Landau levels in the case of two degenerate coupled bands: kagome lattice tight-binding spectrum

The spectrum of charged particles hopping on a kagome lattice in a uniform transverse magnetic field shows an unusual set of Landau levels at low field. They are unusual in two respects: the lowest Landau levels are paramagnetic so their energies decrease linearly with increasing field magnitude, and the spacings between the levels are not equal. These features are shown to follow from the degeneracy of the energy bands in zero magnetic field. We give a general discussion of Landau levels in the case of two degenerate bands, and show how the kagome lattice tight-binding model includes one special case of this more general problem. We also discuss the consequences of this for the behavior of the critical temperature of a kagome grid superconducting wire network, which is the experimental system that originally motivated this work.Comment: 18 pages, 8 figure

Spin-Valve Effect of the Spin Accumulation Resistance in a Double Ferromagnet - Superconductor Junction

We have measured the transport properties of Ferromagnet - Superconductor nanostructures, where two superconducting aluminum (Al) electrodes are connected through two ferromagnetic iron (Fe) ellipsoids in parallel. We find that, below the superconducting critical temperature of Al, the resistance depends on the relative alignment of the ferromagnets' magnetization. This spin-valve effect is analyzed in terms of spin accumulation in the superconducting electrode submitted to inverse proximity effect

Coherent low-energy charge transport in a diffusive S-N-S junction

We have studied the current voltage characteristics of diffusive mesoscopic Nb-Cu-Nb Josephson junctions with highly-transparent Nb-Cu interfaces. We consider the low-voltage and high-temperature regime eV<\epsilon_{c}<k_{B}T where epsilon_{c} is the Thouless energy. The observed excess current as well as the observed sub-harmonic Shapiro steps under microwave irradiation suggest the occurrence of low-energy coherent Multiple Andreev Reflection (MAR).Comment: 4 pages, 4 figures, final versio

Re-entrance of the metallic conductance in a mesoscopic proximity superconductor

We present an experimental study of the diffusive transport in a normal metal near a superconducting interface, showing the re-entrance of the metallic conductance at very low temperature. This new mesoscopic regime comes in when the thermal coherence length of the electron pairs exceeds the sample size. This re-entrance is suppressed by a bias voltage given by the Thouless energy and can be strongly enhanced by an Aharonov Bohm flux. Experimental results are well described by the linearized quasiclassical theory.Comment: improved version submitted to Phys. Rev. lett., 4 pages, 5 included epsf figure

Resistive transport in a mesoscopic proximity superconductor

We review transport measurements in a normal metal (N) in contact with one or two superconducting (S) islands. From the experiment, we distinguish the Josephson coupling, the mesoscopic fluctuations and the proximity effect. In a loop-shaped N conductor, we observe large h/2e-periodic magnetoresistance oscillations that decay with temperature T with a 1/T power-law. This behaviour is the signature of the long-range coherence of the low-energy electron pairs induced by the Andreev reflection at the S interface. At temperature and voltage below the Thouless energy $\hbar D / L^2$, we observe the re-entrance of the metallic resistance. Experimental results agree with the linearized quasiclassical theory.Comment: 8 pages, 6 included epsf figures, Invited paper at the LT21 Conference, Praha, August 1996. To appear in Czech. J. of Phys. 46, Part S6 (1996

Hofstadter butterfly and integer quantum Hall effect in three dimensions

For a three-dimensional lattice in magnetic fields we have shown that the hopping along the third direction, which normally tends to smear out the Landau quantization gaps, can rather give rise to a fractal energy spectram akin to Hofstadter's butterfly when a criterion, found here by mapping the problem to two dimensions, is fulfilled by anisotropic (quasi-one-dimensional) systems. In 3D the angle of the magnetic field plays the role of the field intensity in 2D, so that the butterfly can occur in much smaller fields. The mapping also enables us to calculate the Hall conductivity, in terms of the topological invariant in the Kohmoto-Halperin-Wu's formula, where each of $\sigma_{xy}, \sigma_{zx}$ is found to be quantized.Comment: 4 pages, 6 figures, RevTeX, uses epsf.sty,multicol.st

Unexpected fourfold symmetry in the resistivity of patterned superconductors

We report the magneto-optical observation of a surprising fourfold symmetry of the flux penetration in a superconducting YBa2Cu3O7-delta thin-film disk containing a square array of antidots, leading to an angular variation of the critical current by a factor of nearly 2. This behavior is explained using a vortex channeling model. Potential applications in superconducting devices are discussed

Magneto-optical imaging of magnetic flux patterns in superconducting films with antidots

Superconducting YBaCuO thin films were equipped with a special arrangement of antidots (holes) of 1 micron radius in order to guide the stream of magnetic flux moving in (or out of) the sample. The flux distribution and its dynamics were visualized using real-time magneto-optical imaging. It is clearly demonstrated that one-dimensional antidot arrays strongly facilitate propagation of magnetic flux. We also demonstrate a possibility to alter the direction of flux motion in a controlled way by special arrangement of intercepting antidot arrays. Our resolution was sufficient for observation of flux in particular antidots, which allows a more detailed dynamic analysis of such systems.Comment: 4 pages, 5 figures, submitted to Physica C, Proc. of VORTEX-IV Workshop on Crete-200

Two interacting Hofstadter butterflies

The problem of two interacting particles in a quasiperiodic potential is addressed. Using analytical and numerical methods, we explore the spectral properties and eigenstates structure from the weak to the strong interaction case. More precisely, a semiclassical approach based on non commutative geometry techniques permits to understand the intricate structure of such a spectrum. An interaction induced localization effect is furthermore emphasized. We discuss the application of our results on a two-dimensional model of two particles in a uniform magnetic field with on-site interaction.Comment: revtex, 12 pages, 11 figure

Structure of the superconducting state in a fully frustrated wire network with dice lattice geometry

The superconducting state in a fully frustrated wire network with the dice lattice geometry is investigated in the vicinity of the transition temperature. Using Abrikosov's variational procedure, we write the Ginzburg-Landau free energy functional projected on its unstable supspace as an effective model on the triangular lattice of sixfold coordinated sites. For this latter model, we obtain a large class of degenerate equilibrium configurations in one to one correspondence with those previously constructed for the pure XY model on the maximally frustrated dice lattice. The entropy of these states is proportional to the linear size of the system. Finally we show that magnetic interactions between currents provide a degeneracy lifting mechanism.Comment: The final version (as published in Phys. Rev. B). Substantial corrections have been made to Sec.