∼0.1 Hz.

The influence of thermal fluctuations on uniform and nonuniform superconducting rings according to the Ginzburg-Landau and the Kramer-Watts-Tobin models.

We evaluate the influence of thermal fluctuations on superconducting rings that enclose a magnetic flux, using the time-dependent Ginzburg-Landau model (TDGL) or the Kramer-Watts-Tobin model (KWT), while thermal fluctuations are accounted for by means of Langevin terms. This method is applicable in situations where previous methods are not, such as for nonuniform loops, rings with large width to radius ratio and loops with large coherence length to perimeter ratio. We evaluate persistent currents, the position and statistical behavior of flux-induced vortices, and the lifetime of metastable fluxoid states. The influence of nonuniformity on the persistent current does not depend strongly on the details of the cross section profile; it depends mainly on its first harmonic, but not only on it. As a consequence of nonuniformity the maximum of the persistent current shifts to smaller fluxes and the passage between fluxoid states remains non-hysteretic down to lower temperatures than in the case of a uniform sample. Our results obtained using TDGL agree remarkably well with recent measurements of the persistent current in superconducting rings and with measurements of the position of a vortex that mediates between fluxoid states in an asymmetric disc with a hole; they could also provide a plausible explanation for the unexpectedly short measured lifetimes of metastable states. Comparison of TDGL and KWT indicates that they lead to the same results for the persistent current, whereas KWT leads to larger lifetimes than TDGL.

Piezoelectricity: Quantized Charge Transport Driven by Adiabatic Deformations

We study the (zero temperature) quantum piezoelectric response of Harper-like models with broken inversion symmetry. The charge transport in these models is related to topological invariants (Chern numbers). We show that there are arbitrarily small periodic modulations of the atomic positions that lead to nonzero charge transport. [S0031-9007(96)02168-0] PACS numbers: 72.10.Bg, 77.65. ‐ j The Harper model is a tight-binding quantum Hamiltonian describing the dynamics of noninteracting electrons on a two-dimensional lattice in the presence of magnetic fields. It is known to have interesting Hall transport properties. Here we study the electric response of Harper-like models to adiabatic changes in the hopping amplitudes. Changes in the hopping amplitudes have a natural interpretation as elastic deformation of the underlying lattice. The Harper model is piezoelectric if such deformations drive electron transport. Let us first summarize the central findings: (1) Harperlike models with broken time reversal and broken inversion symmetry have, in general, nontrivial piezoelectric response. (2) Appropriate periodic modulations of the atomic positions give nontrivial integral charge transport given by Chern integers. This implies that an ac driving has a response with a dc component. (3) There are arbitrarily small periodic deformations that transport integral (and nonzero) charges over macroscopic distances. These periodic cycles trap level crossings in parameter space. These results are new for Harper-like models. One may, however, ask in what way they add to the theory of piezoelectricity from a general perspective. It is an observation of King-Smith and Vanderbilt [1] that piezoelectricity is related to the adiabatic curvature and Berry’s phase [2]. More precisely, it is related to the difference of Zak’s phases of band functions [3]. This puts piezoelectricity in one basket with the Hall conductance [4,5] and a collection of other transport phenomena [6‐12], all of which have quantum mechanical geometric significance. The most impressive applications of the theory of KingSmith and Vanderbilt have been the calculations of the piezoelectric coefficients of certain materials [1,13]. On the other hand, the results of this theory concerning the Chern numbers associated to piezoelectricity were rather weak. The only examples known were those associated with the translation of the entire crystal which are in a sense trivial. The Harper model illustrates how knowledge about degeneracies and level crossings translates to a choice of interesting periodic deformations and interesting Chern numbers. We shall focus on a family of Harper models, Hs

Szilard's demon revisited

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