Embedded states in the continuum for ${\mathcal{P T}}$-symmetric systems

TL;DR

This paper introduces a new type of bound state in the continuum within ${ m PT}$-symmetric systems, detailing how to construct such states and their effects on system symmetry phases.

Contribution

It presents the concept of embedded states in the continuum for ${ m PT}$-symmetric lattices and describes methods to create and analyze these states.

Findings

Construction of BICs in ${ m PT}$-symmetric systems

Transition from ${ m PT}$-symmetric to Hamiltonian phase

BICs induce ${ m PT}$ symmetry breaking transition

Abstract

We introduce the novel concept of a bound state in the continuum (BIC) for a binary lattice satisfying the ${\mathcal{P T}}$ symmetry condition. We show how to build such state and the local potential necessary to sustain it. We find that an appropriate choice of the envelope function can bring the system from a ${\mathcal{P T}}$-symmetric phase into a Hamiltonian one. For more general envelope functions, the BIC can still be created but the bounded state will force the system to undergo the ${\mathcal{P T}}$ symmetry breaking transition.