Response to polarization and weak topology in Chern insulators

Abstract

Chern insulators present a topological obstruction to a smooth gauge in their Bloch wave functions that prevents the construction of exponentially-localized Wannier functions - this makes the electric polarization ill-defined. Here, we show that spatial or temporal differences in polarization within Chern insulators are well-defined and physically meaningful because they account for bound charges and adiabatic currents. We further show that the difference in polarization across Chern-insulator regions can be quantized in the presence of crystalline symmetries, leading to "weak" symmetry-protected topological phases. These phases exhibit charge fractional quantization at the edge and corner interfaces and with concomitant topological states. We also generalize our findings to quantum spin-Hall insulators and 3D topological insulators. Our work settles a long-standing question and deems the bulk polarization as the fundamental quantity with a "bulk-boundary correspondence", regardless of whether a Wannier representation is possible.

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Cited by in corpus (4)

• Optimally Localized Wannier Functions for 2D Chern Insulators
• Topological Corner Modes by Composite Wannier States in Glide-Symmetric Photonic Crystal
• Polarization textures in crystal supercells with topological bands
• Localized interfacial Phonon Modes at the Electronic Axion Domain Wall