Bound states in the continuum (BIC) protected by self-sustained potential barriers in a flat band system

TL;DR

This paper explores the existence and protection of bound states in the continuum within a one-dimensional flat band system, revealing universal phenomena under strong potentials and conditions for their stability.

Contribution

It demonstrates the formation of BIC protected by self-sustained barriers in flat band systems and analyzes their behavior under Coulomb and exponential potentials.

Findings

Existence of BIC protected by infinitely high barriers.

Critical potential strengths where bound state energies diverge.

Universal occurrence of BIC in flat band systems with strong potentials.

Abstract

In this work, we investigate the bound states in the continuum (BIC) of a one-dimensional spin-1 flat band system. It is found that, when the potential is sufficiently strong, there exists an effective attractive potential well surrounded by infinitely high self-sustained barriers. Consequently, there exist some BIC in the effective potential well. These bound states are protected by the infinitely high potential barriers, which could not decay into the continuum.} Taking a long-ranged Coulomb potential and a short-ranged exponential potential as two examples, the bound state energies are obtained. For a Coulomb potential, there exists a series of critical potential strengths, near which the bound state energy can go to infinity. For a sufficiently strong exponential potential, there exists two different bound states with a same number of wave function nodes. The existence of BIC protected by the self-sustained potential barriers is quite a universal phenomenon in the flat band system under a strong potential. A necessary condition for the existence of BIC is that the maximum value of potential is larger than two times band gap.