Robust exceptional points in disordered systems

¹ Department of Physics, Eskisehir Technical University - Eskisehir, Turkey
² Department of Physics and Astronomy, University of Texas Rio Grande Valley - Brownsville, TX 78520, USA

^(a) cyuce@eskisehir.edu.tr (corresponding author)

Received: 3 February 2019
Accepted: 2 April 2019

Abstract

We construct a theory to introduce the concept of topologically robust exceptional points (EPs). Starting from an ordered system with N elements, we find the necessary condition to have the highest-order exceptional point, namely the N-th–order EP. Using symmetry considerations, we show that an EP associated with an ordered system is very sensitive to the disorder. Specifically, if the EP associated with the ordered system occurs at the fixed degree of non-Hermiticity , the disordered system will not have an EP at the same which puts an obstacle in front of the observation and applications of EPs. To overcome this challenge, by incorporating an asymmetric coupling we propose a disordered system that has a robust EP. The mode associated with the robust EP is extended all over the space. While our approach can be easily realized in electronic circuits and acoustics, we propose a simple experimentally feasible photonic system to realize our robust EP. Our results will open a new direction to search for topologically robust extended states (as opposed to topological localized states) and find considerable applications in direct observation of EPs, realizing topological sensors and designing robust devices for metrology.