Date of Award


Degree Type


Degree Name

Master of Science


Applied Mathematics


Dr. Vladimir A. Miranskyy


The electronic properties of graphene, a free-standing single layer of carbon atoms, have been studied extensively by many physicists since its experimental discovery in 2004. While most observed phenomena are successfully described within the model with noninteracting charge carriers, the role of interactions between electrons is still a subject of intense research. The focus of this thesis is the study of the dynamical polarization function which is the im­ portant characteristic of the electromagnetic interaction between particles. This function deter­ mines the screening of the Coulomb interaction due to many-body effects and the dispersion relation of collective excitations (plasmons). We obtain the exact analytic result for the polar­ ization function in the one-loop approximation and explore its dependence on such parameters as the band gap, temperature, external magnetic field and scattering rate. This result is also used to study the behavior of the screened static Coulomb potential and, in some cases, to obtain the dispersion of plasmons



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