The Tunneling Of The Dirac Particles In Strained Graphene Through The Static And Time-periodic Potential Barrier

Graphene, a novel 2-D monolayer carbon material with honeycomb lattice structures and exceptional bonding mechanisms, has become an intensive investigation subjects due to its unique mechanical, electronic and optical properties. In recent years, graphene is such a popular material in condensed matter physics that makes scientists even predict the coming of the carbon age. Among the carbon allotrops,2-D graphene and 1-D carbon nanotubes have been two promising obejects expecting to replace the silicon in the future electronic devices. The linear dispersion relation in pristine monolayer graphene makes it own many peculiar properties, such as Klein tunneling, Andreev specular reflection and quantum anomalous Hall effect. The graphene quasiparticles satisfy the Dirac equation in the vicinity of the Fermi energy (about 1 eV), which provides a bridge between the high-energy physics and condensed matter physics, and a platform to test the inaccessible effects in high-energy physics. Our thesis is mainly divided into two parts:(1) In the framework of the nearest-neighbor tight-binding approximation, the effective Hamiltonians for the pristine and the strained monolayer graphene have been derived respectively, describing the motion of Dirac particles in the vicinity of the Fermi levels. The different wave functions of massless Dirac particles in the pristine and strained regions driven by the static and dynamic potential barrier has been obtained using the different effective Hamiltonians, based on which the transmission from each sideband channels can be calculated using the numerical methods. During the numerical studies, we focus on the two cases where the stress exerted along respectively the zigzag and armchair directions. It is found that the transmission can be enhanced or suppressed through the central band and neighboring sidebands if we choose appropriately the strain applied exerted along the zigzag or armchair direction. In addition, there exists a competition between the strain and the dynamic potential on the total transmission. For intuitive purpose, the evolution of the probability density of wavefunctions for Dirac particles with time has also been calculated, which shows the interference between the traveling waves from the different sides and opposite directions. Moreover, the periodicity and continuity of the probability density of wave functions within the interfaces in the different regions have also been demonstrated in the numerical analysis.(2) As a generalization of the second chapter, the masses has been introduced into the dynamic potential barriers, The transmission and reflection of massive Dirac particles through the strained graphene barrier driven by the dynamic potential has been numerically investigated. The results show that the mass of Dirac particles plays an important role in the tunneling. Counter-intuitively, by properly adjusting the parameters from the dynamic potential, the mass can enhance transmission from some sidebands in spite of the fact that the introduction of mass can induce an energy gap potential barrier, which generally suppresses the transmission of particles. Particularly interesting, the massive Dirac particle still can partially penetrate the dynamic potential barriers through the multi-photon dressed states in contrast to the static potential barrier where the massive Dirac particle is completely stopped by the energy gaps generated by the mass of the Dirac particles.