Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909329888641024 |
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| author | Correa, Francisco Inzunza, Luis Jakubský, Vít |
| author_facet | Correa, Francisco Inzunza, Luis Jakubský, Vít |
| contents | Confining Dirac fermions in graphene by electrostatic fields is a challenging task. Electric quantum dots created by a scanning tunneling microscope (STM) tip can trap zero-energy quasi-particles. The Lorentzian quantum well provides a faithful, exactly solvable, approximation to such a potential, hosting zero-energy bound states for certain values of the coupling constant. We show that in this critical configuration, the system can be related to the free particle model by means of a supersymmetric transformation. The revealed shape invariance of the model greatly simplifies the calculation of the zero modes and naturally explains the degeneracy of the zero energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13864 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping Correa, Francisco Inzunza, Luis Jakubský, Vít Mesoscale and Nanoscale Physics High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems Confining Dirac fermions in graphene by electrostatic fields is a challenging task. Electric quantum dots created by a scanning tunneling microscope (STM) tip can trap zero-energy quasi-particles. The Lorentzian quantum well provides a faithful, exactly solvable, approximation to such a potential, hosting zero-energy bound states for certain values of the coupling constant. We show that in this critical configuration, the system can be related to the free particle model by means of a supersymmetric transformation. The revealed shape invariance of the model greatly simplifies the calculation of the zero modes and naturally explains the degeneracy of the zero energy. |
| title | Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping |
| topic | Mesoscale and Nanoscale Physics High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2401.13864 |