Fractional Topological Insulators—A Bosonization Approach

Abstract

A metallic disk with strong spin orbit interaction is investigated. The finite disk geometry introduces a confining potential. Due to the strong spin-orbit interaction and confining potential the metal disk is described by an effective one-dimensional model with a harmonic potential. The harmonic potential gives rise to classical turning points. As a result, open boundary conditions must be used. We bosonize the model and obtain chiral Bosons for each spin on the edge of the disk. When the filling fraction is reduced to the electron-electron interactions are studied by using the Jordan Wigner phase for composite fermions which give rise to a Luttinger liquid. When the metallic disk is in the proximity with a superconductor, a Fractional Topological Insulator is obtained. An experimental realization is proposed. We show that by tunning the chemical potential we control the classical turning points for which a Fractional Topological Insulator is realized.