Interplay between long range hopping and disorder in topological systems

Abstract

We extend the standard SSH model to include long range hopping and disorder, and study how the electronic and topological properties are affected. We show that long range hopping can change the symmetry class and the topological invariant, while diagonal and off-diagonal disorder lead to Anderson localization. Interestingly we find that the Lyapunov exponent $\gamma (E)$ can be linked in two ways to the topological properties in the presence of disorder: Either due to the different response of mid-gap states to increasing disorder, or due to an extra contribution to $\gamma$ due to the presence of edge modes. Finally we discuss its implications in realistic transport measurements.

arXiv comment8 pages, 6figures

References in corpus (25)

• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological Anderson Insulator
• The Zak phase and the existence of edge states in graphene
• Theory of the topological Anderson insulator
• Floquet-Bloch theory and topology in periodically driven lattices
• Disordered quantum gases under control
• Observation of the topological Anderson insulator in disordered atomic wires
• Scalable gate architecture for densely packed semiconductor spin qubits
• Topological phases of generalized Su-Schrieffer-Heeger models
• Majorana Fermions in superconducting wires: effects of long-range hopping, broken time-reversal symmetry and potential landscapes
• A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions
• The fate of topological-insulator surface states under strong disorder
• Topology vs. Anderson localization: non-perturbative solutions in one dimension
• Localization-delocalization transition in a one-dimensional system with long-range correlated off-diagonal disorder
• Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk
• Chiral Topological Superconductors Enhanced by Long-Range Interactions
• Long-range doublon transfer in a dimer chain induced by topology and ac fields
• Anderson localization and topological transition in Chern insulators
• Topological edge states in periodically-driven trapped-ion chains
• Topological phase transition in the quasiperiodic disordered Su-Schriffer-Heeger chain
• Edge-state Blockade of Transport in Quantum Dot Arrays
• Ultracold fermions in a one-dimensional bipartite optical lattice: metal-insulator transitions driven by shaking
• One Dimensional Chain with Long Range Hopping
• Transport signatures in topological systems coupled to AC fields
• Aharonov-Bohm effect in a helical ring with long-range hopping: Effects of Rashba spin-orbit interaction and disorder

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