Edge states and topological phases in non-Hermitian systems
Edge states and topological phases in non-Hermitian systems
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DOI：
10.1103/physrevb.84.205128
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发表时间：
2011-11-17
影响因子：
3.7
通讯作者：
Kohmoto, Mahito
中科院分区：
文献类型：
--
作者：
Esaki, Kenta;Sato, Masatoshi;Kohmoto, Mahito
研究了非厄米系统的边缘态拓扑稳定性。我们研究了两类支持弱非厄米性中的实体本征能的非厄米哈密顿量：SU(1,1) 和 SO(3,2) 哈密顿量。作为 SU(1,1) 哈密顿量，研究了具有虚位现场势的蜂窝晶格上的紧束缚模型。基于系统的伪反厄米性，通过绕数和指数定理讨论了ReE = 0的边缘态及其拓扑稳定性。作为 SU(1,1) 哈密顿量的更高对称推广，我们还考虑 SO(3,2) 模型。我们分别研究了方格上的 Luttinger Hamiltonian 的非厄米泛化和蜂窝格子上的 Kane-Mele 模型的非厄米泛化。使用时间反转算子 Theta 的广义 Kramers 定理，其中 Theta(2) 2 = +1 [M. Sato et al., e-print arXiv: 1106.1806]，我们引入了一个时间反转不变的陈数，从中论证了无间隙边缘模式的拓扑稳定性。
Topological stability of the edge states is investigated for non-Hermitian systems. We examine two classes of non-Hermitian Hamiltonians supporting real bulk eigenenergies in weak non-Hermiticity: SU(1,1) and SO(3,2) Hamiltonians. As an SU(1,1) Hamiltonian, the tight-binding model on the honeycomb lattice with imaginary onsite potentials is examined. Edge states with ReE = 0 and their topological stability are discussed by the winding number and the index theorem based on the pseudo-anti-Hermiticity of the system. As a higher-symmetric generalization of SU(1,1) Hamiltonians, we also consider SO(3,2) models. We investigate non-Hermitian generalization of the Luttinger Hamiltonian on the square lattice and that of the Kane-Mele model on the honeycomb lattice, respectively. Using the generalized Kramers theorem for the time-reversal operator Theta with Theta(2) 2 = +1 [M. Sato et al., e-print arXiv: 1106.1806], we introduce a time-reversal-invariant Chern number from which topological stability of gapless edge modes is argued.