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Superconducting Proximity Effect on the Edge of Fractional Topological Insulators

Meng Cheng

TL;DR

This work analyzes how superconducting proximity on the edge of time-reversal-symmetric fractional topological insulators induces a gapped phase with topological degeneracy arising from fractionalized edge excitations. By mapping the low-energy edge dynamics to a $2m$-state quantum Potts model and identifying localized zero modes at SC/FM interfaces, it derives their algebra and braiding properties, revealing generalized, potentially non-Abelian statistics. The authors show that the edge supports a fractional Josephson effect with period $4\pi m$, reflecting the charge $e/m$ of edge quasiparticles, and discuss experimental signatures and connections to parafermionic physics. Overall, the paper provides a concrete framework for understanding topological degeneracy, zero modes, and braiding in interacting, fractionalized 1D edge systems, with implications for quantum information processing and unconventional superconducting transport.

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 $4π$.

Superconducting Proximity Effect on the Edge of Fractional Topological Insulators

TL;DR

This work analyzes how superconducting proximity on the edge of time-reversal-symmetric fractional topological insulators induces a gapped phase with topological degeneracy arising from fractionalized edge excitations. By mapping the low-energy edge dynamics to a -state quantum Potts model and identifying localized zero modes at SC/FM interfaces, it derives their algebra and braiding properties, revealing generalized, potentially non-Abelian statistics. The authors show that the edge supports a fractional Josephson effect with period , reflecting the charge of edge quasiparticles, and discuss experimental signatures and connections to parafermionic physics. Overall, the paper provides a concrete framework for understanding topological degeneracy, zero modes, and braiding in interacting, fractionalized 1D edge systems, with implications for quantum information processing and unconventional superconducting transport.

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 .

Paper Structure

This paper contains 8 sections, 32 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Edge Theory of FTI
  3. Topological Degeneracy in the Gapped Phase
  4. Low-Energy Effective Hamiltonian and Zero-energy Boundary Modes
  5. Braiding of the $\mathbb{Z}_{2m}$ Zero Modes
  6. Fractional Josephson Effect
  7. Conclusion and Discussion
  8. Acknowledgement

Figures (1)

  • Figure 1: Schematic illustration of superconductor-ferromagnet junctions on the edge of 2D FTI. Localized zero modes appear at the interface between the superconducting regions(SC) and the magnetically insulating regions(FM).