Majorana fermions: Anholonomy of bound states

TL;DR

This paper explores the exotic quantum holonomy and topological properties of Majorana bound states in 1-D p-wave superconductors, revealing their connection to exceptional point singularities and topological phase transitions.

Contribution

It introduces a novel framework linking Majorana states to exceptional point singularities and quantum holonomy, enhancing understanding of their topological nature.

Findings

Majorana states correspond to exceptional point singularities.

Topological phase transition involves degeneracy of exceptional points.

Quantum metric collapse characterizes topological changes.

Abstract

Majorana bound states appearing in 1-D $p$-wave superconductor ($\cal{PWS}$) are found to result in exotic quantum holonomy of both eigenvalues and the eigenstates. Induced by a degeneracy hidden in complex Bloch vector space, Majorana states are identified with a pair of exceptional point ($\cal{EP}$) singularities. Characterized by a collapse of the vector space, these singularities are defects in Hilbert space that lead to M$\ddot{\rm o}$bius strip-like structure of the eigenspace and singular quantum metric. The topological phase transition in the language of $\cal{EP}$ is marked by one of the two exception point singularity degenerating to a degeneracy point with non singular quantum metric. This may provide an elegant and useful framework to characterize the topological aspect of Majorana fermions and the topological phase transition.