The Electronic And Optical Properties Of Strained Graphene In The External Field

The recently discovered graphene is a kind of two-dimensional materials, whose crystal structure is composed of hexagonal 6-membered carbon units repeating infinitely in two dimensions and forming a thin sheet. The chemical bonding in the graphene makes it show versatile and salient physical properties, such as high electron mobility and thermal conductivity, strong strength and anomalous quantum Hall effect (QHE), etc. The pristine graphene Hamiltonian behaves like as a massless Dirac particle with the effective velocity about 1/300 of that of light. Thus, graphene can act as a bridge between the high-energy physics and condensed matter physics. Stress is a effective means change physical properties of graphene, so-called strained engineering.The conduction and valence band of graphene is described in the same equation,which closely related with optical properties.The absorption coefficient and four wave mixing is one of the best ways of detecting electronic properties by optical means.The thesis is divided into two parts:(1) The pristine and strained energy bands of the graphene superlattices have been investigated. By establishing the transfer matrix of the strained graphene superlattices, the analytical expression of the dispersion relation for the triple-barrier Kronig-Penney model has been obtained. Using the numerical methods, the effects of the potential barrier, superlattices constant, and strain along the armchair direction have been given. It is found that the superlattices constant and stress play an crucial in energy shape, the generation of the new Dirac point, the group velocity and density of states, and even dynamics.(2) The linear and nonlinear optical properties of the stress on the graphene pierced by the perpendicular strong magnetic field have been studied. The effects of stress on the Landau levels and the corresponding wavefunctions have been analyzed,The space of stress graphene landau energy levels in the magnetic field becomes narrower. The influence of the stress on the linear absorption has been numerically studied, which shows that the strain generally enhance the linear absorption changing energy levels and the density matrix,the strain in the direction of the zigzag is greater than the effect of the stress along the direction of the armchair about absorption.In the nonlinear optical,we find that the four-wave mixing signal solved by the perturbation method is still enhance by the strain and present a strong change in certain range of detuning.