Lower Bound for the Fermi Level Density of States of a Disordered D-Wave Superconductor in Two Dimensions

We consider a disordered d--wave superconductor in two dimensions. Recently, we have shown in an exact calculation that for a lattice model with a Lorentzian distributed random chemical potential the quasiparticle density of states at the Fermi level is nonzero. As the exact result holds only for the special choice of the Lorentzian, we employ different methods to show that for a large class of distributions, including the Gaussian distribution, one can establish a nonzero lower bound for the Fermi level density of states. The fact that the tails of the distributions are unimportant in deriving the lower bound shows that the exact result obtained before is generic.Comment: 15 preprint pages, no figures, submitted to PR

High-Quality Planar high-Tc Josephson Junctions

Reproducible high-Tc Josephson junctions have been made in a rather simple two-step process using ion irradiation. A microbridge (1 to 5 ?m wide) is firstly designed by ion irradiating a c-axis-oriented YBa2Cu3O7-? film through a gold mask such as the non-protected part becomes insulating. A lower Tc part is then defined within the bridge by irradiating with a much lower fluence through a narrow slit (20 nm) opened in a standard electronic photoresist. These planar junctions, whose settings can be finely tuned, exhibit reproducible and nearly ideal Josephson characteristics. This process can be used to produce complex Josephson circuits.Comment: 4 pages, 5 figures, to be published in Applied Physics Letter

Quantum phases in mixtures of fermionic atoms

A mixture of spin-polarized light and heavy fermionic atoms on a finite size 2D optical lattice is considered at various temperatures and values of the coupling between the two atomic species. In the case, where the heavy atoms are immobile in comparison to the light atoms, this system can be seen as a correlated binary alloy related to the Falicov-Kimball model. The heavy atoms represent a scattering environment for the light atoms. The distributions of the binary alloy are discussed in terms of strong- and weak-coupling expansions. We further present numerical results for the intermediate interaction regime and for the density of states of the light particles. The numerical approach is based on a combination of a Monte-Carlo simulation and an exact diagonalization method. We find that the scattering by the correlated heavy atoms can open a gap in the spectrum of the light atoms, either for strong interaction or small temperatures.Comment: 15 pages, 8 figure

Density of states "width parity" effect in d-wave superconducting quantum wires

We calculate the density of states (DOS) in a clean mesoscopic d-wave superconducting quantum wire, i.e. a sample of infinite length but finite width $N$. For open boundary conditions, the DOS at zero energy is found to be zero if $N$ is even, and nonzero if $N$ is odd. At finite chemical potential, all chains are gapped but the qualtitative differences between even and odd $N$ remain.Comment: 7 pages, 8 figures, new figures and extended discussio

Correlations in Systems of Complex Directed Macromolecules

An ensemble of directed macromolecules on a lattice is considered, where the constituting molecules are chosen as a random sequence of N different types. The same type of molecules experiences a hard-core (exclusion) interaction. We study the robustness of the macromolecules with respect to breaking and substituting individual molecules, using a 1/N expansion. The properties depend strongly on the density of macromolecules. In particular, the macromolecules are robust against breaking and substituting at high densities.Comment: 9 pages, 4 figure

On the fundamental group of the complement of a complex hyperplane arrangement

We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the complement to a line arrangement of a given combinatorial type with respect to isomorphisms inducing the canonical isomorphism of the first homology groups.Comment: 12 pages, Latex2e with AMSLaTeX 1.2, no figures; this last version is almost the same as published in Functional Analysis and its Applications 45:2 (2011), 137-14