## Nonlinear Response of Unbiased and Biased Bilayer Graphene at Terahertz Frequencies

##### Abstract

The main focus of this thesis is the investigation of the nonlinear response of unbiased and biased bilayer graphene to incident radiation at terahertz frequencies. We present a tight-binding model of biased and unbiased bilayer graphene that is used to calculate the nonlinear terahertz response. Dynamic equations are developed for the electron density matrix within the length gauge. These equations facilitate the calculation of interband and intraband carrier dynamics. We then obtain nonlinear transmitted and reflected terahertz fields using the calculated nonlinear interband and intraband current densities.
We examine the nonlinear response of unbiased bilayer graphene as a function of the incident field amplitude. In this case the sample is taken to be undoped. In the reflected field, we find the maximum third harmonic amplitude to be approximately 30\% of the fundamental frequency for an incident field of 1.5 kV cm$^{-1}$, which is greater than that found in undoped monolayer graphene at the same field amplitude.
To examine the nonlinear response of biased bilayer graphene, we investigate two different scenarios. In the first scenario, we consider an undoped sample at fixed temperature. We find that when the external bias has a value of 2 meV, the generated third harmonic in the reflected field is approximately 45\% of the fundamental for an incident field amplitude of 2 kV cm$^{-1}$. When we increase the external bias further to 8 meV, we find the generated third harmonic field is approximately 38\% of the fundamental for an incident field amplitude of 1 kV cm$^{-1}$. For both of these bias values, the generated third harmonic is greater than that found in undoped monolayer graphene. In that system, the generated third harmonic field is approximately 32\% of the fundamental for an incident field amplitude of 200 V cm$^{-1}$
In the second scenario, we consider doped biased bilayer graphene. We fix the carrier density at 2$\times$10$^{12}$ cm$^{-2}$, the incident field amplitude at 50 kV cm$^{-1}$, and examine the response as a function of the external bias. We find the largest third harmonic amplitude is approximately 8\% of the fundamental for a bias of 0 meV (zero bias).