Date of Degree


Document Type


Degree Name





Godfrey Gumbs

Committee Members

Leon Cohen

Oleg Berman

Danhong Huang

Andrii Iurov

Subject Categories

Condensed Matter Physics


condense matter theory, low dimensional material, transmission, magnetic field effect, temperature effect, plasmon


In the past few years, I focused my attention in the study of 2D material's behavior, specifically graphene . We investigated several properties of graphene like transmission of particle through a potential barrier and demonstrated the effect of band gap to suppress the Klein tunneling at head on collision, we presented the results to get the criteria of negative refractive index and Klein tunneling through multiple barrier. Next, we have carried out the calculation of polarization function of graphene in the presence of magnetic field. The effect of integer Landau filling factor is shown and the portrayed results are presented graphically and well analyzed. A comparison of the result is made with finite temperature polarization and the effect of temperature polarization and the effect of temperature is further seen in the Friedel oscillations of shielding potential. \\ Next, we developed the method of determining the surface response function, defined as g-response function to compute the plasmon mode excitation for a structure composed of 2D layer and dielectric material. We present the detail derivation of determining this function and it is further used to study the plasmon mode behavior. Further, the effect of strain on graphene and plasmon phonon coupling are well analyzed and portrayed graphically. \\ In addition, we investigated the behavior of $\alpha$ $-T_3$ lattice and studied the Klein transmission and the effect of magnetic field in the polarization. As was in graphene, Klein transmission is obtained for head on collision which is suppressed when the particle is irradiated with circularly polarized light. In the same fashion with graphene, an investigation of single particle excitation and the collective mode plasmon excitation of $\alpha$ $-T_3$ lattice in the presence of magnetic field is carried out. The direct impact of number of filled Landau Level is seen in the plasmon mode dispersion. Results obtained for $\alpha-T_3$ lattice was compared with the result of graphene. Furthermore, an effect of change of the coupling parameter is seen in the collective mode excitation and interpreted numerically.