Topological Band Theory for Non-Hermitian Hamiltonians

被引:973
作者
Shen, Huitao [1 ]
Zhen, Bo [1 ,2 ]
Fu, Liang [1 ]
机构
[1] MIT, Dept Phys, Cambridge, MA 02139 USA
[2] Univ Penn, Dept Phys & Astron, Philadelphia, PA 19104 USA
关键词
PARITY-TIME SYMMETRY; EXCEPTIONAL POINTS; DIABOLIC POINT; STATES;
D O I
10.1103/PhysRevLett.120.146402
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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.
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页数:6
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