Bound states in the Brillouin zone continuum

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.

arXiv comment20 pages, 12 figures

References in corpus (9)

• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Light-emitting diodes by bandstructure engineering in van der Waals heterostructures
• Electronic transport through a parallel--coupled triple quantum dot molecule: Fano resonances and bound states in the continuum
• Bound states and scattering in quantum waveguides coupled laterally through a boundary window
• Propagating bound states in the continuum in dielectric gratings
• Quasi-bound states in continuum
• The Effect of Evanescent Modes and Chaos on Deterministic Scattering in Electron Waveguides
• Topological linelike bound states in the continuum
• Scattering from Spatially Localized Chaotic and Disordered Systems