# Phase tunable second-order topological superconductor

## TL;DR

This paper proposes a phase-tunable two-dimensional nanowire array to realize second-order topological superconductors with Majorana corner states, demonstrating control over topological phases and robustness against disorder.

## Contribution

It introduces a novel, tunable 2D nanowire array platform for second-order topological superconductivity with detailed characterization and disorder resilience.

## Key findings

- Coupling control via phase-biasing enables access to various topological phases.
- System remains robust against disorder in wires and junctions.
- Identification of a topological Anderson phase induced by disorder.

## Abstract

Two-dimensional second-order topological superconductors (SOTSCs) have gapped bulk and edge states, with zero-energy Majorana bound states localized at corners. Motivated by recent advances in Majorana nanowire experiments, we propose to realize a tunable SOTSC as a two-dimensional nanowire array. We show that the coupling between the Majorana modes of adjacent wires can be controlled by phase-biasing the device, allowing to access a variety of topological phases. We characterize the system using scattering theory, which provides access to its transport properties and its topological invariants. The setup is robust against disorder, both in the nanowires themselves and in the Josephson junctions formed between adjacent wires. Further, we identify a parameter regime in which an initially trivial system is rendered topological upon adding disorder, providing an example of a second-order topological Anderson phase.