Complete escape from localization on a hierarchical lattice: A Koch fractal with all states extended
arXiv:2307.13393 · doi:10.1103/PhysRevB.108.125430
Abstract
An infinitely large Koch fractal is shown to be capable of sustaining only extended, Bloch-like eigenstates, if certain parameters of the Hamiltonian describing the lattice are numerically correlated in a special way, and a magnetic flux of a special strength is trapped in every loop of the geometry. We describe the system within a tight binding formalism and prescribe the desired correlation between the numerical values of the nearest neighbor overlap integrals, along with a special value of the magnetic flux trapped in the triangular loops decorating the fractal. With such conditions, the lattice, despite the absence of translational order of any kind whatsoever, yields an absolutely continuous eigenvalue spectrum, and becomes completely transparent to an incoming electron with any energy within the allowed band. The results are analytically exact. An in-depth numerical study of the inverse participation ratio and the two-terminal transmission coefficient corroborates our findings. Our conclusions remain valid for a large set of lattice models, built with the same structural units, but beyond the specific geometry of a Koch fractal, unraveling a subtle universality in a variety of such low dimensional systems.
References in corpus (25)
- Anderson localization of a non-interacting Bose-Einstein condensate
- Artificial flat band systems: from lattice models to experiments
- Anomalous Localization in Low-Dimensional Systems with Correlated Disorder
- Chiral Flat Bands: Existence, Engineering and Stability
- Physical nature of critical wave functions in Fibonacci systems
- Localization of weakly disordered flat band states
- Standard random walks and trapping on the Koch network with scale-free behavior and small-world effect
- On the role of a new type of correlated disorder in extended electronic states in the Thue-Morse lattice
- Extended states in 1D lattices: application to quasiperiodic copper-mean chain
- Observation of two-dimensional Anderson localisation of ultracold atoms
- Anderson localization of solitons
- Nonlinear caging in All-Bands-Flat Lattices
- Flat bands and nontrivial topological properties in an extended Lieb lattice
- A renormalization group analysis of extended electronic states in 1d quasiperiodic lattices
- Complete absence of localization in a family of disordered lattices
- Disorder effects in the two-dimensional Lieb lattice and its extensions
- Localization, phases and transitions in the three-dimensional extended Lieb lattices
- Electronic properties of the 1D Frenkel-Kontorova model
- Engineering bands of extended electronic states in a class of topologically disordered and quasiperiodic lattices
- Localization properties in Lieb lattices and their extensions
- Tight-binding chains with off-diagonal disorder: Bands of extended electronic states induced by minimal quasi-one dimensionality
- Extended electron states and magneto-transport in a 3-simplex fractal
- Flux driven and geometry controlled spin filtering for arbitrary spins in aperiodic quantum networks
- Strange eigenstates and anomalous transport in a Koch fractal with hierarchical interaction
- Engineering insulator-metal transition in a class of decorated aperiodic lattices: a quantum dynamical study