On a Solution to the Dirac Equation with a Triangular Potential Well
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917843108364288 |
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| author | Payod, Renebeth B. Saroka, Vasil A. |
| author_facet | Payod, Renebeth B. Saroka, Vasil A. |
| contents | Chiral anomalies resulting from the breaking of classical symmetries at the quantum level are fundamental to quantum field theory and gaining ever-growing importance in the description of topological materials in condensed matter physics. Here we present analytical solutions of the Dirac equation for massless 3+1 fermions confined to an infinite stripe and placed into a background gauge field forming a triangular potential well across the width of the stripe. Such an effective 1+1 system hosts zero-energy modes resulting in the gauge field-dependent chiral anomaly structure. This problem has a direct relation to a half-bearded graphene nanoribbon placed into an in-plane external electric field and offers it an exact solution in terms of new special functions that are similar but not reducible to Airy functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04595 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a Solution to the Dirac Equation with a Triangular Potential Well Payod, Renebeth B. Saroka, Vasil A. Mesoscale and Nanoscale Physics High Energy Physics - Theory Mathematical Physics Quantum Physics Chiral anomalies resulting from the breaking of classical symmetries at the quantum level are fundamental to quantum field theory and gaining ever-growing importance in the description of topological materials in condensed matter physics. Here we present analytical solutions of the Dirac equation for massless 3+1 fermions confined to an infinite stripe and placed into a background gauge field forming a triangular potential well across the width of the stripe. Such an effective 1+1 system hosts zero-energy modes resulting in the gauge field-dependent chiral anomaly structure. This problem has a direct relation to a half-bearded graphene nanoribbon placed into an in-plane external electric field and offers it an exact solution in terms of new special functions that are similar but not reducible to Airy functions. |
| title | On a Solution to the Dirac Equation with a Triangular Potential Well |
| topic | Mesoscale and Nanoscale Physics High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2409.04595 |