Nonlinear response of biased bilayer graphene at terahertz frequencies

Abstract

A density-matrix formalism within the length gauge is developed to calculate the nonlinear response of both doped and undoped biased bilayer graphene at terahertz frequencies. Employing a tight-binding model, we derive an effective two-band Hamiltonian with which we calculate the conduction and valence band dispersion, as well as their respective Bloch states. We then solve for the dynamic equations of the density-matrix elements, allowing for the calculation of the intraband and interband current densities and the transmitted and reflected terahertz fields. We find that the third harmonic amplitude generated for undoped biased bilayer graphene with a gap size of 4 meV is larger than that for monolayer graphene or unbiased bilayer graphene for an incident 1 THz single-cycle pulse with a field amplitude of 2.0 kV/cm. We also find for doped biased bilayer graphene that, although the dispersion becomes highly nonparabolic as a bias is applied, the third harmonic is a maximum when there is no bias and diminishes with an increase in bias.