Aperiodic Weak Topological Superconductors

TL;DR

This paper introduces a real-space method to identify weak topological superconductors in aperiodic systems like quasicrystals, enabling analysis beyond traditional momentum-space approaches and assessing disorder robustness.

Contribution

It develops a novel real-space formulation of weak topological invariants using the Clifford pseudospectrum, applicable to disordered and aperiodic systems.

Findings

The method detects non-trivial topological phases in aperiodic superconductors.

It demonstrates robustness of topological edge modes against disorder.

Provides a quantitative measure of disorder tolerance for topological protection.

Abstract

Weak topological phases are usually described in terms of protection by the lattice translation symmetry. Their characterization explicitly relies on periodicity since weak invariants are expressed in terms of the momentum-space torus. We prove the compatibility of weak topological superconductors with aperiodic systems, such as quasicrystals. We go beyond usual descriptions of weak topological phases and introduce a novel, real-space formulation of the weak invariant, based on the Clifford pseudospectrum. A non-trivial value of this index implies a non-trivial bulk phase, which is robust against disorder and hosts localized zero-energy modes at the edge. Our recipe for determining the weak invariant is directly applicable to any finite-sized system, including disordered lattice models. This direct method enables a quantitative analysis of the level of disorder the topological protection can withstand.