Date of Graduation

Spring 2018

Document Type

Honors Research Project

Degree Name

Bachelor of Science



Research Sponsor

Dr. Ben Yu-Kuang Hu

First Reader

Jutta Luettmer-Strathmann

Second Reader

Robert R. Mallik


Mitchell Duffer

Major: Physics

Project Sponsor: Ben Yu-Kuang Hu

Number of Project Credits: 2

Two Stream Instability in Graphene

We investigate the unstable modes of the two-stream instability in graphene to determine if they can occur. This instability occurs when a population of electrons streams past another inside graphene. We obtain the unstable modes by numerically determining the zeros of the non-equilibrium graphene dielectric function using MATLAB. The dielectric function used in this study, in contrast to previous studies, includes the effects of the particle-hole excitation continuum (PHEC) that normally quells the evolution of unstable plasmons. MATLAB’s built in zero solver is employed to solve the sixth order polynomial and determine its roots. For some range of parameters, the zeros are found to exist in the upper half of the complex plane. This indicates that there is a range of unstable modes that exists even with the incorporation of PHEC. The presence of these unstable modes signifies that the plasmons’ amplitudes increase with time.