Energy spectrum for two-dimensional potentials in very high magnetic fields

A method, analogous to supersymmetry transformation in quantum mechanics, is developed for a particle in the lowest Landau level moving in an arbitrary potential. The method is applied to two-dimensional potentials formed by Dirac delta scattering centers. In the periodic case, the problem is solved exactly for rational values of the magnetic flux (in units of flux quantum) per unit cell. The spectrum is found to be self-similar, resembling the Hofstadter butterfly.Comment: 9 pages, 3 figures, REVTEX, to appear in Phys. Rev. B, Sep. 1

Suppression of superconductivity in high-TcT_c cuprates due to nonmagnetic impurities: Implications for the order parameter symmetry

We studied the effects of nonmagnetic impurities on high-temperature superconductors by solving the Bogoliubov-de Gennes equations on a two-dimensional lattice via exact diagonalization technique in a fully self-consistent way. We found that s-wave order parameter is almost unaffected by impurities at low concentrations while $d_{x^2-y^2}$-wave order parameter exhibits a strong linear decrease with impurity concentration. We evaluated the critical impurity concentration $n_i^c$ at which superconductivity ceases to be 0.1 which is in good agreement with experimental values. We also investigated how the orthorhombic nature of the crystal structure affects the suppression of superconductivity and found that anisotropy induces an additional s-wave component. Our results support $d_{x^2-y^2}$-wave symmetry for tetragonal and $s+d_{x^2-y^2}$-wave symmetry for orthorhombic structure.Comment: LaTeX, 5 pages, 4 figures, uses grafik.sty (included

Entanglement of hard-core bose gas in degenerate levels under local noise

Quantum entanglement properties of the pseudo-spin representation of the BCS model is investigated. In case of degenerate energy levels, where wave functions take a particularly simple form, spontaneous breaking of exchange symmetry under local noise is studied. Even if the Hamiltonian has the same symmetry, it is shown that there is a non-zero probability to end up with a non-symmetric final state. For small systems, total probability for symmetry breaking is found to be inversely proportional to the system size

Disorder and localization in the lowest Landau level in the presence of dilute point scatterers

Cataloged from PDF version of article.We study the localization properties of a two-dimensional noninteracting electron gas in the presence of randomly distributed short-range scatterers in very high magnetic fields. We evaluate the participation number of the eigenstates obtained by exact diagonalization technique. At low impurity concentrations we obtain self-averaged values showing that all states, except those exactly at the Landau level, are localized with finite localization length. We conclude that in this dilute regime the localization length does not diverge. We also find that the maximum localization length increases exponentially with impurity concentration. Our calculations suggest that scaling behavior may be absent even for higher concentrations of scatterers. (C) 1999 Elsevier Science Ltd. All rights reserved

Metal nanoring and tube formation on carbon nanotubes

The structural and electronic properties of aluminum covered single wall carbon nanotubes (SWNT) are studied from first-principles for a large number of coverage. Aluminum-aluminum interaction that is stronger than aluminum-tube interaction, prevents uniform metal coverage, and hence gives rise to the clustering. However, a stable aluminum ring and aluminum nanotube with well defined patterns can also form around the semiconducting SWNT and lead to metallization. The persistent current in the Al nanoring is discussed to show that a high magnetic field can be induced at the center of SWNT.Comment: Submitted to Physical Review

Decoherence induced spontaneous symmetry breaking

We study time dependence of exchange symmetry properties of Bell states when two qubits interact with local baths having identical parameters. In case of classical noise, we consider a decoherence Hamiltonian which is invariant under swapping the first and second qubits. We find that as the system evolves in time, two of the three symmetric Bell states preserve their qubit exchange symmetry with unit probability, whereas the symmetry of the remaining state survives with a maximum probability of 0.5 at the asymptotic limit. Next, we examine the exchange symmetry properties of the same states under local, quantum mechanical noise which is modeled by two identical spin baths. Results turn out to be very similar to the classical case. We identify decoherence as the main mechanism leading to breaking of qubit exchange symmetry.Comment: 12 page