Strongly Localized Electrons in a Magnetic Field: Exact Results on Quantum Interference and Magnetoconductance

We study quantum interference effects on the transition strength for strongly localized electrons hopping on 2D square and 3D cubic lattices in a magnetic field B. In 2D, we obtain closed-form expressions for the tunneling probability between two arbitrary sites by exactly summing the corresponding phase factors of all directed paths connecting them. An analytic expression for the magnetoconductance, as an explicit function of the magnetic flux, is derived. In the experimentally important 3D case, we show how the interference patterns and the small-B behavior of the magnetoconductance vary according to the orientation of B.Comment: 4 pages, RevTe

Recursion and Path-Integral Approaches to the Analytic Study of the Electronic Properties of C60C_{60}

The recursion and path-integral methods are applied to analytically study the electronic structure of a neutral $C_{60}$ molecule. We employ a tight-binding Hamiltonian which considers both the $s$ and $p$ valence electrons of carbon. From the recursion method, we obtain closed-form {\it analytic} expressions for the $\pi$ and $\sigma$ eigenvalues and eigenfunctions, including the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) states, and the Green's functions. We also present the local densities of states around several ring clusters, which can be probed experimentally by using, for instance, a scanning tunneling microscope. {}From a path-integral method, identical results for the energy spectrum are also derived. In addition, the local density of states on one carbon atom is obtained; from this we can derive the degree of degeneracy of the energy levels.Comment: 19 pages, RevTex, 6 figures upon reques

Analytical results on quantum interference and magnetoconductance for strongly localized electrons in a magnetic field: Exact summation of forward-scattering paths

We study quantum interference effects on the transition strength for strongly localized electrons hopping on 2D square and 3D cubic lattices in the presence of a magnetic field B. These effects arise from the interference between phase factors associated with different electron paths connecting two distinct sites. For electrons confined on a square lattice, with and without disorder, we obtain closed-form expressions for the tunneling probability, which determines the conductivity, between two arbitrary sites by exactly summing the corresponding phase factors of all forward-scattering paths connecting them. An analytic field-dependent expression, valid in any dimension, for the magnetoconductance (MC) is derived. A positive MC is clearly observed when turning on the magnetic field. In 2D, when the strength of B reaches a certain value, which is inversely proportional to twice the hopping length, the MC is increased by a factor of two compared to that at zero field. We also investigate transport on the much less-studied and experimentally important 3D cubic lattice case, where it is shown how the interference patterns and the small-field behavior of the MC vary according to the orientation of B. The effect on the low-flux MC due to the randomness of the angles between the hopping direction and the orientation of B is also examined analytically.Comment: 24 pages, RevTeX, 8 figures include

Quantum Interference on the Kagom\'e Lattice

We study quantum interference effects due to electron motion on the Kagom\'e lattice in a perpendicular magnetic field. These effects arise from the interference between phase factors associated with different electron closed-paths. From these we compute, analytically and numerically, the superconducting-normal phase boundary for Kagom\'e superconducting wire networks and Josephson junction arrays. We use an analytical approach to analyze the relationship between the interference and the complex structure present in the phase boundary, including the origin of the overall and fine structure. Our results are obtained by exactly summing over one thousand billion billions ($\sim 10^{21}$) closed paths, each one weighted by its corresponding phase factor representing the net flux enclosed by each path. We expect our computed mean-field phase diagrams to compare well with several proposed experiments.Comment: 9 pages, Revtex, 3 figures upon reques

Analytical solution for the Fermi-sea energy of two-dimensional electrons in a magnetic field: lattice path-integral approach and quantum interference

We derive an exact solution for the total kinetic energy of noninteracting spinless electrons at half-filling in two-dimensional bipartite lattices. We employ a conceptually novel approach that maps this problem exactly into a Feynman-Vdovichenko lattice walker. The problem is then reduced to the analytic study of the sum of magnetic phase factors on closed paths. We compare our results with the ones obtained through numerical calculations.Comment: 5 pages, RevTe

Mesoscale magnetism at the grain boundaries in colossal magnetoresistive films

We report the discovery of mesoscale regions with distinctive magnetic properties in epitaxial La$_{1-x}$Sr$_{x}$MnO$_{3}$ films which exhibit tunneling-like magnetoresistance across grain boundaries. By using temperature-dependent magnetic force microscopy we observe that the mesoscale regions are formed near the grain boundaries and have a different Curie temperature (up to 20 K {\it higher}) than the grain interiors. Our images provide direct evidence for previous speculations that the grain boundaries in thin films are not magnetically and electronically sharp interfaces. The size of the mesoscale regions varies with temperature and nature of the underlying defect.Comment: 4 pages of text, 4 figure

Lattice-Boltzmann and finite-difference simulations for the permeability for three-dimensional porous media

Numerical micropermeametry is performed on three dimensional porous samples having a linear size of approximately 3 mm and a resolution of 7.5 $\mu$m. One of the samples is a microtomographic image of Fontainebleau sandstone. Two of the samples are stochastic reconstructions with the same porosity, specific surface area, and two-point correlation function as the Fontainebleau sample. The fourth sample is a physical model which mimics the processes of sedimentation, compaction and diagenesis of Fontainebleau sandstone. The permeabilities of these samples are determined by numerically solving at low Reynolds numbers the appropriate Stokes equations in the pore spaces of the samples. The physical diagenesis model appears to reproduce the permeability of the real sandstone sample quite accurately, while the permeabilities of the stochastic reconstructions deviate from the latter by at least an order of magnitude. This finding confirms earlier qualitative predictions based on local porosity theory. Two numerical algorithms were used in these simulations. One is based on the lattice-Boltzmann method, and the other on conventional finite-difference techniques. The accuracy of these two methods is discussed and compared, also with experiment.Comment: to appear in: Phys.Rev.E (2002), 32 pages, Latex, 1 Figur

Enhanced UV photosensitivity from rapid thermal annealed vertically aligned ZnO nanowires

We report on the major improvement in UV photosensitivity and faster photoresponse from vertically aligned ZnO nanowires (NWs) by means of rapid thermal annealing (RTA). The ZnO NWs were grown by vapor-liquid-solid method and subsequently RTA treated at 700°C and 800°C for 120 s. The UV photosensitivity (photo-to-dark current ratio) is 4.5 × 103 for the as-grown NWs and after RTA treatment it is enhanced by a factor of five. The photocurrent (PC) spectra of the as-grown and RTA-treated NWs show a strong peak in the UV region and two other relatively weak peaks in the visible region. The photoresponse measurement shows a bi-exponential growth and bi-exponential decay of the PC from as-grown as well as RTA-treated ZnO NWs. The growth and decay time constants are reduced after the RTA treatment indicating a faster photoresponse. The dark current-voltage characteristics clearly show the presence of surface defects-related trap centers on the as-grown ZnO NWs and after RTA treatment it is significantly reduced. The RTA processing diminishes the surface defect-related trap centers and modifies the surface of the ZnO NWs, resulting in enhanced PC and faster photoresponse. These results demonstrated the effectiveness of RTA processing for achieving improved photosensitivity of ZnO NWs