PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials

Abstract

We study the parity- and time-reversal PT symmetric non-Hermitian Su-Schrieffer-Heeger (SSH) model with two conjugated imaginary potentials $\pm i\gamma$ at two end sites. The SSH model is known as one of the simplest two-band topological models which has topologically trivial and nontrivial phases. We find that the non-Hermitian terms can lead to different effects on the properties of the eigenvalues spectrum in topologically trivial and nontrivial phases. In the topologically trivial phase, the system undergos an abrupt transition from unbroken PT-symmetry region to spontaneously broken $\mathcal{P}\mathcal{T}$-symmetry region at a certain ${\gamma }_c$, and a second transition occurs at another transition point ${\gamma }_{c^{{}^{\prime }}}$ when further increasing the strength of the imaginary potential $\gamma$. But in the topologically nontrivial phase, the zero-mode edge states become unstable for arbitrary nonzero $\gamma$ and the $\mathcal{P}\mathcal{T}$-symmetry of the system is spontaneously broken, which is characterized by the emergence of a pair of conjugated imaginary modes.

arXiv comment6 pages, 4 figures, Phys. Rev. A in press

References in corpus (33)

• Topological Insulators
• Topological insulators and superconductors
• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Making Sense of Non-Hermitian Hamiltonians
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Complex Extension of Quantum Mechanics
• Visualization of Branch Points in PT-Symmetric Waveguides
• Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems
• The Zak phase and the existence of edge states in graphene
• Edge states and topological phases in non-Hermitian systems
• PT symmetry and spontaneous symmetry breaking in a microwave billiard
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Topological phases of generalized Su-Schrieffer-Heeger models
• Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
• Nonlinear suppression of time-reversals in PT-symmetric optical couplers
• Extension of PT-Symmetric Quantum Mechanics to Quantum Field Theory with Cubic Interaction
• Topological orbital ladders
• PT-Symmetric Talbot Effects
• Distribution of Eigenvalues in Non-Hermitian Anderson Model
• Solutions of PT symmetric tight-binding chain and its equivalent Hermitian counterpart
• Pseudo Parity-Time Symmetry in Optical Systems
• Robust and fragile PT-symmetric phases in a tight-binding chain
• Particle number fractionization of an atomic Fermi-Dirac gas in an optical lattice
• S-matrix theory for transmission through billiards in tight-binding approach
• Physics counterpart of the PT non-hermitian tight-binding chain
• The robust $\mP\mT$-symmetric chain and properties of its Hermitian counterpart
• Degrees and signatures of broken PT-symmetry in (non-uniform) lattices
• Non-Hermitian spectra and Anderson localization
• Convective and absolute PT symmetry breaking in tight-binding lattices
• Probability-preserving evolution in a non-Hermitian two-band model

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