Quasiperiodicity and 2D Topology in 1D Charge Ordered Materials

Abstract

It has recently been argued that individual 1D quasicrystals can be ascribed 2D topological quantum numbers and a corresponding set of topologically protected edge modes. Here, we demonstrate the equivalence of such 1D quasicrystals to a mean-field treatment of incommensurate charge order in 1D materials. Using the fractal nature of the spectrum of commensurate charge-ordered states we consider incommensurate order as a limiting case of commensurate orders. We show that their topological properties arise from a 2D parameter space spanned by both phase and wave vector, bringing the observation of 2D edge modes in line with the standard classification of topological order.The equivalence also provides a set of real-world quasiperiodic materials which can be readily experimentally examined. We propose an experimental test of both the quasicrystalline and topological character of these systems in the form of a quantized adiabatic particle transport upon dragging the charge-ordered state.

5 pages, 3 figures

References in corpus (6)

• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• The space group classification of topological band insulators
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Topological classification with additional symmetries from Clifford algebras
• Topological equivalence of crystal and quasicrystal band structures
• The net charge at interfaces between insulators

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• Bulk topological signatures of a quasicrystal
• A higher-dimensional quasicrystalline approach to the Hofstadter and Fibonacci butterflies topological phase diagram and band conductance: symbolic sequences, Sturmian coding and self-similar rules at all magnetic fluxes
• Superconductivity and charge-density-wave in the Holstein model on the Penrose Lattice
• Visualising the connection between edge states and the mobility edge in adiabatic and non-adiabatic topological charge transport
• Hamiltonian Cycles on Ammann-Beenker Tilings
• Superconvergence of Topological Entropy in the Symbolic Dynamics of Substitution Sequences
• Visualizing topological transport
• Quantum state transfer and maximal entanglement between distant qubits using a minimal quasicrystal pump