Optimally Localized Wannier Functions for 2D Chern Insulators
| Autor: | Gunawardana, Thivan M., Turner, Ari M., Barnett, Ryan |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Phys. Rev. Research 6, 023046 (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevResearch.6.023046 |
| Popis: | The construction of optimally localized Wannier functions (and Wannier functions in general) for a Chern insulator has been considered to be impossible owing to the fact that the second moment of such functions is generally infinite. In this manuscript, we propose a solution to this problem in the case of a single band. We accomplish this by drawing an analogy between the minimization of the variance and the minimization of the electrostatic energy of a periodic array of point charges in a smooth neutralizing background. In doing so, we obtain a natural regularization of the diverging variance and this leads to an analytical solution to the minimization problem. We demonstrate our results numerically for a particular model system. Furthermore, we show how the optimally localized Wannier functions provide a natural way of evaluating the electric polarization for a Chern insulator. Comment: 16 pages, 4 figures |
| Databáze: | arXiv |
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