Exact eigenvectors and eigenvalues of the finite Kitaev chain and its topological properties

Abstract

We present a comprehensive, analytical treatment of the finite Kitaev chain for arbitrary chemical potential. We derive the momentum quantization conditions and present exact analytical formulae for the resulting energy spectrum and eigenstate wave functions, encompassing boundary and bulk states. In accordance with an analysis based on the winding number topological invariant, and as expected from the bulk-edge correspondence, the boundary states are topological in nature. They can have zero, exponentially small or even finite energy. A numerical analysis confirms their robustness against disorder.

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Cited by in corpus (33)

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• Topological superconductivity and Majorana states in low-dimensional systems
• Flat-band-based multifractality in the all-band-flat diamond chain
• Observation of edge and bulk states in a three-site Kitaev chain
• Strain topological metamaterials
• Duality of Topological Edge States in a Mechanical Kitaev Chain
• Robustness of Majorana edge states of short-length Kitaev chains coupled with environment
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a Kitaev chain with one pair of gain-loss potentials
• Aharonov-Bohm interference as a probe of Majorana fermions
• Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions
• Simulating Majorana zero modes on a noisy quantum processor
• Dynamic generation of nonequilibrium superconducting states in Kitaev chain
• From edge to bulk: Cavity induced displacement of topological non-local qubits
• Multiplicative Majorana zero-modes
• Signatures of Kondo-Majorana interplay in ac response
• Simulation of Kitaev model using one-dimensional chain of superconducting qubits and environmental effect on topological states
• Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain with $s-p$ orbitals
• Impurity-induced counter skin-effect and linear modes in non-Hermitian systems
• Moiré dispersion of edge states in spin chains on superconductors
• On symmetric Tetranacci polynomials in mathematics and physics
• Edge state behavior in a Su-Schrieffer-Heeger like model with periodically modulated hopping
• Dynamics of Majorana zero modes across hybrid Kitaev chain
• Loschmidt echo and Momentum Distribution in a Kitaev Spin Chain
• Emergent topological phases in an extended Su-Schrieffer-Heeger model with Rashba spin-orbit interaction, higher order hopping and domain wall
• Anomalous parametric resonance in a spin-1/2 chain: dynamical effects of nontrivial topology
• Light-element and purely charge-based topological materials
• Nonuniform Parafermion Chains: Low-Energy Physics and Finite-Size Effects
• Analytical classification of Majorana zero-mode spatial profiles in extended Kitaev chains: probability maxima can shift inward
• Charge current and phase diagram of the disordered open longer-range Kitaev chain
• Topological signatures in a weakly dissipative Kitaev chain of finite length