Designer quantum states on a fractal substrate: compact localization, flat bands and the edge modes
arXiv:2302.04554 · doi:10.1016/j.physe.2023.115762
Abstract
Compact localized single particle eigenstates on a deterministic fractal substrate, modelled by a triangular Sierpinski gasket of arbitrarily large size, are unravelled and examined analytically. We prescribe an exact real space renormalization group (RSRG) decimation scheme within a tight binding formalism to discern these states, and argue that the number of such states can be infinite if the fractal substrate is enlarged to its thermodynamic limit. Interestingly, these localized states turn out to populate the non-dispersive, flat bands in a periodic array of Sierpinski gasket motifs, however large they may be. Our results match and corroborate the recently observed compact localized, flat band states engineered on two dimensional photonic waveguide networks with a fractal geometry, and provide a whole subset of them, which, in principle, should be observable in fractal photonic lattice experiments.
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- Engineering flux-controlled flat bands and topological states in a Stagome lattice
- The Fractal-Lattice Hubbard Model
- Aharonov-Bohm caging of an electron in a quantum fractal
- A fractal geometry immersed in a hierarchical magnetic flux distribution
- Topological Degeneracy Induced Flat Bands in two-Dimensional Holed Systems
- Compact localized currents in flat bands with broken time-reversal symmetry
- Proximity-induced flat bands and topological properties in a decorated diamond chain