Edge states and topological phases in non-Hermitian systems

By Kenta Esaki, Masatoshi Sato, K. Hasebe, M. Kohmoto. 2011

392 citations recorded by the source corpus.

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 Re$E=0$ 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 $\ensuremath{\Theta}$ with ${\ensuremath{\Theta}}^{2}=+1$ [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.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/da7a480ce5f8021a598df28071b9ea69e713ac26

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Non-Hermitian systems and topology: A transfer-matrix perspective (2018, background): “[96] Masatoshi Sato, Kazuki Hasebe, Kenta Esaki, and Mahito Kohmoto, “Edge states and topological phases in non-Hermitian systems,” Prog.”
Topological Phases of Non-Hermitian Systems (2018, background): “[66] Kenta Esaki, Masatoshi Sato, Kazuki Hasebe, and Mahito Kohmoto, “Edge states and topological phases in nonhermitian systems,” Phys.”
Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems. (2016, background): “Previous researchers [11, 12, 16, 38] have focused on the winding numbers of the eigenvectors ψ±.”
Edge States and Topological Invariants of Non-Hermitian Systems. (2018, neutral): “[48] Kenta Esaki, Masatoshi Sato, Kazuki Hasebe, and Mahito Kohmoto, “Edge states and topological phases in non-hermitian systems,” Phys.”
Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class (2020, background): “A crucial distinction is Kramers degeneracy due to T T ∗ = −1 [17, 35].”
Interplay of non-Hermitian skin effects and Anderson localization in nonreciprocal quasiperiodic lattices (2019, background): “Especially, the non-Hermitian topology is attracting special attention for the violation of the conventional bulk-boundary correspondence of Hermitian topological systems, and new ways of topological characterization are needed [39–62].”
Non-Hermitian Chern Bands. (2018, positive): “Our non-Bloch Chern number is defined as the standard Chern number of H̃ðk̃Þ (not of HðkÞ [44,45]).”