2017/06/30 by Huitao Shen, Bo Zhen, Liang Fu · 7 citations
Physics and Astronomy · #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevlett.120.146402
published as Phys. Rev. Lett. 120, 146402 (2018) · 6 pages, 3 figures + 6 pages of supplemental material
arxiv created 2017/08/22 · arxiv updated 2018/04/11
We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped" bands in one and two dimensions by explicitly finding their topological invariants. We find nontrivial generalizations of the Chern number in two dimensions, and a new classification in one dimension, whose topology is determined by the energy dispersion rather than the energy eigenstates. We then study the bulk-edge correspondence and the topological phase transition in two dimensions. Different from the Hermitian case, the transition generically involves an extended intermediate phase with complex-energy band degeneracies at isolated "exceptional points" in momentum space. We also systematically classify all types of band degeneracies.