Stable vortex-antivortex molecules in mesoscopic superconducting triangles

A thermodynamically stable vortex-antivortex pattern has been revealed in mesoscopic type I superconducting triangles, contrary to type II superconductors where similar patterns are unstable. The stable vortex-antivortex "molecule" appears due to the interplay between two factors: a repulsive vortex-antivortex interaction in type I superconductors and the vortex confinement in the triangle.Comment: 5 pages, 4 figures, E-mail addresses: [email protected], [email protected], [email protected], [email protected]

Magnetic susceptibility of ultra-small superconductor grains

For assemblies of superconductor nanograins, the magnetic response is analyzed as a function of both temperature and magnetic field. In order to describe the interaction energy of electron pairs for a huge number of many-particle states, involved in calculations, we develop a simple approximation, based on the Richardson solution for the reduced BCS Hamiltonian and applicable over a wide range of the grain sizes and interaction strengths at arbitrary distributions of single-electron energy levels in a grain. Our study is focused upon ultra-small grains, where both the mean value of the nearest-neighbor spacing of single-electron energy levels in a grain and variations of this spacing from grain to grain significantly exceed the superconducting gap in bulk samples of the same material. For these ultra-small superconductor grains, the overall profiles of the magnetic susceptibility as a function of magnetic field and temperature are demonstrated to be qualitatively different from those for normal grains. We show that the analyzed signatures of pairing correlations are sufficiently stable with respect to variations of the average value of the grain size and its dispersion over an assembly of nanograins. The presence of these signatures does not depend on a particular choice of statistics, obeyed by single-electron energy levels in grains.Comment: 40 pages, 12 figures, submitted to Phys. Rev. B, E-mail addresses: [email protected], [email protected], [email protected]

Superconductivity in a Mesoscopic Double Square Loop: Effect of Imperfections

We have generalized the network approach to include the effects of short-range imperfections in order to analyze recent experiments on mesoscopic superconducting double loops. The presence of weakly scattering imperfections causes gaps in the phase boundary $B(T)$ or $\Phi(T)$ for certain intervals of $T$, which depend on the magnetic flux penetrating each loop. This is accompanied by a critical temperature $T_c(\Phi)$, showing a smooth transition between symmetric and antisymmetric states. When the scattering strength of imperfections increases beyond a certain limit, gaps in the phase boundary $T_c(B)$ or $T_c(\Phi)$ appear for values of magnetic flux lying in intervals around half-integer $\Phi_0=hc/2e$. The critical temperature corresponding to these values of magnetic flux is determined mainly by imperfections in the central branch. The calculated phase boundary is in good agreement with experiment.Comment: 9 pages, 6 figure

Polynomial kernelization for removing induced claws and diamonds

A graph is called (claw,diamond)-free if it contains neither a claw (a $K_{1,3}$) nor a diamond (a $K_4$ with an edge removed) as an induced subgraph. Equivalently, (claw,diamond)-free graphs can be characterized as line graphs of triangle-free graphs, or as linear dominoes, i.e., graphs in which every vertex is in at most two maximal cliques and every edge is in exactly one maximal clique. In this paper we consider the parameterized complexity of the (claw,diamond)-free Edge Deletion problem, where given a graph $G$ and a parameter $k$, the question is whether one can remove at most $k$ edges from $G$ to obtain a (claw,diamond)-free graph. Our main result is that this problem admits a polynomial kernel. We complement this finding by proving that, even on instances with maximum degree $6$, the problem is NP-complete and cannot be solved in time $2^{o(k)}\cdot |V(G)|^{O(1)}$ unless the Exponential Time Hypothesis fai

Short-Distance Structure of Nuclei

One of Jefferson Lab's original missions was to further our understanding of the short-distance structure of nuclei. In particular, to understand what happens when two or more nucleons within a nucleus have strongly overlapping wave-functions; a phenomena commonly referred to as short-range correlations. Herein, we review the results of the (e,e'), (e,e'p) and (e,e'pN) reactions that have been used at Jefferson Lab to probe this short-distance structure as well as provide an outlook for future experiments.Comment: 16 pages, 8 figures, for publication in Journal of Physics

Categorification of skew-symmetrizable cluster algebras

We propose a new framework for categorifying skew-symmetrizable cluster algebras. Starting from an exact stably 2-Calabi-Yau category C endowed with the action of a finite group G, we construct a G-equivariant mutation on the set of maximal rigid G-invariant objects of C. Using an appropriate cluster character, we can then attach to these data an explicit skew-symmetrizable cluster algebra. As an application we prove the linear independence of the cluster monomials in this setting. Finally, we illustrate our construction with examples associated with partial flag varieties and unipotent subgroups of Kac-Moody groups, generalizing to the non simply-laced case several results of Gei\ss-Leclerc-Schr\"oer.Comment: 64 page

Phonons and thermal transport in Si/SiO2_2 multishell nanotubes: Atomistic study

Thermal transport in the Si/SiO$_2$ multishell nanotubes is investigated theoretically. The phonon energy spectra are obtained using the atomistic Lattice Dynamics approach. Thermal conductivity is calculated using the Boltzmann transport equation within the relaxation time approximation. Redistribution of the vibrational spectra in multishell nanotubes leads to a decrease of the phonon group velocity and the thermal conductivity as compared to homogeneous Si nanowires. Phonon scattering on the Si/SiO$_2$ interfaces is another key factor of strong reduction of the thermal conductivity in these structures (down to 0.2 W/mK at room temperature). We demonstrate that phonon thermal transport in Si/SiO$_2$ nanotubes can be efficiently suppressed by a proper choice of nanotube's geometrical parameters: lateral cross-section, thickness and number of shells.Comment: 14 pages, 4 figure