# Bound states in the Brillouin zone continuum

## TL;DR

This paper investigates how a 2D periodic lattice can support bound states within the continuum spectrum, revealing symmetry-protected states and long-lived quasibound states with potential generalizations to other lattice systems.

## Contribution

It introduces the concept of symmetry-protected bound states in the continuum within a 2D lattice system, expanding understanding of scattering and bound states in periodic structures.

## Key findings

- Identification of two types of BICs: reflection symmetry protected and translational symmetry protected.
- Existence of long-lived quasibound states in the lattice.
- Potential for generalization to other 2D periodic lattices.

## Abstract

Systems with space-periodic Hamiltonians have unique scattering properties. The discrete translational symmetry associated with periodicity of the Hamiltonian creates scattering channels that govern the scattering process. We consider a two-dimensional scattering system in which one dimension is a periodic lattice and the other is localized in space. The scattering and decay processes can then be described in terms of channels indexed by the Bloch momentum. We find the 1D periodic lattice can sustain two types of bound states in the positive energy continuum (BICs): one protected by reflection symmetry, the other protected by discrete translational symmetry. The lattice also sustains long-lived quasibound states. We expect that our results can be generalized to the behavior of states in the continuum of 2D periodic lattices.