Conductance of Atomic-Sized Lead Contacts in an Electrochemical Environment

Atomic-sized lead (Pb) contacts are deposited and dissolved in an electrochemical environment, and their transport properties are measured. Due to the electrochemical fabrication process, we obtain mechanically unstrained contacts and conductance histograms with sharply resolved, individual peaks. Charge transport calculations based on density functional theory (DFT) for various ideal Pb contact geometries are in good agreement with the experimental results. Depending on the atomic configuration, single-atom-wide contacts of one and the same metal yield very different conductance values.Comment: 5 pages, 4 figure

On the Green's Function of the almost-Mathieu Operator

The square tight-binding model in a magnetic field leads to the almost-Mathieu operator which, for rational fields, reduces to a $q\times q$ matrix depending on the components $\mu$, $\nu$ of the wave vector in the magnetic Brillouinzone. We calculate the corresponding Green's function without explicit knowledge of eigenvalues and eigenfunctions and obtain analytical expressions for the diagonal and the first off-diagonal elements; the results which are consistent with the zero magnetic field case can be used to calculate several quantities of physical interest (e. g. the density of states over the entire spectrum, impurity levels in a magnetic field).Comment: 9 pages, 3 figures corrected some minor errors and typo

Pre-selectable integer quantum conductance of electrochemically fabricated silver point contacts

The controlled fabrication of well-ordered atomic-scale metallic contacts is of great interest: it is expected that the experimentally observed high percentage of point contacts with a conductance at non-integer multiples of the conductance quantum G_0 = 2e^2/h in simple metals is correlated to defects resulting from the fabrication process. Here we demonstrate a combined electrochemical deposition and annealing method which allows the controlled fabrication of point contacts with pre-selectable integer quantum conductance. The resulting conductance measurements on silver point contacts are compared with tight-binding-like conductance calculations of modeled idealized junction geometries between two silver crystals with a predefined number of contact atoms

Supersymmetric Extension of the Quantum Spherical Model

In this work, we present a supersymmetric extension of the quantum spherical model, both in components and also in the superspace formalisms. We find the solution for short/long range interactions through the imaginary time formalism path integral approach. The existence of critical points (classical and quantum) is analyzed and the corresponding critical dimensions are determined.Comment: 21 pages, fixed notation to match published versio

Dynamic instability in resonant tunneling

We show that an instability may be present in resonant tunneling through a quantum well in one, two and three dimensions, when the resonance lies near the emitter Fermi level. A simple semiclassical model which simulates the resonance and the projected density of states by a nonlinear conductor, the Coulomb barrier by a capacitance, and the time evolution by an iterated map, is used. The model reproduces the observed hysteresis in such devices, and exhibits a series of bifurcations leading to fast chaotic current fluctuations.Comment: 7 pages, 2 figure

Dirac-Foldy term and the electromagnetic polarizability of the neutron

We reconsider the Dirac-Foldy contribution $\mu^2/m$ to the neutron electric polarizability. Using a Dirac equation approach to neutron-nucleus scattering, we review the definitions of Compton continuum ($\bar{\alpha}$), classical static ($\alpha^n_E$), and Schr\"{o}dinger ($\alpha_{Sch}$) polarizabilities and discuss in some detail their relationship. The latter $\alpha_{Sch}$ is the value of the neutron electric polarizability as obtained from an analysis using the Schr\"{o}dinger equation. We find in particular $\alpha_{Sch} = \bar{\alpha} - \mu^2/m$ , where $\mu$ is the magnitude of the magnetic moment of a neutron of mass $m$. However, we argue that the static polarizability $\alpha^n_E$ is correctly defined in the rest frame of the particle, leading to the conclusion that twice the Dirac-Foldy contribution should be added to $\alpha_{Sch}$ to obtain the static polarizability $\alpha^n_E$.Comment: 11 pages, RevTeX, to appear in Physical Review

One-dimensional fermions with incommensuration

We study the spectrum of fermions hopping on a chain with a weak incommensuration close to dimerization; both q, the deviation of the wave number from pi, and delta, the strength of the incommensuration, are small. For free fermions, we use a continuum Dirac theory to show that there are an infinite number of bands which meet at zero energy as q approaches zero. In the limit that the ratio q/ \delta --> 0, the number of states lying inside the q=0 gap is nonzero and equal to 2 \delta /\pi^2. Thus the limit q --> 0 differs from q=0; this can be seen clearly in the behavior of the specific heat at low temperature. For interacting fermions or the XXZ spin-1/2 chain close to dimerization, we use bosonization to argue that similar results hold; as q --> 0, we find a nontrivial density of states near zero energy. However, the limit q --> 0 and q=0 give the same results near commensurate wave numbers which are different from pi. We apply our results to the Azbel-Hofstadter problem of electrons hopping on a two-dimensional lattice in the presence of a magnetic field. Finally, we discuss the complete energy spectrum of noninteracting fermions with incommensurate hopping by going up to higher orders in delta.Comment: Revtex, 23 pages including 7 epsf figures; this is a greatly expanded version of cond-mat/981133

Vascular grading of angiogenesis: prognostic significance in breast cancer

The study aimed to evaluate the prognostic value of angiogenesis by vascular grading of primary breast tumours, and to evaluate the prognostic impact of adding the vascular grade to the Nottingham Prognostic Index (NPI). The investigation included 836 patients. The median follow-up time was 11 years and 4 months. The microvessels were immunohistochemically stained by antibodies against CD34. Angiogenesis was graded semiquantitatively by subjective scoring into three groups according to the expected number of microvessels in the most vascular tumour area. The vascular grading between observers was moderately reproduced (κ = 0.59). Vascular grade was significantly associated with axillary node involvement, tumour size, malignancy grade, oestrogen receptor status and histological type. In univariate analyses vascular grade significantly predicted recurrence free survival and overall survival for all patients (P< 0.0001), node-negative patients (P< 0.0001) and node-positive patients (P< 0.0001). Cox multivariate regression analysis showed that vascular grading contributed with independent prognostic value in all patients (P< 0.0001). A prognostic index including the vascular grade had clinical impact for 24% of the patients, who had a shift in prognostic group, as compared to NPI, and implied a better prognostic dissemination. We concluded that the angiogenesis determined by vascular grading has independent prognostic value of clinical relevance for patients with breast cancer. © 2000 Cancer Research Campaig