Creation and manipulation of anyons in a layered superconductor–two-dimensional electron gas system

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 superconducting 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 of ±e/2 and has a statistical angle of π/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 method for measuring 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 laboratory and its potential applications in quantum information processing with non-Abelian anyons.