Hopf insulators represent a unique class of topological insulators that exist
exclusively in two-band systems and are inherently unstable upon the inclusion
of additional bands. Meanwhile, recent studies have shown that non-Hermiticity
gives rise to distinctive complex-energy gap structures, known as point gaps,
and associated topological phases with no analogs in Hermitian systems.
Tuttavia, non-Hermitian counterparts of Hopf insulators have remained largely
elusive. Here, we generally classify topological phases of two-band
non-Hermitian systems based on the homotopy theory and uncover Hopf-type
point-gap topology present only for two bands. Specifically, we reveal such
Hopf-type point-gap topology for three-dimensional systems with chiral symmetry
(class AIII) and four-dimensional systems with no symmetry (class A).
Explicitly constructing prototypical models from the Hermitian Hopf insulator,
we further demonstrate that these non-Hermitian topological phases lead to
anomalous point-gapless boundary states spectrally detachable from the bulk
bands.

Questo articolo esplora i giri e le loro implicazioni.

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