Staircase to Higher-Order Topological Phase Transitions

TL;DR

This paper explores a series of higher-order topological phase transitions in a one-dimensional superconductor, revealing how the transition order varies with interaction range and identifying critical behaviors and potential experimental realizations.

Contribution

It introduces a novel series of topological phase transitions of increasing order, including an infinite-order transition at a specific interaction decay exponent.

Findings

Higher-order topological phase transitions depend on the pairing interaction range.

Critical exponents satisfy hyperscaling relations.

Potential experimental platforms include magnetic atoms in superconductors.

Abstract

We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of the pairing interaction, which is parametrized by an algebraic decay with exponent $\alpha$. Remarkably, in the limit $\alpha = 1$ the order of the topological transition becomes infinite. We compute the critical exponents for the series of higher-order transitions in exact form and find that they fulfill the hyperscaling relation. We also study the critical behaviour at the boundary of the system and discuss potential experimental platforms of magnetic atoms in superconductors.