Magnetic flux response of non-Hermitian topological phases

Abstract

We derive the response of non-Hermitian topological phases with intrinsic point gap topology to localized magnetic flux insertions. In two spatial dimensions, we identify the necessary and sufficient conditions for a flux skin effect that localizes an extensive number of in-gap modes at a flux core. In three dimensions, we furthermore establish the existence of: a flux spectral jump, where flux tube insertion fills up the entire point gap only at a single parallel crystal momentum; a higher-order flux skin effect, which occurs at the ends of flux tubes in presence of pseudo-inversion symmetry; and a flux Majorana mode that represents a spectrally isolated mid-gap state in the complex energy plane. We uniquely associate each non-Hermitian symmetry class with intrinsic point gap topology with one of these cases or a trivial flux response, and discuss possible experimental realizations.

Infernal and exceptional edge modes: non-Hermitian topology beyond the skin effect

“…As such, it provides a robust observable for NH systems, which in general can be highly sensitive to infinitesimal errors. Moreover, only the SIBC spectrum-and not the spectrum under open boundary conditions (OBC) -allows for a one-to-one correspondence between the bulk topological invariants, calculated in periodic boundary conditions (PBC), and boundary dispersion [71]. Our approach, therefore, differs from the OBC treatment of Nakamura et al [72].…”