Date

2017

Document Type

Dissertation

Degree

Doctor of Philosophy

Department

Physics

First Adviser

Rotkin, Slava V.

Other advisers/committee members

Gunton, James D.; Hickman, Peet A.; Stavola, Michael J.; Xu, Xiaoji G.

Abstract

We theoretically study the heat transfer mechanism between graphene and a polarsubstrate. We develop a thermodynamic theory of heat transfer between grapheneand a SiC substrate based on the master equation method. In the presence of strongcoupling between surface plasmon- and phonon-polaritons in graphene and the sub-strate, a quantum master equation can be used to describe the relaxation dynamicsof hybrid modes of our system.We explore quantization of surface plasmons in a graphene nanodisk structureand derive the response of the graphene nanodisk to an external field. Discretefrequencies and corresponding wavefunctions of localized plasmons in the graphenenanodisk are due to space quantization. The specific case of a dipole excitation isstudied to represent the near-field experiments. The approximately spherical tipof a near-field microscope is modeled as a point-dipole with an known orientation(polarization). Due to the finite(non-zero) width of plasmon resonances in the disk,the response function may allow the near-field patterns with combined angular sym-metry, obtained as a composition of modes with different angular momentum andradial quantum numbers.Furthermore, we investigate the surface plasmon hybridization between the quan-tized modes in a disk and an infinite monolayer of graphene. We also consider newmechanism for mixing of the angular plasmon modes. In the case of mismatchedlattice between the disk and the monolayer the angular momentum is not conserved.We introduce a scalar perturbation with a spatial pattern which resembles one ofa moire pattern in graphene bilayer. Such a perturbation that varies smoothlywithin the graphene nanodisk and has 3-fold symmetry modulates the conductivityof graphene. We observe coupling between plasmon modes with different angularquantum number which occurs due to perturbation. The shape of the hybrid wave-function is analyzed in terms of broken axial symmetry of the system. Responsefunction of the hybrid system is derived and near-field maps were computed.

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