Artículo de revista
Discrete embedded modes in the continuum in 2D lattices
Fecha
2020Registro en:
Physics Letters A Volumen: 384 Número: 27 Número de artículo: 126704 Fecha de publicación: Sep 28 2020
10.1016/j.physleta.2020.126704
Autor
Molina Gálvez, Mario
Institución
Resumen
We study the problem of constructing bulk and surface embedded modes (EMs) inside the quasi-continuum band of a square lattice, using a potential engineering approach a la Wigner and von Neumann. Building on previous results for the one-dimensional (1D) lattice, and making use of separability, we produce examples of two-dimensional envelope functions and the two-dimensional (2D) potentials that produce them. The 2D embedded mode decays like a stretched exponential, with a supporting potential that decays as a power law. The separability process can cause that a 1D impurity state (outside the 1D band) can give rise to a 2D embedded mode (inside the band). The embedded mode survives the addition of random perturbations of the potential; however, this process introduces other localized modes inside the band, and causes a general tendency towards localization of the perturbed modes.