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

@article{Zhang2022BoundSI,
  title={Bound states in the continuum (BIC) protected by self-sustained potential barriers in a flat band system},
  author={Yi-Cai Zhang},
  journal={Scientific Reports},
  year={2022},
  volume={12}
}
  • Yi-Cai Zhang
  • Published 30 November 2021
  • Physics
  • Scientific Reports
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… 
Infinite bound states and 1/n energy spectrum induced by a Coulomb-like potential of type III in a flat band system
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
Wave function collapses and 1/n energy spectrum induced by a Coulomb potential in a one-dimensional flat band system
We investigate the bound state problem in a one-dimensional flat band system with a Coulomb potential. It is found that, in the presence of a Coulomb potential of type I (with three equal diagonal
Infinite bound states and hydrogen atom-like energy spectrum induced by a flat band
In this work, we investigate the bound-state problem in a one-dimensional spin-1 Dirac Hamiltonian with a flat band. It is found that the flat band has significant effects on the bound states. For
Proposed realization of critical regions in a one-dimensional flat band lattice with a quasi-periodic potential
In the previous work, the concept of critical region in a generalized Aubry-Andr´e model (Ganeshan-Pixley-Das Sarma’s model) has been set up. In this work we propose that the critical region can be

References

SHOWING 1-10 OF 53 REFERENCES
Infinite bound states and 1/n energy spectrum induced by a Coulomb-like potential of type III in a flat band system
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
Infinite bound states and hydrogen atom-like energy spectrum induced by a flat band
In this work, we investigate the bound-state problem in a one-dimensional spin-1 Dirac Hamiltonian with a flat band. It is found that the flat band has significant effects on the bound states. For
Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models
We study the transport properties of an arbitrary two-terminal Hermitian system within a tight-binding approximation and derive an expression for the transparency in a form that enables one to
Superconducting transitions in flat-band systems
The physics of strongly correlated quantum particles within a flat band was originally explored as a route to itinerant ferromagnetism and, indeed, a celebrated theorem by Lieb rigorously establishes
Solvable model of bound states in the continuum (BIC) in one dimension
Historically, most of the quantum mechanical results have originated in one dimensional model potentials. However, Von-Neumann’s Bound states in the Continuum (BIC) originated in specially
A band of bound states in the continuum induced by disorder
TLDR
This work proposes a simple mechanism to achieve a band of bound states in the continuum in a class of disordered quasi-1D and quasi-2D systems, where the bound states and extended states overlap completely in a spectral range.
Preformed pairs in flat Bloch bands
In a flat Bloch band the kinetic energy is quenched and single particles cannot propagate since they are localized due to destructive interference. Whether this remains true in the presence of
Electron states for gapped pseudospin-1 fermions in the field of a charged impurity
The electron states of gapped pseudospin-1 fermions of the $\alpha-{\cal T}_3$ lattice in the Coulomb field of a charged impurity are studied. The free $\alpha-{\cal T}_3$ model has three dispersive
Comment on “Electron states for gapped pseudospin-1 fermions in the field of a charged impurity”
In a recent paper [Phys. Rev. B 99, 155124 (2019)], the spectrum of a regularized Coulomb charge was studied in gapped pseudospin-1 systems generated by an
Bound states in the continuum realized in the one-dimensional two-particle Hubbard model with an impurity.
TLDR
A bound state of the one-dimensional two-particle (bosonic or fermionic) Hubbard model with an impurity potential has the Bethe-ansatz form, although the model is nonintegrable.
...
...