Quantum interference effects in condensed matter systems: Multi-loop Aharonov-Bohm Feynman lattice path-integral analytical approach.

Abstract

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 $\pi$ and $\sigma$ 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.