Edge states and topological phases in non-Hermitian systems

2011/07/20 by Kenta Esaki, Masatoshi Sato, Kazuki Hasebe +1 · 11 citations
Mathematics · Physics and Astronomy · #Atiyah–Singer index theorem #Combinatorics #Condensed matter physics #Gapless playback #Hamiltonian (control theory) #Hermitian matrix #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Quantum, superfluid, helium dynamics #Topological Materials and Phenomena #Topology (electrical circuits) #Winding number #cond-mat.mes-hall #cond-mat.other #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1103/physrevb.84.205128

published as Phys. Rev. B 84, 205128 (2011) · 29 pages, 19 figures, typos fixed

arxiv created 2011/07/20 · openalex publication_date 2011/11/17 · arxiv updated 2012/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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 \ensuremathΘ with \ensuremathΘ²=+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.

Citations

• Time-Reversal Symmetry in Non-Hermitian Systems
• Observation of the Spin Hall Effect in Semiconductors
• Topology of Andreev bound states with flat dispersion
• Homotopy and Quantization in Condensed Matter Physics
• SU(2)non-Abelian holonomy and dissipationless spin current in semiconductors
• Vortex pinning and non-Hermitian quantum mechanics
• Making sense of non-Hermitian Hamiltonians
• Classification of topological insulators and superconductors in three spatial dimensions
• Non-Abelian gauge field theory of the spin-orbit interaction and a perfect spin filter
• Quantum Spin Hall Effect in Graphene
• Quantized Hall Conductance in a Two-Dimensional Periodic Potential
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Spin-Hall Insulator
• Topological Transition in a Non-Hermitian Quantum Walk
• Dissipationless Quantum Spin Current at Room Temperature
• On complexified mechanics and coquaternions
• Pseudo-Hermitian Representation of Quantum Mechanics

Cited by

• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Pseudo-Hermitian Systems, Involutive Symmetries and Pseudofermions
• PTsymmetry in the non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Finite-size effects in non-Hermitian topological systems
• Real and imaginary edge states in stacked Floquet honeycomb lattices
• Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Topological Phase Transition Driven by Infinitesimal Instability: Majorana Fermions in Non-Hermitian Spintronics
• Bulk and edge-state arcs in non-Hermitian coupled-resonator arrays
• Topological Quantum Walks in Momentum Space with a Bose-Einstein Condensate

Related

• Edge states and topological invariants of non-Hermitian systems
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Topological characterization of phase transitions and critical edge states in one-dimensional non-Hermitian systems with sublattice symmetry
• Topological phases of non-Hermitian systems
• Dynamically stable topological edge states in an extended Su-Schrieffer-Heeger ladder with balanced perturbation