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.PACS numbers: 74.60. Ec; 74.55.+h; 74.20.De Symmetrically-confined vortex matter in superconductors, superfluids and Bose-Einstein condensates offers unique possibilities to study the interplay between the C ∞ symmetry of the magnetic field and the discrete symmetry of the boundary conditions. More specifically, superconductivity in mesoscopic equilateral triangles, squares etc. in the presence of a magnetic field nucleates by conserving the imposed symmetry (C 3 , C 4 ) of the boundary conditions [1] and the applied vorticity. As a result, in an equilateral triangle, for example, in an applied magnetic field H generating two flux quanta, 2Φ 0 , superconductivity appears as the C 3 -symmetric combination 3Φ 0 − Φ 0 (further on denoted as "3 − 1") of three vortices and one antivortex in the center. These symmetry-induced antivortices can be important not only for superconductors but also for symmetrically confined superfluids and Bose-Einstein condensates. Since the order parameter patterns reported in Refs. [1] have been obtained in the framework of the linearized Ginzburg-Landau (GL) theory, this approach is valid only close to the nucleation line T c (H). Can then these novel symmetry-induced vortex-antivortex patterns survive deep in the superconducting state? Several attempts have been already made to answer this crucial question. In the limit of an extreme type II superconductor (κ ≫ 1), it has been shown that for a thin-film square, a configuration of one antivortex in the center and four vortices on the diagonals of the square is unstable away from the phase boundary [2]. According to the analysis based on the coupled nonlinear GL equations, the vortex-antivortex pairs are unstable and no antivortices appear spontaneously at the T, H points far away from the T c (H) line [3]. Possible scenarios of penetration of a vortex into a mesoscopic superconducting triangle with increasing magnetic field have been studied in Ref. [4]. Two different states were considered: a single vortex state and a state in the form of a symmetric combination of three vortices and an antivortex with vorticity L av = −2 ("3 − 2" combination). The calculations [4] have shown that while a single vortex enters the triangle through a midpoint of one side, the "3 − 2" combination turns out to be energetically favorable when the vortices are close to the center of the triangle. Equilibrium is achieved when a single vortex is in the center of the triangle. When approaching the phase boundary, the free energy of a single-vortex state tends to coincide with the free energy of the "3 − 2" combination [4], thus confirming conclusions [1,2] that formation ...
The Richardson exact solution for the reduced BCS Hamiltonian is applied to examine how sensitive are the pairing characteristics (condensation energy, spectroscopic gap, parity gap) to a specific configuration of single-electron energy levels in nanosize metallic grains. Using single-electron energy spectra in parallelepiped-shaped potential boxes with various volumes and aspect ratios as a model of energy levels in grains, we show that this sensitivity is extremely high. Just due to such an extreme sensitivity, the detailed shape of grains cannot be detected through the pairing characteristics, averaged over an ensemble of grains, even in the case of relatively small size dispersion within this ensemble. We analyse the effect of the pairing interaction on the excited-level spacings in superconducting grains and comment on the influence of shape-dependent fluctuations in single-electron energy spectra on the possibility to reveal this effect through tunnelling measurements.
A theory of polar optical vibrations in multilayer semiconductor structures is developed taking into account phonon dispersion. A method of diagonalization of the equations of motion for inertial polarization vectors in the finite basis is used, that is founded on a finite number of degrees of freedom of the system. The Hamiltonian of the electron--phonon interaction is deduced. The dispersion law and the spatial dependence of the obtained eigenmodes are in good agreement with experimental data and microscopic models. It is shown that the electron scattering rate in a magnetic field depends on the chosen model of polar optical vibrations.
on the occasion of his 80th birthday A theory of the potential due to the slow polarization field is developed for multi-layer systems with an arbitrary number of layers. The general expression of the potential is specialized for threelayer and periodic systems. As result of diagonalization of the energy of the polarization vibration field, the bulk and surface vibrations are separated and the spectrum of their eigenfrequencies is determined both, for systems with a finite number of layers (inparticular, for a layer of a heteropolar semiconductor between a substrate of an ionic crystal and a homopolar dielectric medium) and for periodic systems. Finally, the exact electron-phonon interaction Hamiltonian for multilayer systems is obtained in the second quantization representation. Pa3BHTa TeOpHR IlOTeHUHaJIa, 06yCJIOBJIeHHOrO nOJIeM HHepUHOHHO~ IlOJIHpH3aqMH, B MHOrOCJIOfiHbIX CHCTeMaX C IlpOH3BOJIbHbIM g H C J I O M CJIOeB. 0 6 u e e BbIpameHHe AJIH nOTeHlJHaJIa HOHKPeTH311POBaHO AJIR TpeXCJIO@HbIX H IIepHOAHqeCKHX CHCTeM. B pe3YJIb-HbIe H IlOBePXHOCTHbIe KOJIe6aHHH H OIlpeAeJIeH CIIeHTp HX CO6CTBeHHbIX saCTOT H a K EJWl CHCTeM C KOHegHbIM gHCJIOM CJIOeB (B YaCTHOCTH, AJIH CJIOH reTepOIIOJIHpHOr0 IIOJIy-IlpOBOAHHHa MeHcAy ~O~J I O ? K l~O~ 113 HOHHOrO HpHCTaJIJIa H I' OMeOIlOJlHpHOi% n113JIeKTpH-seCHOii CpeAOii), TaH H AJIR IIepHOAHYeCKHX CHCTeM. HaHoHeq, IlOJIyqeH TOYHbIB FaMHJIb-TOHHaH-3JIeKTPOH-#OHOHHOrO B3aHMOJ(efiCTBHR AJIH MHOrOCJIOfiHbIX CHCTeM B IIpen-CTaBJIeHHH BTOPHsHOrO KBaHTOBaHHH.TaTe ~n a r o~a n a a a q a~ 3~ep1-m n o n~ ~O J I H~H~~~H O H H~I X HOJIe6aHHii pa3~ene~b1 o6-be~-
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