Zero modes of the Kitaev chain with phase-gradients and longer range couplings

Abstract

We present an analytical solution for the full spectrum of Kitaev's one-dimensional p-wave superconductor with arbitrary hopping, pairing amplitude and chemical potential in the case of an open chain. We also discuss the structure of the zero-modes in the presence of both phase gradients and next nearest neighbor hopping and pairing terms. As observed by Sticlet et al., one feature of such models is that in a part of the phase diagram, zero-modes are present at one end of the system, while there are none on the other side. We explain the presence of this feature analytically, and show that it requires some fine-tuning of the parameters in the model. Thus as expected, these `one-sided' zero-modes are neither protected by topology, nor by symmetry.

18 pages, V2, 2 Figures added and minor changes

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Cited by in corpus (15)

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• Boundaries of boundaries: a systematic approach to lattice models with solvable boundary states of arbitrary codimension
• Majorana Bound States in Double Nanowires with Reduced Zeeman Thresholds due to Supercurrents
• Resilience of Majorana Fermions in the face of Disorder
• Flat bands and entanglement in the Kitaev ladder
• Topological quantum phase transitions and criticality in a longer-range Kitaev chain
• Quantum-dot-based Kitaev chains: Majorana quality measures and scaling with increasing chain length
• Topological phase transitions in random Kitaev $\alpha$-chains
• Softening of Majorana edge states by long-range couplings
• Effects of Peierls phases in open linear chains
• Critical region of topological trivial and nontrivial phases in interacting Kitaev chain with spatially varying potentials
• Polarity of the fermionic condensation in the $p$-wave Kitaev model on a square lattice
• Brick Wall Quantum Circuits with Global Fermionic Symmetry
• Analytical classification of Majorana zero-mode spatial profiles in extended Kitaev chains: probability maxima can shift inward