Recent progress in nanotechnology has stimulated interest in mesoscopic superconductors as components for quantum computing and cryoelectronics. The critical parameters for superconductivity (current and field) of a mesoscopic sample are determined by the pattern of vortices in it, which in turn is controlled by the symmetry imposed by the shape of the sample (see ref. 1 and references therein). Hitherto it has been unclear what happens when the number of vortices is not consistent with the natural symmetry. Here we show that additional vortex–antivortex pairs nucleate spontaneously so as to preserve the symmetry of the sample. For example, in a square with three vortices, the spontaneously generated pair, along with the original three vortices, distribute themselves so that the four vortices sit in the four corners, with the antivortex in the centre. The measured superconducting phase boundary (of superconducting transition temperature Tc versus magnetic field strength) is in very good agreement with the calculations, giving direct experimental evidence for these symmetry-induced vortex–antivortex pairs. Vortex entry into the sample is also changed: vortices enter a square in fours, with antivortices generated to preserve the imposed vorticity. The symmetry-induced nucleation of antivortices is not restricted to superconductors, but should also apply to symmetrically confined superfluids and Bose–Einstein condensates.

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Symmetry-induced formation of antivortices in mesoscopic superconductors.

The stability of cationic gold clusters doped with one transition metal atom was investigated by a mass spectrometric analysis of fragments resulting from high fluence irradiation of a cluster beam. Strongly enhanced abundances are found for Au5X+, X = V, Mn, Cr, Fe, Co, Zn, which implies that these species are far more stable towards fragmentation than their neighbouring cluster sizes. Here we interpret the enhanced stability of these clusters within a shell model approach for two-dimensional (2D) systems: the number of delocalized electrons in Au5X+ is six, which is a magic number for 2D systems. Quantum chemical calculations for AuNZn+ (N = 2-6) predict planar structures that are stabilized by the influence of the dopant atom. Also, the main features of the calculated molecular orbitals are well reproduced by a simple electron-in-a-box model. The present report constitutes the first observation of 2D magic numbers in size dependent properties of metal clusters.

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Two-dimensional magic numbers in mass abundances of photofragmented bimetallic clusters

Two unique silver nanoclusters protected by alkynyl and diphosphine ligands have been synthesized Single crystal structural determination reveals that they have a centered anticuboctahedral Ag13 kernel Such a kernel is observed for the first time in a coinage metal nanocluster This work offers new insights into the fact that the PhCC ligand represents a new direction in synthesizing novel metal nanoclusters

Alkynyl-protected silver nanoclusters featuring an anticuboctahedral kernel

Donor impurity states and related optical responses in triangular quantum dots under applied electric field

The linear and nonlinear coefficients for the optical absorption and relative refractive index change associated with intersubband transitions of electrons in the conduction band of a two-dimensional quantum dot of triangular shape are calculated for x -polarization and y -polarization of the incident light. Both the effective mass and parabolic band approximations have been considered. The results show that the increase in the size of the triangular quantum dot leads to the expected fall of the intersubband energy transition and that there is an increment in the values of the associated off-diagonal electric dipole moment matrix elements. All this reflects in the increase of the amplitude of the nonlinear optical absorption resonant peak, as well as in the growth of the total relative refractive index in the system.

Electron-related optical responses in triangular quantum dots

The complete solution for the quantum‐mechanical problem of a particle in an equilateral triangle is derived. By use of projection operators, eigenfunctions belonging explicitly to each of the irreducible representations of the symmetry group C3V are constructed. The most natural definition of the quantum numbers p and q includes not only integers but also nonintegers of the class (1)/(3) and (2)/(3) modulo 1. Some relevant features relating to symmetry and degeneracy are also discussed.

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S. M. Blinder

Papers

Solution of the Schrödinger equation for a particle in an equilateral triangle