Invisible surface defects in a tight-binding lattice

TL;DR

This paper demonstrates the existence of special surface defects in a one-dimensional tight-binding lattice that support invisible Tamm states, which do not alter the phase of reflected waves, and analyzes their fragility under disorder.

Contribution

It introduces a class of surface defects supporting invisible Tamm states with embedded energies and algebraic localization, expanding understanding of surface states in lattices.

Findings

Invisible surface states can be sustained by specific defects.

Reflected waves from these states have the same phase as in a defect-free lattice.

These states are fragile and decay under disorder.

Abstract

Surface Tamm states arise in one-dimensional lattices from some defects at the lattice edge and their energy generally falls in a gap of the crystal. The defects at the surface change rather generally the phase of propagative Bloch waves scattered off at the lattice edge, so that an observer, far from the surface, can detect the existence of edge defects from e.g. time-of-flight measurements as a delay or an advancement of a Bloch wave packet. Here we show that a special class of defects can sustain surface Tamm states which are invisible, in a sense that reflected waves acquire the same phase as in a fully homogeneous lattice with no surface state. Surface states have an energy embedded into the tight-binding lattice band and show a lower than exponential (algebraic) localization. Like most of bound states in the continuum of von Neumann - Wigner type, such states are fragile and decay into resonance surface states in presence of perturbations or lattice disorder. The impact of structural lattice imperfections and disorder on the invisibility of the defects is investigated by numerical simulations.