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.

arXiv comment6 pages, 5 figures

References in corpus (63)

• Statistical mechanics of complex networks
• Topological insulators and superconductors
• Classification of topological quantum matter with symmetries
• Random-Matrix Theory of Quantum Transport
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Anderson Transitions
• Kwant: a software package for quantum transport
• Topological States and Adiabatic Pumping in Quasicrystals
• The (High Quality) Topological Materials In The World
• Catalogue of Topological Electronic Materials
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Scaling Theory of the Integer Quantum Hall Effect
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Topological states in engineered atomic lattices
• Amorphous topological insulators constructed from random point sets
• Four-Dimensional Quantum Hall Effect in a Two-Dimensional Quasicrystal
• Design and characterization of electronic fractals
• Higher-Order Topological Insulators in Quasicrystals
• Topological Insulators in Random Lattices
• Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice
• Designer quantum states of matter created atom-by-atom
• Majorana bound states without vortices in topological superconductors with electrostatic defects
• Topological phases without crystalline counterparts
• Photonic Floquet topological insulators in a fractal lattice
• Higher-order topological insulators in amorphous solids
• Topolectric circuits: Theory and construction
• Thermal metal in network models of a disordered two-dimensional superconductor
• Aperiodic Weak Topological Superconductors
• Magnetotransport of dirty-limit van Hove singularity quasiparticles
• Amorphous photonic topological insulator
• Topological Amorphous Metals
• Structural Disorder Induced Second-order Topological Insulators in Three Dimensions
• Topological Weaire-Thorpe models of amorphous matter
• Topological states on fractal lattices
• Topology in the Sierpiński-Hofstadter problem
• Higher-Order topological insulator in a dodecagonal quasicrystal
• Toward Realistic Amorphous Topological Insulators
• The existence of robust edge currents in Sierpinsky Fractals
• Hall conductivity of Sierpinski carpet
• Conventional superconductivity in quasicrystals
• Amorphous topological superconductivity in a Shiba glass
• Effective mass and tricritical point for lattice fermions localized by a random mass
• Photonic Chern insulator through homogenization of an array of particles
• Anyons and Fractional Quantum Hall Effect in Fractal Dimensions
• Localization in random fractal lattices
• Topological phase transitions in glassy quantum matter
• Symmetry-Protected Topological Phases in a Rydberg Glass
• Amorphous topological phases protected by continuous rotation symmetry
• Criticality in amorphous topological matter -- beyond the universal scaling paradigm
• Topological and conventional phases of a three dimensional electron glass
• Amorphous Bi${}_2$Se${}_3$ structural, electronic, and topological nature by first-principles
• Bulk Spectrum and K-theory for Infinite-Area Topological Quasicrystal
• Power-law energy level-spacing distributions in fractals
• Origin and localization of topological band gaps in gyroscopic metamaterials
• Application of Convolutional Neural Network to Quantum Percolation in Topological Insulators
• Structural disorder-driven topological phase transition in noncentrosymmetric BiTeI
• 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
• Effect of coordination on topological phases on self-similar structures
• Laughlin topology on fractal lattices without area law entanglement
• Renormalization group analysis of Dirac fermions with random mass

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• 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