Superconducting Proximity Effect on the Edge of Fractional Topological Insulators

TL;DR

This paper investigates how superconductivity affects the edge states of fractional topological insulators, revealing zero-energy modes with nontrivial braiding and fractional Josephson effects.

Contribution

It introduces a detailed analysis of zero-energy modes and their braiding properties in fractional topological insulators under superconducting proximity.

Findings

Localized zero-energy modes emerge at interfaces.

Zero modes exhibit nontrivial braiding statistics.

Josephson current shows fractional 4π-periodic behavior.

Abstract

We study the superconducting proximity effect on the helical edge states of time-reversal-symmetric fractional topological insulators(FTI). The Cooper pairing of electrons results in many-particle condensation of the fractionalized excitations on the edge. We find in the strong-coupling phase, localized zero-energy modes emerge on interfaces between superconducting regions and magnetically insulating regions, which are responsible for topological degeneracy of the ground states. By mapping the low-energy effective Hamiltonian to quantum Potts model, we determine the operator algebra of the zero modes and show that they exhibit nontrivial braiding properties. We then demonstrate that Josephson current in the junction between superconductors mediated by the edge states of the FTI exhibit fractional Josephson effect with period that is multiples of $4\pi $.