Robustness of Topological Superconductivity in Proximity-Coupled Topological Insulator Nanoribbons

TL;DR

This paper investigates the robustness of topological superconductivity in TI nanoribbons coupled to superconductors, emphasizing the importance of interface transparency and symmetric structures for maintaining a strong induced gap.

Contribution

It develops a low-energy effective theory that explicitly includes proximity effects and analyzes how interface properties influence the induced superconducting gap in TI nanoribbons.

Findings

Induced gap depends on interface transparency and band structure.

Single-interface structures are prone to gap collapse when chemical potential varies.

Symmetric TI-superconductor structures can sustain robust topological superconductivity.

Abstract

We study the low-energy physics of topological insulator (TI) nanoribbons proximity-coupled to s-wave superconductors (SCs) by explicitly incorporating the proximity effects that emerge at the TI-SC interface. We construct a low-energy effective theory that incorporates the proximity effect through an interface contribution containing both normal and anomalous terms and an energy-renormalization matrix. We show that the strength of the proximity-induced gap is determined by the transparency of the interface and the amplitude of the low-energy TI states at the interface. Consequently, the induced gap is strongly band-dependent and collapses for bands containing states with low amplitude at the interface. We find that states with energies within the bulk TI gap have surface-type character and, in the presence of proximity-induced or applied bias potentials, have most of their weight near either the top or the bottom surface of the nanoribbon. As a result, single interface TI-SC structures are susceptible to experiencing a collapse of the induced gap whenever the chemical potential is far enough from the value corresponding to the bulk TI Dirac point and crosses weakly coupled bands. We also find that changing the chemical potential in single-interface structures using gate potentials may be ineffective, as it does not result in a significant increase of the induced gap. On the other hand, we find that symmetric structures, such as a TI nanowire sandwiched between two superconductors, are capable of realizing the full potential of TI-based structures to harbor robust topological superconducting phases.