$Z_4$ parafermion $\pm \pi/2$ modes in interacting periodically driven superconducting chain

TL;DR

This paper predicts the emergence of $Z_4$ parafermion edge modes in a periodically driven superconducting chain with interactions, providing a new route to realize exotic quasiparticles without complex systems.

Contribution

It introduces a theoretical model demonstrating $Z_4$ parafermion modes in an interacting, periodically driven superconducting chain, with exact solutions at specific parameters.

Findings

$Z_4$ parafermion modes appear as $ extpm rac{ extpi}{2T}$ quasienergies.

Modes are robust against parameter variations and disorder.

Exact analytical derivation at special parameter values.

Abstract

We theoretically report the emergence of $Z_4$ parafermion edge modes in a periodically driven spinful superconducting chain with modest fermionic Hubbard interaction. These parafermion edge modes represent $\pm \pi/(2T)$ quasienergy excitations ($T$ being the driving period), which have no static counterpart and arise from the interplay between interaction effect and periodic driving. At special parameter values, these exotic quasiparticles can be analytically and exactly derived. Strong numerical evidence of their robustness against variations in parameter values and spatial disorder is further presented. Our proposal offers a route toward realizing parafermions without fractional quantum Hall systems or complicated interactions.