10 research outputs found
Analytical approaches for the electronic structure of C60
We use the recursion and path-integral methods to analytically study the electronic properties of a neutral C60 molecule. We obtain closed-form analytic expressions of the eigenvalues and eigenfunctions for both [pi] and [sigma] states as well as the Green functions and the local densities of states, which can be probed experimentally, around any site and around several ring clusters.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30394/1/0000013.pd
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
Quantum interference from sums over closed paths for electrons on a three-dimensional lattice in a magnetic field: total energy, magnetic moment, and orbital susceptibility
We study quantum interference effects due to electron motion on a
three-dimensional cubic lattice in a continuously-tunable magnetic field of
arbitrary orientation and magnitude. These effects arise from the interference
between magnetic phase factors associated with different electron closed paths.
The sums of these phase factors, called lattice path-integrals, are
``many-loop" generalizations of the standard ``one-loop" Aharonov-Bohm-type
argument. Our lattice path integral calculation enables us to obtain various
important physical quantities through several different methods. The spirit of
our approach follows Feynman's programme: to derive physical quantities in
terms of ``sums over paths". From these lattice path-integrals we compute
analytically, for several lengths of the electron path, the half-filled
Fermi-sea ground-state energy of noninteracting spinless electrons in a cubic
lattice. Our results are valid for any strength of the applied magnetic field
in any direction. We also study in detail two experimentally important
quantities: the magnetic moment and orbital susceptibility at half-filling, as
well as the zero-field susceptibility as a function of the Fermi energy.Comment: 14 pages, RevTe
Recursion and Path-Integral Approaches to the Analytic Study of the Electronic Properties of
The recursion and path-integral methods are applied to analytically study the
electronic structure of a neutral molecule. We employ a tight-binding
Hamiltonian which considers both the and valence electrons of carbon.
From the recursion method, we obtain closed-form {\it analytic} expressions for
the and 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
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 () 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
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 in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals
We investigate analytically and numerically the mean-field
superconducting-normal phase boundaries of two-dimensional superconducting wire
networks and Josephson junction arrays immersed in a transverse magnetic field.
The geometries we consider include square, honeycomb, triangular, and kagome'
lattices. Our approach is based on an analytical study of multiple-loop
Aharonov-Bohm effects: the quantum interference between different electron
closed paths where each one of them encloses a net magnetic flux. Specifically,
we compute exactly the sums of magnetic phase factors, i.e., the lattice path
integrals, on all closed lattice paths of different lengths. A very large
number, e.g., up to for the square lattice, exact lattice path
integrals are obtained. Analytic results of these lattice path integrals then
enable us to obtain the resistive transition temperature as a continuous
function of the field. In particular, we can analyze measurable effects on the
superconducting transition temperature, , as a function of the magnetic
filed , originating from electron trajectories over loops of various
lengths. In addition to systematically deriving previously observed features,
and understanding the physical origin of the dips in as a result of
multiple-loop quantum interference effects, we also find novel results. In
particular, we explicitly derive the self-similarity in the phase diagram of
square networks. Our approach allows us to analyze the complex structure
present in the phase boundaries from the viewpoint of quantum interference
effects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure
Quantum interference effects in condensed matter systems: Multi-loop Aharonov-Bohm Feynman lattice path-integral analytical approach.
We investigate quantum interference effects--due to electron motion on lattices immersed in a magnetic field--in a variety of condensed matter systems. These effects arise from the interference between magnetic phase factors associated with different electron paths. The spirit of our approach follows Feynman's programme: to derive physical quantities in terms of "sums over paths". First, using sums-over-paths on the lattice, we derive the exact solution of the half-filled Fermi-sea ground-state energy of tight-binding spinless electrons in two-dimensional (2D) bipartite lattices. Second, we study quantum interference effects produced by tight-binding electrons on a 3D cubic lattice in a continuously-tunable magnetic field with arbitrary orientation. For this system, we obtain exact expressions for the total kinetic energy, magnetic moment, and orbital susceptibility. Third, from the sums of magnetic phase factors on closed paths, we compute--analytically and numerically--the superconducting-normal phase boundary for a variety of superconducting wire networks and Josephson junction arrays. Fourth, we study quantum interference effects for strongly localized electrons by exactly summing all forward-scattering paths between any initial and final sites. Closed-form results for the tunneling probability, with and without disorder, are obtained in 2D. An analytic expression for the magnetoconductance, valid for any dimension, is derived. The behavior of the magnetoconductance in the low flux regime--the range explored in most experiments--are examined in detail. Fifth, we study the electronic structure of single- and multiple-shell carbon fullerenes. The exact solution for and states of a neutral C\sb{60} molecule are derived through the analytical application of both the recursion and moments methods. Finally, we study the electronic states of giant single-shell and nested multi-shell carbon fullerenes.Ph.D.PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104654/1/9542894.pdfDescription of 9542894.pdf : Restricted to UM users only