Surface physics dominated by the bulk properties is attracting much attention. For example, bulk-boundary correspondence predicts topological surface states. Another important context where surface properties are determined by the bulk is the electric polarization: surface electric charge is the bulk property modulo a quantum [1]. This fact might be regarded as a kind of BBC, in the sense that physical quantity apparently sensitive to the surface properties is determined by the bulk. It is an interesting question whether other physical quantities satisfy this “BBC”.
Recently, Tamura et al. proposed by numerics that surface accumulation of odd-frequency Cooper pairs is the bulk property[2]. They named this relation “spectral bulk-boundary correspondence (SBBC)”. SBBC is an interesting relation, but formal proof and physical explanation have been lacking.

In this work, we prove SBBC based on the analogy with electric polarization: SBBC can be regarded as the polarization of the chirality. We discuss the similarities and differences between electric and chirality polarizations.

[1] D. Vanderbilt and R. D. King-Smith, Phys. Rev. B 48, 4442 (1993).
[2] S. Tamura, S. Hoshino, and Y. Tanaka, arXiv:1809.05687.