Effective Long-Range Pairing and Hopping in Topological Nanowires Weakly Coupled to $ s $-Wave Superconductors

TL;DR

This paper develops an effective theory for long-range proximity effects in topological nanowires weakly coupled to s-wave superconductors, revealing how nonlocal interactions influence topological phases and Majorana modes.

Contribution

It introduces a model capturing long-range pairing and hopping in weakly coupled nanowires, extending beyond local proximity effects to better match experimental observations.

Findings

Long-range interactions significantly alter the topological phase diagram.

Weak coupling induces smaller superconducting gaps consistent with experiments.

Lower magnetic fields are sufficient to generate Majorana zero modes.

Abstract

In this Letter, we first formulate an effective theory, which generally captures long-range proximity effects of a surface system weakly coupled to an s-wave superconductor. The long-range proximity effects include both the emergent long-range pairing and hopping interactions in the surface system. We then model the Rashba spin-orbit-coupled nanowire in proximity with an s-wave superconductor by taking into account the emergent nonlocal effects in the weak-coupling limit. In this limit the induced superconducting pair potential is found much smaller than that of the host superconductor, which is in good agreement with recent experiments. Compared with the previously considered strong coupling limit with local proximity effects, the long-range interactions can significantly modify the topological phase diagram, and considerably lower the threshold magnetic field for the emergence of Majorana zero modes.