Topological transitions induced by strain in the kagome lattice

We study the effects of a uniform strain on the electronic and topological properties of the 2D kagome lattice using a tight-binding formalism that includes intrinsic and Rashba spin-orbit coupling (SOC). The degeneracy at the Γ point, where a flat-band-parabolic-band touching occurs, evolves into a pair of (tilted) type-I Dirac cones owing to a uniform strain, as shown by effective Hamiltonians, where the anisotropy and tilting of the bands depend on the magnitude and direction of the strain field. Interestingly, we find that the Dirac cones become type-III (including flat dispersions) when the strain is applied along the bonds of the lattice. As expected, the inclusion of intrinsic SOC opens a gap at the emergent Dirac points, making the strained flat band topological, as characterized by a nontrivial Z₂ index. We show that the strain drives the systems into a trivial or topological phase for strains of a few percent, allowing topological transitions via uniform deformations. Additionally, when the Rashba interaction is included, semimetallic phases appear in the topological phase diagrams. These findings suggest an alternative way of engineering anisotropic tilted Dirac bands with tunable topological properties in strained kagome lattices.