Infinite bound states and $1/n$ energy spectrum induced by a Coulomb-like potential of type III in a flat band system

Abstract

In this work, we investigate the bound states in a one-dimensional spin-1 flat band system with a Coulomb-like potential of type III, which has a unique non-vanishing matrix element in basis $|1⟩$. It is found that, for such a kind of potential, there exists infinite bound states. Near the threshold of continuous spectrum, the bound state energy is consistent with the ordinary hydrogen-like atom energy level formula with Rydberg correction. In addition, the flat band has significant effects on the bound states. For example, there are infinite bound states which are generated from the flat band. Furthermore, when the potential is weak, the bound state energy is proportional to the Coulomb-like potential strength $\alpha$. When the bound state energies are very near the flat band, they are inversely proportional to the natural number $n$ (e.g., $E_n\propto 1/n,n=1,2,3,...$). Further we find that the energy spectrum can be well described by quasi-classical approximation (WKB method). Finally, we give a critical potential strength ${\alpha }_c$ at which the bound state energy reaches the threshold of continuous spectrum. \textbf{After crossing the threshold, the bound states in the continuum (BIC) may exist in such a flat band system.

arXiv admin note: text overlap with arXiv:2205.07386

References in corpus (11)

• Observation of a localized flat-band state in a photonic Lieb lattice
• Band geometry, Berry curvature and superfluid weight
• Topological flat band models with arbitrary Chern numbers
• Superconducting Transitions in Flat Band Systems
• Superconductivity in repulsively interacting fermions on a diamond chain: flat-band induced pairing
• Electron states for gapped pseudospin-1 fermions in the field of charged impurity
• One-dimensional Coulomb problem in Dirac materials
• Dynamics of a quasiparticle in the $\alpha$-T${}_3$ model: Role of pseudospin polarization and transverse magnetic field on \textbf{\textit{zitterbewegung}}
• Origin of flat-band superfluidity on the Mielke checkerboard lattice
• Superfluid density and collective modes of fermion superfluid in dice lattice
• Infinite bound states and hydrogen atom-like energy spectrum induced by a flat band

Cited by in corpus (5)

• 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
• Bound states in the continuum (BIC) protected by self-sustained potential barriers in a flat band system
• Bound states and point interactions of the one-dimensional pseudospin-one Hamiltonian
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential