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- W4313304553 abstract "In this communication, we study the level-spectra statistics when a noninteracting electron gas is confined in textit{Sierpi'{n}ski Carpet} (textit{SC}) lattices. These textit{SC} lattices are constructed under two representative patterns of the $self$ and $gene$ patterns, and classified into two subclass lattices by the area-perimeter scaling law. By the singularly continuous spectra and critical traits using two level-statistic toolsiffalse the nearest spacing distribution and alternative gap-ratio distributionfi, we ascertain that both obey the critical phase due to broken translation symmetry and the long-range order of scaling symmetry. The Wigner-like conjecture is confirmed numerically since both belong to the Gaussian orthogonal ensemble. An analogy was observed in a quasiperiodic lattice~cite{Zhong1998Level}. In addition, this critical phase isolates the crucial behavior near the metal-insulator transition edge in Anderson model. The lattice topology of the self-similarity feature can induce level clustering behavior." @default.
- W4313304553 created "2023-01-06" @default.
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- W4313304553 date "2022-12-28" @default.
- W4313304553 modified "2023-10-13" @default.
- W4313304553 title "Level-spectra Statistics in Planar Fractal Tight-Binding Models" @default.
- W4313304553 doi "https://doi.org/10.48550/arxiv.2212.13972" @default.
- W4313304553 hasPublicationYear "2022" @default.
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