Superconducting edge states in a topological insulator

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Quantum Phenomena

Background:

• Topological insulators possess unique conducting edge states protected by time-reversal symmetry.
• Understanding the stability of these edge states against perturbations is crucial for their technological application.
• Interactions and disorder can significantly impact the behavior of these conducting states.

Purpose of the Study:

• To investigate the stability of multiple conducting edge states in topological insulators under time-reversal symmetric perturbations.
• To model the system as a multi-channel Luttinger liquid and analyze the effects of strong interactions and weak disorder.
• To determine the conditions under which the superconducting regime of edge states remains stable.

Main Methods:

• Formulation of a low-energy effective theory for a clean, translation-invariant system.
• Inclusion of disorder terms compatible with time-reversal symmetry.
• Analysis of a multi-channel Luttinger liquid model with N Kramers doublets at the edge.

Main Results:

• In a clean system, N-1 edge states are gapped by Josephson couplings, leaving one gapless mode.
• Disorder perturbation involves simultaneous backscattering across all N channels.
• Disorder relevance depends on channel number parity; it becomes irrelevant for a large number of edge modes.

Conclusions:

• Increasing the number of edge modes renders disorder irrelevant, ensuring the stability of the superconducting regime.
• The superconducting state in topological insulator edge states is robust against perturbations, even with repulsive interactions.
• This work provides insights into the robust nature of topological superconductivity.