Nonlinear response of gated graphene in a strong radiation field Anahit Djotyan and Artak Avetisyan Yerevan State University Saratov Fall Meeting September 22-25

Electronic structure of graphene  Massless relativistic Dirac particles  Zero gap semiconductor Graphene grown epitaxially on SiC has a band gap of about 0.2 eV [1] S.Y. Zhou et al., Nature Mater. 6, 770 2007. In bilayer graphene a gap can be tuned by gates [2,3] [2] E. McCann et al., Solid State Com 143, 110 (2007) [3] Eduardo V. Castro, K. S. Novoselov, et.al., PRL 99, 16802 (2007

only two tight-binding parameters Induced gaps in bilayer graphene Important to include all the SWMcC parameters only two tight-binding parameters

Interaction of a strong electromagnetic wave with AB-stacked bilayer Low-energy excitations vertical interlayer hopping can be described with 2 by 2 Hamiltonian. the interaction Hamiltonian between a laser field and bilayer the laser pulse propagates in the perpendicular direction to graphene plane (XY) and the electric field of pulse lies in the graphene plane

The free solutions in bilayer graphene with an energy gap Energy spectrum of bilayer graphene The free solutions in bilayer graphene with an energy gap

Expanding the fermionic field operator over the free wave function of bilayer

Laser interaction with bilayer graphene with opened energy gap The dipole matrix element for the light interaction with the bilayer depends on electron momentum In cartesian coordinates, the dipole matrix element

In Heisenberg representation operator evolution The single-particle density matrix in momentum space : Evolution of the interband polarization Heisenberg representation

Total Coulomb Hamiltonian

The final form for the nonlinear equations For excitonic effects we apply the Random Phase approximation (RPA) to the many particle system. We express four field operator averages as products of polarization and population The final form for the nonlinear equations in graphene bilayer in the presence of laser pulse: where are functions of and energy gap

Larger value of the frequency the red triangle is larger

Excitonic absorption in gated graphene monolayer Fine structure constant Opened energy gap Mass of the particle in the gated graphene is defined as At photon energy we obtain the exciton peak with

Conclusion We found that changing the energy gap linearly on time, the electron population can be transferred from the top of valence band to the bottom of conduction one after the time t_(final), when the gap comes into resonance with the electromagnetic field. This is an alternative and more suitable way to bring the system into the resonance in comparison with the method of frequency chirped pulse. We see that for larger value of the frequency, the red triangle is larger in a figure, and correspondingly larger number of electrons are transferred to the conduction band. It is connected with the fact that for larger value of the gap the bilayer has more flat bands near the Fermi level. Estimations show that the density of electrons in the triangle is about 10¹¹sm-². For monolayer graphene, the excitonic peak in the light absorption is obtained at the energy about 4.15R* in linear regime, which is in good agreement with experimental results. The nonlinear optical spectra for monolayer and multilayers of graphene will be investigated on the basis of developed methods. The high density of excitons can lead to Bose condensation phenomenon.