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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2408.07778 |
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| _version_ | 1866913706409984000 |
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| author | Díaz-Bonifaz, Ricardo Y. Ramírez, Carlos |
| author_facet | Díaz-Bonifaz, Ricardo Y. Ramírez, Carlos |
| contents | Magnetic fields can be introduced into discrete models of quantum systems by the Peierls substitution. For tight-binding Hamiltonians, the substitution results in a set of (Peierls) phases that are usually calculated from the magnetic vector potential. As the potential is not unique, a convenient gauge can be chosen to fit the geometry and simplify calculations. However, if the magnetic field is non-uniform, finding a convenient gauge is challenging. In this work we propose to bypass the vector potential determination by calculating the Peierls phases exclusively from the gauge-invariant magnetic flux. The phases can be assigned following a graphic algorithm reminiscent of the paper and pencil game "dots and boxes". We showcase the method implementation by calculating the interference phenomenon in a modified Aharonov-Bohm ring and propose a phase assignation alternative to the Landau gauge to reproduce the Half Integer Quantum Hall Effect in graphene. A non-uniform magnetic field case is addressed by considering a multi-domain Chern insulator to study the effects of domain walls in resistance and current quantization. It is found that adding decoherence and a finite temperature into the model results in quantized resistances that are in good agreement with experiments made with multi-domain intrinsic topological insulators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07778 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dots and Boxes Algorithm for Peierls Substitution: Application to Multidomain Topological Insulators Díaz-Bonifaz, Ricardo Y. Ramírez, Carlos Mesoscale and Nanoscale Physics Quantum Physics Magnetic fields can be introduced into discrete models of quantum systems by the Peierls substitution. For tight-binding Hamiltonians, the substitution results in a set of (Peierls) phases that are usually calculated from the magnetic vector potential. As the potential is not unique, a convenient gauge can be chosen to fit the geometry and simplify calculations. However, if the magnetic field is non-uniform, finding a convenient gauge is challenging. In this work we propose to bypass the vector potential determination by calculating the Peierls phases exclusively from the gauge-invariant magnetic flux. The phases can be assigned following a graphic algorithm reminiscent of the paper and pencil game "dots and boxes". We showcase the method implementation by calculating the interference phenomenon in a modified Aharonov-Bohm ring and propose a phase assignation alternative to the Landau gauge to reproduce the Half Integer Quantum Hall Effect in graphene. A non-uniform magnetic field case is addressed by considering a multi-domain Chern insulator to study the effects of domain walls in resistance and current quantization. It is found that adding decoherence and a finite temperature into the model results in quantized resistances that are in good agreement with experiments made with multi-domain intrinsic topological insulators. |
| title | Dots and Boxes Algorithm for Peierls Substitution: Application to Multidomain Topological Insulators |
| topic | Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2408.07778 |