Effects of uniaxial and shear strains on the electronic spectrum of Lieb and kagome lattices

We systematically study the effects of the shear and uniaxial strains, applied along different crystallographic directions, on the electronic spectrum of Lieb and kagome lattices by using the tight-binding model with a general Hamiltonian that describes both lattices by means of only one control parameter. Our findings show that such deformations do not open an energy gap in their electronic spectra but can cause (i) approximation of the energy cones, (ii) anisotropy in the energy levels, and (iii) deformation of the flat band, such that the triply degenerate Dirac point in the Lieb lattice transforms into two doubly degenerate Dirac points. By analyzing hypothetical strain cases in which the values of the hopping parameters do not change, we observe that effects such as deformation in the flat band and division of the triply degenerate Dirac point are only due to the hopping parameter changes caused by the strain. Moreover, we identify cases in which there are non-null strain-induced pseudovector potentials in Lieb and kagome lattices.