"Identifying signatures of the electron-phonon interaction in 2D and 3D Dirac-like materials"
Recently, interest has been directed toward identifying and characterizing materials with 3D Dirac-like energy dispersions. Currently there are several candidates for these types of materials, for which experimental probing of their optical response has not yet been done. In this work we theoretically calculate the optical conductivity and density of states of a 3D analogue to the low energy model of graphene. Using the Dirac equation which effectively describes the low energy physics of the 2D Dirac fermions found in graphene, we describe a model 3D material with similar properties. Though these materials of differing dimensionality share linear energy dispersions, they differ in their bare frequency dependent optical response. A 2D Dirac band structure produces a constant absorption in the interband regime, while a 3D analogue displays an interband absorption which is linear in frequency. We will also present our theoretical results for the electron self-energy of the 3D Dirac cone with the inclusion of an electron-phonon interaction (EPI). Using a Holstein model for the EPI and allowing for varying chemical potential, bandwidth, and electron-phonon mass renormalization, we show how the self-energy modifies the electronic density of states and in turn the optical conductivity. The results for 3D are contrasted with the 2D case, as previously explored for graphene. As is seen in the theory for graphene, the appearance of a Holstein sideband in the conductivity indicates a new interband and intraband channel has opened due to scattering of phonons. Further optical spectral weight redistribution will be shown to be due to the presence of interactions. Compared to graphene, it is seen that higher dimensionality causes a reduction of the EPI imprint in the optical response. With our results we identify signatures of the EPI which can be used as a tool to understand experimental results probing the optical response and electronic properties of 3D analogues to the 2D Dirac fermions in graphene.
Dr. Xiaorong Qin, Chair
Dr. Elisabeth J. Nicol, Advisor
Dr. Martin Williams
Dr. Alexandros Gezerlis