Partial topological Zak phase and dynamical confinement in non-Hermitian bipartite system

Abstract

Unlike a Chern number in $2$D and $3$D topological system, Zak phase takes a subtle role to characterize the topological phase in $1$D. On the one hand, it is not a gauge invariant, on the other hand, the Zak phase difference between two quantum phases can be used to identify the topological phase transitions. A non-Hermitian system may inherit some characters of a Hermitian system, such as entirely real spectrum, unitary evolution, topological energy band, etc. In this paper, we study the influence of non-Hermitian term on the Zak phase for a class of non-Hermitian systems. We show exactly that the real part of the Zak phase remains unchanged in a bipartite lattice. In a concrete example, $1$D Su-Schrieffer-Heeger (SSH) model, we find that the real part of Zak phase can be obtained by an adiabatic process. To demonstrate this finding, we investigate a scattering problem for a time-dependent scattering center, which is a magnetic-flux-driven non-Hermitian SSH ring. Owing to the nature of the Zak phase, the intriguing features of this design are the wave-vector independence and allow two distinct behaviors, perfect transmission or confinement, depending on the timing of a flux impulse threading the ring. When the flux is added during a wavepacket travelling within the ring, the wavepacket is confined in the scatter partially. Otherwise, it exhibits perfect transmission through the scatter. Our finding extends the understanding and broaden the possible application of geometric phase in a non-Hermitian system.

11 pages, 7 figures

References in corpus (25)

• Making Sense of Non-Hermitian Hamiltonians
• Edge states and topological invariants of non-Hermitian systems
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Visualization of Branch Points in PT-Symmetric Waveguides
• Non-Hermitian Chern bands
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Topological Transition in a Non-Hermitian Quantum Walk
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Faster than Hermitian Quantum Mechanics
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Evidence for Superfluidity of Ultracold Fermions in an Optical Lattice
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Topological phase in a non-Hermitian PT symmetric system
• Dynamical quantum phase transitions in non-Hermitian lattices
• Interaction-controlled transport of an ultracold Fermi gas
• Geometric nature of the environment-induced Berry phase and geometric dephasing
• Topological invariants in dissipative extensions of the Su-Schrieffer-Heeger model
• Geometric Phase for Non-Hermitian Hamiltonians and Its Holonomy Interpretation
• Topological photonic states in one-dimensional dimerized ultracold atomic chains
• PT Symmetric Floquet Topological Phase in SSH Model
• Dynamical topological invariant for non-Hermitian Rice-Mele model
• Probability-preserving evolution in a non-Hermitian two-band model
• Sudden death of particle-pair Bloch oscillation and unidirectional propagation in a one-dimensional driven optical lattice

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• Dynamical characterization of non-Hermitian Floquet topological phases in one-dimension
• Bulk-edge correspondence and long range hopping in the topological plasmonic chain
• Topological Phase Transition Independent of System Non-Hermiticity
• Fate of zero modes in a finite Su-Schrieffer-Heeger Model with $\mathcal{P}\mathcal{T}$ Symmetry
• Inversion symmetric non-Hermitian Chern insulator
• Non-Hermitian anomalous skin effect
• Spontaneous topological pumping in non-Hermitian systems
• Topology of multipartite non-Hermitian one-dimensional systems
• Complex Berry phase and imperfect non-Hermitian phase transitions
• Non-Hermiticity induced Exceptional Points and Skin Effect in the Dice-Haldane Model
• Two-dimensional anisotropic non-Hermitian Lieb lattice
• Edge states in a non-Hermitian topological crystalline insulator
• Non-Hermitian Bloch-Zener phase transition
• Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point
• Quantum phase transition without gap opening
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Topological states at exceptional points
• Emergent Non-Hermitian Edge Polarisation in an Hermitian Tight-binding Model
• Entanglement entropy distinguishes PT-symmetry and topological phases in a class of non-unitary quantum walks
• Semi-localization transition driven by a single asymmetrical tunneling
• Coherent confinement and unidirectional dynamics of a wave packet induced by a non-Hermitian Su-Schrieffer-Heeger segment