Chirality polarizations and spectral bulk-boundary correspondence

Abstract

Surface physics dominated by bulk properties has been one of the central interests in modern condensed matter physics, from electric polarization to bulk-boundary correspondence of topological insulators and superconductors. Here, we extend theory of electric polarization to chirality polarizations, that is, surface charges corresponding to local antisymmetries characterized as a bulk property. Using the notion of chirality polarizations, we prove the recently proposed spectral bulk-boundary correspondence, a generalization of bulk-boundary correspondence in chiral symmetric systems into complex frequencies. We show a physically transparent proof via Wannier functions and a formal proof by considering the change of surface chirality charges, highlighting the similarities and the differences between electric polarization and chirality polarizations.

arXiv comment10 pages, 1 figure (Appendix: 7 pages, 1 figure)

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Cited by in corpus (11)

• Wannier representation of Floquet topological states
• Non-Abelian Bloch oscillations in higher-order topological insulators
• Bulk odd-frequency pairing in the superconducting Su-Schrieffer-Heeger model
• Generalization of spectral bulk-boundary correspondence
• Topological indicators for systems with open boundaries: Application to the Kitaev wire
• Odd-frequency superconducting pairing due to multiple Majorana edge modes in driven topological superconductors
• Odd-frequency pairing in a nonunitary p-wave superconductor with multiple Majorana fermions
• Generation of Pure Spin Current with Insulating Antiferromagnetic Materials
• Impact of impurity scattering on odd-frequency spin-triplet pairing near the edge of the Kitaev chain
• Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators
• Bulk-boundary correspondence in topological systems with the momentum dependent energy shift