Journal
PHYSICAL REVIEW B
Volume 101, Issue 20, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.101.205417
Keywords
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Funding
- Vannevar Bush Faculty Fellowship from the U.S. Department of Defense [N00014-17-1-3030]
- National Science Foundation [CBET-1641069]
- U.S. Department of Energy Office of Science, Office of High Energy Physics [DE-SC0019380]
- Simons foundation
- Gordon and Betty Moore Foundation's EPiQS Initiative [GBMF4302]
- Ambizione Program of the Swiss National Science Foundation [185806]
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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. Our approach, which is based on homotopy theory, makes no particular assumptions on the band gap, and predicts significant extensions to the previous classification frameworks. In particular, we show that the one-dimensional invariant generalizes from Z winding number to the non-Abelian braid group, and that depending on the braid group invariants, the two-dimensional invariants can be cyclic groups Z(n) (rather than Z Chern number). We interpret these results in terms of a correspondence with gapless systems, and we illustrate them in terms of analogies with other problems in band topology, namely, the fragile topological invariants in Hermitian systems and the topological defects and textures of nematic liquids.
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