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The gapped graphene is technologically more important as electronic devices made up of conventional semiconductors are based on the presence of a gap between the valence and conduction bands. In this paper, we report our analytical and numerical calculation of conductivity of gapped graphene on SiO₂ substrate and its variation with the governing parameters of carrier density, band gap, long range charge impurity scatterers, short range neutral defect scatterers, impurity distance from the graphene interface and potential strength of short range scattering centers. We find that the conductivity for unscreened potential decreases with increasing band gap but when screening is incorporated the trend is not only reversed but there is a sharp enhancement in its magnitude also. The sub linear behavior seen in conductivity in the case of gapless graphene at high carrier concentration due to enhanced scattering from the short range neutral defects is also observed for gapped graphene, and it is further observed that increasing the potential strength of the defect scatterers brings in the same behavior at relatively smaller carrier densities.

The Dirac-like quasiparticles in honeycomb graphene lattice are taken to possess a non-zero effective mass. The charge carriers involve to interact with a femtosecond strong laser pulse. Due to the scattering time of electrons in graphene ($\tau \approx$10–100 fs), the one femtosecond optical pulse is used to establish the coherence effect and, consequently, it can be realized to use the time-dependent Schrödinger equation for electron coupled with strong electromagnetic field. Generalized wave vector of relativistic electrons interacting with electric field of laser pulse causes to obtain a time-dependent electric dipole matrix element. Using the coupled differential equations of a two-state system of graphene, the density of probability of population transition between valence (VB) and conduction bands (CB) of gapped graphene is calculated. In particular, the effect of bandgap energy on dipole matrix elements at the Dirac points and resulting CB population (CBP) is investigated. The irreversible electron dynamics is achieved when the optical pulse end. Increasing the energy gap of graphene results in decreasing the maximum CBP.

We study the frictional drag phenomenon in a double-layer system made of two parallel gapped graphene layers by calculating the Coulomb drag resistivity. The random-phase approximation is employed to determine the polarizability functions of layers and the frequency-dependent dielectric function of the structure. Our computations illustrate that the Coulomb drag resistivity in double-layer gapped graphene systems show some interesting different features, compared to that in other double-layer ones. Coulomb drag resistivity in the system steadily increases as temperature increases but quickly decreases with the increase in interlayer distance. With small interlayer separations, the drag resistivity behaves as a smoothly increasing function of the bandgap. Nevertheless, with sufficiently large separations, the Coulomb drag resistivity increases with small bandgaps but decreases with larger ones. We observe that a finite bandgap has remarkable contributions to the frictional drag phenomenon, therefore it is necessary to take into account this factor in calculations to make better agreements with experimental works.