Topological Classification of Non-Hermitian Hamiltonians

Understand

We revisit the problem of classifying topological band structures in non-Hermitian systems.

• Recently, a solution has been proposed, which is based on redefining the notion of energy band gap in two different ways, leading to the so-called "point-gap" and "line-gap" schemes.
• However, simple Hamiltonians without band degeneracies can be constructed which correspond to neither of the two schemes.
• Here, we resolve this shortcoming of the existing classifications by developing the most general topological characterization of non-Hermitian bands for systems without a symmetry.