The fermion doubling theorem (ニールセン＝二宮の定理) plays a pivotal role in Hermitian topological materials. It states, for example, that Weyl points must come in pairs in three-dimensional semimetals.
In this talk, I review the doubling theorem for various Hermitian systems and present an extension of the doubling theorem to non-Hermitian lattice Hamiltonians.
We work on two-dimensional non-Hermitian systems without any symmetry constraints, which can host two different types of topological point nodes, namely, (i) Fermi points and (ii) exceptional points. We show that these two types of protected point nodes obey doubling theorems, which require that the point nodes come in pairs.

Reference: Phys. Rev. Lett. 126, 086401 (2021)

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