Generalized Majorana edge modes in a number-conserving periodically driven $p$-wave superconductor

TL;DR

This paper investigates a number-conserving, periodically driven $p$-wave superconductor that hosts generalized Majorana modes capable of encoding qubits, with implications for topological quantum computing.

Contribution

It introduces a solvable model supporting generalized Majorana zero and $$ modes, defines their topological invariants, and demonstrates their robustness and braiding properties.

Findings

Supports generalized Majorana modes in a number-conserving system

Defines winding numbers for topological characterization

Shows robustness and braiding of Majorana qubits

Abstract

We study an analytically solvable and experimentally relevant number-conserving periodically driven $p$-wave superconductor. Such a system is found to support generalized Majorana zero and $\pi$ modes which, despite being non-Hermitian, are still capable of encoding qubits. Moreover, appropriate winding numbers characterizing the topology of such generalized Majorana modes are defined and explicitly calculated. We further discuss the fate of the obtained generalized Majorana modes in the presence of finite charging energy. Finally, we shed light on the quantum computing prospects of such modes by demonstrating the robustness of their encoded qubits and explicitly braiding a pair of generalized Majorana modes.