# Flat band localization due to self-trapped orbital

## TL;DR

This paper introduces a novel wave localization mechanism in periodic systems via self-trapped orbitals, leading to perfect flat bands without disorder, demonstrated in electronic and electromagnetic waveguides.

## Contribution

The study reveals a new flat band localization mechanism based on self-trapped orbitals, distinct from known mechanisms, applicable across various wave systems.

## Key findings

- Electrons can be fully localized in a designed 2DEG waveguide.
- Flat bands arise from self-trapped orbitals in engineered boundary conditions.
- Electromagnetic waveguides exhibit similar flat band localization phenomena.

## Abstract

We discover a new wave localization mechanism in a periodic system without any disorder, which can produce a novel type of perfect flat band and is distinct from the known localization mechanisms, i.e., Anderson localization and flat band lattices. The first example we give is a designed electron waveguide on 2DEG with special periodic confinement potential. Numerical calculations show that, with proper confinement geometry, electrons can be completely localized in an open waveguide. We interpret this flat band localization phenomenon by introducing the concept of self-trapped orbitals. In our treatment, each unit cell of the waveguide is equivalent to an artificial atom, where the self-trapped orbital is one of its eigenstates with unique spatial distribution. These self-trapped orbitals form the flat bands in the waveguide. This flat band localization through self-trapped orbitals is a general phenomenon of wave motion, which can arise in any wave systems with carefully engineered boundary conditions. We then design a metallic waveguide array to illustrate that similar flat band localization can be readily realized and observed with electromagnetic waves.