Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2406.16130 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910509765230592 |
|---|---|
| author | Yao, Qi Yang, Xiaotian Iliasov, Askar A. Katsnelson, Mikhail I. Yuan, Shengjun |
| author_facet | Yao, Qi Yang, Xiaotian Iliasov, Askar A. Katsnelson, Mikhail I. Yuan, Shengjun |
| contents | Electronic states play a crucial role in many quantum systems of moire superlattices, quasicrystals, and fractals. As recently reported in \textit{Sierpiński} lattices [Phys. Rev. B 107, 115424 (2023)], the critical states are revealed by the energy level-correlation spectra, which are caused by the interplay between aperiodicity and determined self-similarity characters. In the case of the \textit{Sierpiński Carpet}, our results further demonstrate that there is some degree of spatial overlap between these electronic states. These states could be strongly affected by its `seed lattice' of the $generator$, and slightly modulated by the dilation pattern and the geometrical self-similarity level. These electronic states are multifractal by scaling the $q$-order inverse participation ratio or fractal dimension, which correlates with the subdiffusion behavior. In the $gene$ pattern, the averaged state-based multifractal dimension of second-order would increase as its \textit{Hausdoff dimension} increases. Our findings could potentially contribute to understanding quantum transports and single-particle quantum dynamics in fractals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16130 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wave functions in the Critical Phase: a Planar \textit{Sierpiński} Fractal Lattice Yao, Qi Yang, Xiaotian Iliasov, Askar A. Katsnelson, Mikhail I. Yuan, Shengjun Mesoscale and Nanoscale Physics Other Condensed Matter Electronic states play a crucial role in many quantum systems of moire superlattices, quasicrystals, and fractals. As recently reported in \textit{Sierpiński} lattices [Phys. Rev. B 107, 115424 (2023)], the critical states are revealed by the energy level-correlation spectra, which are caused by the interplay between aperiodicity and determined self-similarity characters. In the case of the \textit{Sierpiński Carpet}, our results further demonstrate that there is some degree of spatial overlap between these electronic states. These states could be strongly affected by its `seed lattice' of the $generator$, and slightly modulated by the dilation pattern and the geometrical self-similarity level. These electronic states are multifractal by scaling the $q$-order inverse participation ratio or fractal dimension, which correlates with the subdiffusion behavior. In the $gene$ pattern, the averaged state-based multifractal dimension of second-order would increase as its \textit{Hausdoff dimension} increases. Our findings could potentially contribute to understanding quantum transports and single-particle quantum dynamics in fractals. |
| title | Wave functions in the Critical Phase: a Planar \textit{Sierpiński} Fractal Lattice |
| topic | Mesoscale and Nanoscale Physics Other Condensed Matter |
| url | https://arxiv.org/abs/2406.16130 |