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arXiv · 1806.01111

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

Sina Gholizadeh·Mohammad Yahyavi·Balázs Hetényi
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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 (St\v{r}eda-Widom). Approximate implementation of this result indicates that this quantity is sensitive to the topological behavior of the model.

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Sina Gholizadeh, Mohammad Yahyavi, Balázs Hetényi. 2018-05-16. Extended Creutz ladder with spin-orbit coupling: a one-dimensional analog of the Kane-Mele model. https://doi.org/10.1209/0295-5075/122/27001

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