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

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.

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• Infinite bound states and hydrogen atom-like energy spectrum induced by a flat band
• Proposed realization of critical regions in a one-dimensional flat band lattice with a quasi-periodic potential
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential