Engineering tilted Dirac cones and topological phase transitions in strained kagome lattices

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 in a nontrivial way 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 sawtooth direction. As expected, the inclusion of SOC opens a gap at the emergent Dirac points, making the strained flat band to become topological, as characterized by a nontrivial Z₂ index. We show that the strain drives the systems into a trivial phase for strains of a few percent (with Grüneisen parameter and Poisson ratio values taken as in graphene), allowing topological transitions via uniform deformations. These findings suggest an alternative way of engineering anisotropic tilted Dirac bands with tunable topological properties in strained kagome lattices.