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.

15 pages, 6 captioned figures (32 panels in total)

References in corpus (11)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Topological Crystalline Insulators
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• The space group classification of topological band insulators
• Transmission of topological surface states through surface barriers
• Stacked topological insulator built from bismuth-based graphene sheet analogues
• Prediction of weak topological insulators in layered semiconductors
• Three-dimensional phase diagram of disordered HgTe/CdTe Quantum spin-Hall wells
• Disorder-Induced Multiple Transition involving Z2 Topological Insulator

Cited by in corpus (8)

• Bulk-boundary correspondence from the inter-cellular Zak phase
• Topological edge states on time-periodically strained armchair graphene nanoribbons
• Topological classification of Higher-order topological phases with nested band inversion surfaces
• 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
• Random-Flux-Induced Transition Sequence between Weak and Strong Topological Phases with Anisotropic Localization Properties
• Non-unique connection between bulk topological invariants and surface physics