Fractional Fermions with Non-Abelian Statistics

TL;DR

This paper proposes a new class of low-dimensional topological models that host fractionally charged fermions with non-Abelian braiding statistics, characterized by a topological phase transition and robust edge states.

Contribution

It introduces a novel ladder-based topological model supporting fractional fermions with non-Abelian statistics, analyzed both analytically and numerically.

Findings

Identification of a topological phase transition with gap closing and reopening.

Existence of degenerate mid-gap bound states localized at ladder ends.

Robustness of bound states against various perturbations.

Abstract

We introduce a novel class of low-dimensional topological tight-binding models that allow for bound states that are fractionally charged fermions and exhibit non-Abelian braiding statistics. The proposed model consists of a double (single) ladder of spinless (spinful) fermions in the presence of magnetic fields. We study the system analytically in the continuum limit as well as numerically in the tight-binding representation. We find a topological phase transition with a topological gap that closes and reopens as a function of system parameters and chemical potential. The topological phase is of the type BDI and carries two degenerate mid-gap bound states that are localized at opposite ends of the ladders. We show numerically that these bound states are robust against a wide class of perturbations.