Exotic Topological Types of Majorana Zero-modes and Their Universal Quantum Manipulation

TL;DR

This paper rigorously classifies four types of Majorana zero-modes in topological superconductors, introduces three exotic models with unique topological charges, and discusses their potential for universal quantum computation.

Contribution

It provides a general index theorem for boundary-bulk correspondence and introduces new models with distinct topological charges of Majorana zero-modes.

Findings

Four topologically distinct Majorana zero-modes types identified

Three exotic models with unique topological charges developed

Potential for universal topological quantum computation demonstrated

Abstract

From our general index theorem that characterises faithfully the boundary-bulk correspondence of topological superconductors and insulators, we reveal rigorously that four topologically distinct types of Majorana zero-modes can emerge at the ends of superconducting wires with various symmetry classes. More intriguingly, we establish three exotic one-dimensional models that have different types of topological charge of Majorana zero-modes, and disclose exactly the corresponding topological properties, which are respectively different from those of the Kitaev model because their topological essences (i.e., the types of topological charge) are distinct. Moreover, we also address their application in universal quantum manipulation, which is very promising for realising universal topological quantum computation.