Characterizing the weak topological properties: Berry phase point of view

Abstract

We propose classification schemes for characterizing two-dimensional topological phases with nontrivial weak indices. Here, "weak" implies that the Chern number in the corresponding phase is trivial, while the system shows edge states along specific boundaries. As concrete examples, we analyze different versions of the so-called Wilson-Dirac model with (i) anisotropic Wilson terms, (ii) next nearest neighbor hopping terms, and (iii) a superlattice generalization of the model, here in the tight-binding implementation. For types (i) and (ii) a graphic classification of strong properties is successfully generalized for classifying weak properties. As for type (iii), weak properties are attributed to quantized Berry phase pi along a Wilson loop.

arXiv comment15 pages, 6 captioned figures (32 panels in total)

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• Plexcitons: Dirac points and topological modes
• Topological bound states in interacting Su-Schrieffer-Heeger rings
• Topological edge states on time-periodically strained armchair graphene nanoribbons
• Topological classification of Higher-order topological phases with nested band inversion surfaces
• Dimensional crossover of transport characteristics in topological insulator nanofilms
• Counter-propagating edge states in Floquet topological insulating phases
• Comparative study of Weyl semimetal, topological and Chern insulators: thin-film point of view
• Kinetic magnetoelectric effect in topological insulators
• Topological phase-diagram of time-periodically rippled zigzag graphene nanoribbons
• Disentangled topological numbers by a purification of entangled mixed states for non-interacting fermion systems
• Quantum Monte Carlo simulation of topological phase transitions
• Manipulating quantum channels in weak topological insulator nanoarchitectures
• Random-Flux-Induced Transition Sequence between Weak and Strong Topological Phases with Anisotropic Localization Properties
• A spin pump characterized by entanglement Chern numbers
• Non-unique connection between bulk topological invariants and surface physics