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arXiv · 2101.12219

Spin-orbit coupling in the kagome lattice with flux and time-reversal symmetry

Irakli Titvinidze·Julian Legendre·Maarten Grothus·Bernhard Irsigler·Karyn Le Hur·Walter Hofstetter
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Abstract

We study the topological properties of a spin-orbit coupled Hofstadter model on the Kagome lattice. The model is time-reversal invariant and realizes a $\mathbb{Z}_2$ topological insulator as a result of artificial gauge fields. We develop topological arguments to describe this system showing three inequivalent sites in a unit cell and a flat band in its energy spectrum in addition to the topological dispersive energy bands. We show the stability of the topological phase towards spin-flip processes and different types of on-site potentials. In particular, we also address the situation where on-site energies may differ inside a unit cell. Moreover, a staggered potential on the lattice may realize topological phases for the half-filled situation. Another interesting result is the occurrence of a topological phase for large on-site energies. To describe topological properties of the system we use a numerical approach based on the twisted boundary conditions and we develop a mathematical approach, related to smooth fields.

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Irakli Titvinidze, Julian Legendre, Maarten Grothus, Bernhard Irsigler, Karyn Le Hur, Walter Hofstetter. 2021-01-28. Spin-orbit coupling in the kagome lattice with flux and time-reversal symmetry. https://doi.org/10.1103/physrevb.103.195105

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