We describe and analyze in detail our recent theoretical proposal for the realization and manipulation of anyons in a weakly interacting system consisting of a two-dimensional electron gas in the integer quantum Hall regime adjacent to a type-II supe
rconducting film with an artificial array of pinning sites. The anyon is realized in response to a defect in the pinned vortex lattice and carries a charge pm e/2 and a statistical angle pi/4. We establish this result, both analytically and numerically, in three complementary approaches: (i) a continuum model of two-dimensional electrons in the vortex lattice of the superconducting film; (ii) a minimal tight-binding lattice model that captures the essential features of the system; and (iii) an effective theory of the superconducting vortex lattice superposed on the integer quantum Hall state. We propose a novel method to measure the fractional charge directly in a bulk transport experiment and an all-electric setup for an ``anyon shuttle implementing the braiding operations. We briefly discuss conditions for fabricating the system in the lab and its potential applications in quantum information processing with non-Abelian anyons.
We propose a two-dimensional time-reversal invariant system of essentially non-interacting electrons on a square lattice that exhibits configurations with fractional charges e/2. These are vortex-like topological defects in the dimerization order par
ameter describing spatial modulation in the electron hopping amplitudes. Charge fractionalization is established by a simple counting argument, analytical calculation within the effective low-energy theory, and by an exact numerical diagonalization of the lattice Hamiltonian. We comment on the exchange statistics of fractional charges and possible realizations of the system.
