Phase diagram of disordered higher-order topological insulator: A machine learning study

Abstract

A higher-order topological insulator is a new concept of topological states of matter, which is characterized by the emergent boundary states whose dimensionality is lower by more than two compared with that of the bulk, and draws a considerable interest. Yet, its robustness against disorders is still unclear. Here we investigate a phase diagram of higher-order topological insulator phases in a breathing kagome model in the presence of disorders, by using a state-of-the-art machine learning technique. We find that the corner states survive against the finite strength of disorder potential as long as the energy gap is not closed, indicating the stability of the higher-order topological phases against the disorders.

arXiv comment9 pages, 8 figures

References in corpus (43)

• Topological Insulators
• Topological insulators and superconductors
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Quantized Electric Multipole Insulators
• Periodic table for topological insulators and superconductors
• Higher-Order Topological Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Searching for Exotic Particles in High-Energy Physics with Deep Learning
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Zoo of quantum-topological phases of matter
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• The space group classification of topological band insulators
• Topolectrical circuits
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Topological classification with additional symmetries from Clifford algebras
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• Higher-order topological electric circuits and topological corner resonance on the breathing Kagome and pyrochlore lattices
• Lattice models with exactly solvable topological hinge and corner states
• Anderson localisation in tight-binding models with flat bands
• Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems
• Identifying Quantum Phase Transitions with Adversarial Neural Networks
• Disordered weak and strong topological insulators
• Disorder effect on 3-dimensional $Z_2$ quantum spin Hall systems
• $Z_Q$ Topological Invariants for Polyacetylene, Kagome and Pyrochlore lattices
• Three-dimensional phase diagram of disordered HgTe/CdTe Quantum spin-Hall wells
• Deep Learning Topological Invariants of Band Insulators
• Self-learning Monte Carlo with Deep Neural Networks
• Learning Disordered Topological Phases by Statistical Recovery of Symmetry
• Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions
• Edge-of-edge States
• Disorder-induced metal-insulator transitions in three-dimensional topological insulators and superconductors
• The Noncommutative Index Theorem and the Periodic Table for Disordered Topological Insulators and Superconductors
• Topological invariants and corner states for Hamiltonians on a three-dimensional lattice
• The $Z_2$ Index of Disordered Topological Insulators with Time Reversal Symmetry
• Construction of Hamiltonians by supervised learning of energy and entanglement spectra
• Machine-learning Selection of Optical Transients in Subaru/Hyper Suprime-Cam Survey
• Topological Corner States on Kagome Lattice Based Chiral Higher-Order Topological Insulator
• SSH model with long-range hoppings: topology, driving and disorder
• A New Numerical Method for ${\mathbb{Z}}_2$ Topological Insulators with Strong Disorder

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• Higher-order topological phases in crystalline and non-crystalline systems: a review
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• Flat bands and higher-order topology in polymerized triptycene: Tight-binding analysis on decorated star lattices
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• Network model for magnetic higher-order topological phases
• Discovering quasiorder parameters in the Potts model: A bridge between machine learning and critical phenomena
• Recent progress on disorder-induced topological phases
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