Extended Creutz ladder with spin-orbit coupling: a one-dimensional analog of the Kane-Mele model

Abstract

We construct a topological ladder model, one-dimensional, following the steps which lead to the Kane-Mele model in two dimensions. Starting with a Creutz ladder we modify it so that the gap closure points can occur at either $k=\pi /2$ or $-\pi /2$. We then couple two such models, one for each spin channel, in such a way that time-reversal invariance is restored. We also add a Rashba spin-orbit coupling term. The model falls in the CII symmetry class. We derive the relevant $2\mathbb{Z}$ topological index, calculate the phase diagram and demonstrate the existence of edge states. We also give the thermodynamic derivation of the quantum spin Hall conductance (Středa-Widom). Approximate implementation of this result indicates that this quantity is sensitive to the topological behavior of the model.

arXiv commentto appear in EPL (reference will be added later)

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• Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder
• Generalized lattice Wilson-Dirac fermions in (1+1) dimensions for atomic quantum simulation and topological phases
• Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder
• Edge mode manipulation through commensurate multifrequency driving
• Catalog of noninteracting tight-binding models with two energy bands in one dimension
• Topological properties of a periodically driven Creutz ladder
• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• A simple electronic ladder model harboring ${\mathbb{Z}}_4$ parafermions
• Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits
• Tunable zero modes and quantum interferences in flat-band topological insulators
• Higher order topology in a Creutz ladder