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Wave function collapses and 1/n energy spectrum induced by a Coulomb potential in a one-dimensional flat band system |
| Yi-Cai Zhang(张义财)† |
| School of Physics and Materials Science, Guangzhou University, Guangzhou 510006, China |
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Abstract 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 elements), similarly to that in the two-dimensional case, the flat band could not survive. At the same time, the flat band states are transformed into localized states with a logarithmic singularity near the center position. In addition, the wave function near the origin would collapse for an arbitrarily weak Coulomb potential. Due to the wave function collapses, the eigen-energies for a shifted Coulomb potential depend sensitively on the cut-off parameter. For a Coulomb potential of type II, there exist infinite bound states that are generated from the flat band. Furthermore, when the bound state energy is very near the flat band, the energy is inversely proportional to the natural number, e.g.,$E_n\propto$ 1/n, n=1,2,3,... It is expected that the 1/n energy spectrum could be observed experimentally in the near future.
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Received: 05 October 2021
Revised: 02 November 2021
Accepted manuscript online:
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PACS:
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03.65.Ge
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(Solutions of wave equations: bound states)
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03.65.Pm
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(Relativistic wave equations)
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67.85.-d
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(Ultracold gases, trapped gases)
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| Fund: This work was supported by the National Natural Science Foundation of China (Grant No.11874127). |
Corresponding Authors:
Yi-Cai Zhang,E-mail:zhangyicai123456@163.com
E-mail: zhangyicai123456@163.com
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| About author: 2021-11-4 |
Cite this article:
Yi-Cai Zhang(张义财) Wave function collapses and 1/n energy spectrum induced by a Coulomb potential in a one-dimensional flat band system 2022 Chin. Phys. B 31 050311
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