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arXiv · 2212.13972

Level-spectra Statistics in Planar Fractal Tight-Binding Models

Qi Yao·Xiao-Tian Yang·Askar A. Iliasov·M. I. Katsnelson·Shengjun Yuan
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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 tools\iffalse the nearest spacing distribution and alternative gap-ratio distribution\fi, 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.

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Qi Yao, Xiao-Tian Yang, Askar A. Iliasov, M. I. Katsnelson, Shengjun Yuan. 2022-12-28. Level-spectra Statistics in Planar Fractal Tight-Binding Models. https://doi.org/10.1103/physrevb.107.115424

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