Effect of strain on band engineering in gapped graphene

We study the effect of strain on the band engineering in gapped graphene subject to external sources. By applying the Floquet theory, we determine the effective Hamiltonian of electron dressed by a linearly, circularly, and an elliptically polarized dressing field in the presence of strain along armchair and zigzag directions. Our results show that the energy spectrum exhibits different symmetries, and for the strainless case, it takes an isotropic and anisotropic forms whatever the values of irradiation intensity, whereas it is linear as in the case of pristine graphene. It increases slowly when strain is applied along the armchair direction but rapidly for the zigzag case. Moreover, it is found that the renormalized band gap changes along different strain magnitudes and does not change for the polarization phase $$\theta $$ θ compared to linear and circular polarizations where its values change oppositely. Graphic Abstract (color online) The energy spectrum $$\varepsilon $$ ε of electron dressed by the linearly polarized field versus the wave vector component $$k_x$$ k x for $${\Delta _{g}}=2$$ Δ g = 2 meV, $$\hbar \omega =10$$ ħ ω = 10 meV with three values of the irradiation intensities $$I=0.0$$ I = 0.0 (blue and magenta lines), $$I=13.3$$ I = 13.3 $$\hbox {kW/cm}^{2}$$ kW/cm 2 (green and orange lines), $$I=26.7$$ I = 26.7 $$\hbox {kW/cm}^{2}$$ kW/cm 2 (red and black lines). (a): Effect of armchair strain direction with $$S=0.7$$ S = 0.7 . (b): Effect of zigzag strain direction with $$S=0.15$$ S = 0.15 .