Topological Random Fractals

Abstract

We introduce the notion of topological electronic states on random lattices in non-integer dimensions. By considering a class $D$ model on critical percolation clusters embedded in two dimensions, we demonstrate that these topological random fractals exhibit a robust mobility gap, support quantized conductance and represent a well-defined thermodynamic phase of matter. The finite-size scaling analysis further suggests that the critical properties are not consistent with the class $D$ systems in two dimensions. Our results establish topological random fractals as the most complex systems known to support nontrivial band topology with their distinct unique properties.

6 pages, 5 figures

References in corpus (15)

• Anderson Transitions
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Photonic Floquet topological insulators in a fractal lattice
• Toward Realistic Amorphous Topological Insulators
• Conventional superconductivity in quasicrystals
• Photonic Chern insulator through homogenization of an array of particles
• Localization in random fractal lattices
• Symmetry-Protected Topological Phases in a Rydberg Glass
• Amorphous Bi${}_2$Se${}_3$ structural, electronic, and topological nature by first-principles
• Application of Convolutional Neural Network to Quantum Percolation in Topological Insulators
• Robustness of chiral edge modes in fractal-like-lattices below two dimensions: A case study
• Multicriticality of Two-dimensional Class D Disordered Topological Superconductors
• Universal critical exponent in class D superconductors
• Laughlin topology on fractal lattices without area law entanglement
• Renormalization group analysis of Dirac fermions with random mass

Cited by in corpus (17)

• Inner Skin Effects on Non-Hermitian Topological Fractals
• Observation of nonlinear fractal higher-order topological insulator
• Topological edge and corner states in Bi fractals on InSb
• Noncrystalline topological superconductors
• Observation of squeezed Chern insulator in an acoustic fractal lattice
• Laughlin topology on fractal lattices without area law entanglement
• Non-Hermitian Quantum Fractals
• Quantum Hall effect and Landau levels without spatial long-range correlations
• Fractal Nodal Band Structures
• Anomalous quantum transport in fractal lattices
• Josephson effect in a fractal geometry
• Entanglement Fractalization
• Topological insulators on fractal lattices: A general principle of construction
• Properties of Laughlin states on fractal lattices
• Topology and criticality in non-Hermitian multimodal optical resonators through engineered losses
• Bose-Einstein condensation in exotic lattice geometries
• Topological states and flat bands in exactly solvable decorated Cayley trees