# Band twisting and resilience to disorder in long-range topological superconductors

## TL;DR

This paper investigates how long-range interactions in topological superconductors lead to unique edge states and resilience to disorder, revealing new topological phenomena and potential experimental realizations.

## Contribution

It uncovers the formation of nonlocal-massive Dirac fermions and their robustness in long-range topological superconductors, highlighting novel band structure features and disorder resilience.

## Key findings

- Nonlocal-massive Dirac fermions do not localize under disorder.
- Edge gap and double peak DOS structure linked to band twisting.
- Potential for experimental observation in atom arrays and Josephson junctions.

## Abstract

Planar topological superconductors with power-law-decaying pairing display different kinds of topological phase transitions where quasiparticles dubbed nonlocal-massive Dirac fermions emerge. These exotic particles form through long-range interactions between distant Majorana modes at the boundary of the system. We show how these propagating-massive Dirac fermions neither mix with bulk states nor Anderson-localize up to large amounts of static disorder despite being finite energy. Analyzing the density of states (DOS) and the band spectrum of the long-range topological superconductor, we identify the formation of an edge gap and a surprising double peak structure in the DOS which can be linked to a twisting of energy bands with nontrivial topology. Our findings are amenable to experimental verification in the near future using atom arrays on conventional superconductors, planar Josephson junctions on two-dimensional electron gases, and Floquet driving of topological superconductors.