Wave functions in the Critical Phase: a Planar \textit{Sierpiński} Fractal Lattice
arXiv:2406.16130 · doi:10.1103/PhysRevB.110.035403
Abstract
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 , and slightly modulated by the dilation pattern and the geometrical self-similarity level. These electronic states are multifractal by scaling the -order inverse participation ratio or fractal dimension, which correlates with the subdiffusion behavior. In the 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.
arXiv comment10 pages, 6 figures. Accepted by Phys. Rev. B
References in corpus (34)
- Anderson Transitions
- Statistics of energy levels and eigenfunctions in disordered systems
- Statistics and Scaling in Disordered Mesoscopic Electron Systems
- Design and characterization of electronic fractals
- One dimensional quasiperiodic mosaic lattice with exact mobility edges
- Mutifractal Analysis of Broadly Distributed Observables at Criticality
- Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices
- Localization and adiabatic pumping in a generalized Aubry-André-Harper model
- Photonic Floquet topological insulators in a fractal lattice
- Physical nature of critical wave functions in Fibonacci systems
- Realization of the square-root higher-order topological insulator in electric circuits
- Transport and optical properties of an electron gas in a Sierpinski carpet
- Exact new mobility edges between critical and localized states
- On the role of a new type of correlated disorder in extended electronic states in the Thue-Morse lattice
- The two-dimensional Anderson model of localization with random hopping
- Observation of topological phase with critical localization in a quasi-periodic lattice
- Scaling of Level Statistics at the Disorder-Induced Metal-Insulator Transition
- Realization and detection of non-ergodic critical phases in optical Raman lattice
- Sub-diffusion in the Anderson model on random regular graph
- Extended states in 1D lattices: application to quasiperiodic copper-mean chain
- Hall conductivity of Sierpinski carpet
- Critical eigenstates and their properties in one and two dimensional quasicrystals
- Plasmon confinement in fractal quantum systems
- A renormalization group analysis of extended electronic states in 1d quasiperiodic lattices
- Optical conductivity of a quantum electron gas in a Sierpinski carpet
- Localization of Electronic Wave Functions on Quasiperiodic Lattices
- One-parameter Superscaling at the Metal-Insulator Transition in Three Dimensions
- Observation of squeezed Chern insulator in an acoustic fractal lattice
- Electronic properties and quantum transports in functionalized graphene Sierpinski carpet fractals
- Designer quantum states on a fractal substrate: compact localization, flat bands and the edge modes
- A Time-Dependent Random State Approach for Large-scale Density Functional Calculations
- Level-spectra Statistics in Planar Fractal Tight-Binding Models
- Generalized Dielectric Breakdown Model
- Complete escape from localization on a hierarchical lattice: A Koch fractal with all states extended