This study theoretically investigates the changes in the energy spectrum of the graphene monolayer subjected to different periodic potential to allow manipulation of the energy spectrum. Floquet theory and the resonance approximation are used to analyse the energy spectrum. Thus, we reviewed the application of single laser potential; linearly polarised and circularly polarised and concluded that the gap opening in the spectrum is determined by the polarisation of the laser field. Then we apply a time periodic electric filed and found that such single potential is not enough to break the topological symmetry.
We investigate the manipulation of the spectrum in 1- spatial periodic magnetic field and 2- linearly polarised laser beam with an external periodically modulated static magnetic/electric field. We investigated in particular, the creation and the destruction of the Dirac-Weyl points. We found that at certain conditions the graphene is transformed into the two-dimensional Weyl metals, where each of the two original graphene Dirac cones is split into pairs of the Weyl cones. We also show that altering the laser's beam incidence (tilting) angle may lead to appearing and disappearing of the pairs of Weyl points, the opening gap in the spectrum, and its efficient manipulation. Deformation and symmetry breaking can be achieved via different laser s frequencies and amplitudes, hence the anisotropy can be controlled.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.