Geometric Phases in Majorana Zero-Energy State

TL;DR

This paper introduces a generalized geometric phase for Majorana zero-energy states, which can be non-zero and controllable, with potential applications in topological quantum computing.

Contribution

It proposes a new form of geometric phase for Majorana states and demonstrates its calculation in a hybrid system, expanding understanding of their quantum properties.

Findings

Non-zero geometric phases for Majorana states in specific systems

Potential use in topological quantum computation

Analysis of non-adiabatic geometric phases via path integral

Abstract

The usual Berry phase for a Majorana zero-energy state is zero. In this manuscript, we propose a generalized geometric phase for Majorana zero-energy state, which is non-zero for the electron or hole, respectively. We calculate these non-zero geometric phases in a Ferromagnet (FI)/Topological Insulator (TI)/Superconductor (SC) hybrid system, whose magnetization can be manipulated by changing adiabatically the spin degree of freedom. The non-zero geometric phases have potential application on the topological quantum computation treatment of Majorana zero-energy modes. We also discuss the non-adiabatic geometric phase associated with Majorana zero-energy state by the path integral method.