Transmission Resonance in an Infinite Strip of Phason-Defects of a Penrose Approximant Network

An exact method that analytically provides transfer matrices in finite networks of quasicrystalline approximants of any dimensionality is discussed. We use these matrices in two ways: a) to exactly determine the band structure of an infinite approximant network in analytical form; b) to determine, also analytically, the quantum resistance of a finite strip of a network under appropriate boundary conditions. As a result of a subtle interplay between topology and phase interferences, we find that a strip of phason-defects along a special symmetry direction of a low 2-d Penrose approximant, leads to the rigorous vanishing of the reflection coefficient for certain energies. A similar behavior appears in a low 3-d approximant. This type of ``resonance" is discussed in connection with the gap structure of the corresponding ordered (undefected) system.Comment: 18 pages special macros jnl.tex,reforder.tex, eqnorder.te

Strong Enhancement of Superconducting Correlation in a Two-Component Fermion Gas

We study high-density electron-hole (e-h) systems with the electron density slightly larger than the hole density. We find a new superconducting phase, in which the excess electrons form Cooper pairs moving in an e-h BCS phase. The coexistence of the e-h and e-e orders is possible because e and h have opposite charges, whereas analogous phases are impossible in the case of two fermion species that have the same charge or are neutral. Most strikingly, the e-h order enhances the superconducting e-h order parameter by more than one order of magnitude as compared with that given by the BCS formula, for the same value of the effective e-e attractive potential \lambda^{ee}. This new phase should be observable in an e-h system created by photoexcitation in doped semiconductors at low temperatures.Comment: 5 pages including 5 PostScript figure

Wigner Crystallization of a two dimensional electron gas in a magnetic field: single electrons versus electron pairs at the lattice sites

The ground state energy and the lowest excitations of a two dimensional Wigner crystal in a perpendicular magnetic field with one and two electrons per cell is investigated. In case of two electrons per lattice site, the interaction of the electrons {\em within} each cell is taken into account exactly (including exchange and correlation effects), and the interaction {\em between} the cells is in second order (dipole) van der Waals approximation. No further approximations are made, in particular Landau level mixing and {\em in}complete spin polarization are accounted for. Therefore, our calculation comprises a, roughly speaking, complementary description of the bubble phase (in the special case of one and two electrons per bubble), which was proposed by Koulakov, Fogler and Shklovskii on the basis of a Hartree Fock calculation. The phase diagram shows that in GaAs the paired phase is energetically more favorable than the single electron phase for, roughly speaking, filling factor $f$ larger than 0.3 and density parameter $r_s$ smaller than 19 effective Bohr radii (for a more precise statement see Fig.s 4 and 5). If we start within the paired phase and increase magnetic field or decrease density, the pairs first undergo some singlet- triplet transitions before they break.Comment: 11 pages, 7 figure