Amorphous topological phases protected by continuous rotation symmetry

Abstract

Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous topological materials, where the Hamiltonian is invariant on average under reflection over any axis due to continuous rotation symmetry. While the local disorder caused by the amorphous structure weakens the topological protection, we demonstrate that the edge remains protected from localization. In order to classify such phases we perform a systematic search over all the possible symmetry classes in two dimensions and construct the example models realizing each of the proposed topological phases. Finally, we compute the topological invariant of these phases as an integral along a meridian of the spherical Brillouin zone of an amorphous Hamiltonian.

arXiv comment15 pages, 10 figures

References in corpus (44)

• Topological Insulators
• Topological insulators and superconductors
• Topological Photonics
• Topological Photonics
• Classification of topological quantum matter with symmetries
• Random-Matrix Theory of Quantum Transport
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological Crystalline Insulators
• Periodic table for topological insulators and superconductors
• Topological quantum chemistry
• Kwant: a software package for quantum transport
• The Kernel Polynomial Method
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Topological Boundary Modes in Isostatic Lattices
• Topological mechanics of gyroscopic metamaterials
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Topolectrical circuits
• Topological classification of crystalline insulators through band structure combinatorics
• Nearsightedness of Electronic Matter
• Topology of crystalline insulators and superconductors
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Topological classification with additional symmetries from Clifford algebras
• Topological Insulators in Random Lattices
• Topological Mirror Superconductivity
• Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
• Efficient numerical computation of the Pfaffian for dense and banded skew-symmetric matrices
• Topological phases without crystalline counterparts
• Delocalization in coupled one-dimensional chains
• Statistical Topological Insulators
• Topological Amorphous Metals
• Structural Disorder Induced Second-order Topological Insulators in Three Dimensions
• Topological Weaire-Thorpe models of amorphous matter
• Higher-Order topological insulator in a dodecagonal quasicrystal
• Amorphous topological superconductivity in a Shiba glass
• Quantum gyro-electric effect: Photon spin-1 quantization in continuum topological bosonic phases
• Computation of topological phase diagram of disordered Pb${}_{1-x}$Sn${}_x$Te using the kernel polynomial method
• Qsymm: Algorithmic symmetry finding and symmetric Hamiltonian generation
• Kane-Mele with a twist: Quasicrystalline higher-order topological insulators with fractional mass kinks
• Non-local topological electromagnetic phases of matter
• Topological phase transitions in glassy quantum matter
• Amorphous topological phases protected by continuous rotation symmetry
• Conductance distribution in quasi-one-dimensional disordered quantum wires
• Bimodal conductance distribution of Kitaev edge modes in topological superconductors
• A general algorithm for computing bound states in infinite tight-binding systems

Cited by in corpus (20)

• Observation of spin-momentum locked surface states in amorphous Bi${}_2$Se${}_3$
• Amorphous topological matter: theory and experiment
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Local Topological Markers in Odd Spatial Dimensions and Their Application to Amorphous Topological Matter
• Symmetry-Protected Topological Phases in a Rydberg Glass
• Amorphous topological phases protected by continuous rotation symmetry
• Fractionalization and topology in amorphous electronic solids
• Topological Random Fractals
• An Exact Chiral Amorphous Spin Liquid
• Topological Anderson amorphous insulator
• Obstructed insulators and flat bands in topological phase-change materials
• Average Symmetry Protected Higher-order Topological Amorphous Insulators
• Structural spillage: an efficient method to identify non-crystalline topological materials
• Topological diffusive metal in amorphous transition metal monosilicides
• Quantum Hall effect and Landau levels without spatial long-range correlations
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Isotropic 3D topological phases with broken time reversal symmetry
• Aharanov-Bohm oscillations and perfectly transmitted mode in amorphous topological insulator nanowires
• Topological band insulators without translational symmetry
• Non-self-averaging topological Anderson insulator