Origin of robust exceptional points: a restricted bulk zero mode

TL;DR

This paper investigates the origin and robustness of exceptional points in one-dimensional cavity arrays, revealing their dependence on array size and symmetry, and introduces a concept of restricted bulk zero modes that underpin their stability.

Contribution

It demonstrates that robust exceptional points are linked to restricted bulk zero modes and depend on the parity of the cavity array size, providing insights for higher-dimensional systems.

Findings

Robust exceptional points exist only in arrays with an even number of cavities.

The location of exceptional points in odd arrays depends inversely on array size.

Robust exceptional points are associated with second and third order degeneracies.

Abstract

Recently a type of robust exceptional points was found that is insensitive to the coupling disorder in the bulk. Here we show that a disparity emerges when the number of coupled cavities in this one-dimensional array changes from even to odd. The robust exceptional point only exists in the former case, whereas the location of the exceptional point in the latter depends inversely on the size of the cavity array and is subjected to coupling disorder in the bulk. We further show that the exceptional points in these two cases are second and third order, respectively. We elucidate the origin of the robust EP as a restricted bulk zero mode, which shares the same robustness against coupling disorder and has a finite amplitude adjacent to the boundary. This finding enables us to identify robust EPs in higher dimensional systems reliably, which can exist in the presence of either sublattice symmetry or the non-Hermitian particle-hole symmetry evolved from it.