Topological phases in Kitaev chain with imbalanced pairing

Abstract

We systematically study a Kitaev chain with imbalanced pair creation and annihilation, which is introduced by non-Hermitian pairing terms. Exact phase diagram shows that the topological phase is still robust under the influence of the conditional imbalance. The gapped phases are characterized by a topological invariant, the extended Zak phase, which is defined by the biorthonormal inner product. Such phases are destroyed at the points where the coalescence of groundstates occur, associating with the time-reversal symmetry breaking. We find that the Majorana edge modes also exist for the open chain within unbroken time-reversal symmetric region, demonstrating the bulk-edge correspondence in such a non-Hermitian system.

arXiv comment8 pages, 4 figures

References in corpus (37)

• Topological Insulators
• Topological insulators and superconductors
• Non-Abelian Anyons and Topological Quantum Computation
• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Unpaired Majorana fermions in quantum wires
• Topological Photonics
• Making Sense of Non-Hermitian Hamiltonians
• New directions in the pursuit of Majorana fermions in solid state systems
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Edge states and topological phases in non-Hermitian systems
• Topological chiral magnonic edge mode in a magnonic crystal
• Parity-time-symmetric quantum critical phenomena
• Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
• A review of progress in the physics of open quantum systems: theory and experiment
• Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries
• Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
• Solutions of PT symmetric tight-binding chain and its equivalent Hermitian counterpart
• On Pseudo-Hermitian Hamiltonians and Their Hermitian Counterparts
• Relation between $\mathcal{P}\mathcal{T}$-symmetry breaking and topologically nontrivial phases in the SSH and Kitaev models
• PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model
• Majorana Fermions: The race continues
• Topological quantum wires with balanced gain and loss
• Metric Operator in Pseudo-Hermitian Quantum Mechanics and the Imaginary Cubic Potential
• Non-Abelian Majorana Doublets in Time-Reversal Invariant Topological Superconductor
• Physics counterpart of the PT non-hermitian tight-binding chain
• Majorana Edge Modes with Gain and Loss
• Delta-Function Potential with a Complex Coupling
• Non-Hermitian anisotropic XY model with intrinsic rotation-time reversal symmetry
• Conventional quantum phase transition driven by complex parameter in non-Hermitian PT-symmetric Ising model
• Momentum-independent reflectionless transmission in the non-Hermitian time-reversal symmetric system
• A physical interpretation for the non-Hermitian Hamiltonian
• Dissipation in a topological Josephson junction
• Chern number in Ising models with spatially modulated real and complex fields
• Finite-temperature quantum criticality in a complex-parameter plane

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