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Sina Gholizadeh

Master’s degree: Analysis of the magnetic translation group and investigation of a one-dimensional topological model (Bilkent University2017-08)


Research Projects:

We construct a topological one-dimensional ladder model 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 (Středa-Widom) of the quantum spin Hall conductance. Approximate implementation of this result indicates that this quantity is sensitive to the topological behavior of the model.


Selected Publications:

Extended Creutz ladder with spin-orbit coupling: A one-dimensional analog of the Kane-Mele model 
S. Gholizadeh, M. Yahyavi, B Hetényi
EPL, 122 27001, (2018).