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

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.

26 pages, 16 figures

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Cited by in corpus (5)

• Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries
• Tilted Dirac cones and topological transitions in strained kagome lattices
• Hubbard model on the kagome lattice with time-reversal invariant flux and spin-orbit coupling
• Superfluid transition temperature and fluctuation theory of spin-orbit and Rabi-coupled fermions with tunable interactions
• Multiple topological corner states in the continuum of extended kagome lattice