Effect of the spin-orbit on the photocurrent in graphene R-J Tarento and P Joyes Laboratoire de Physique des Solides Orsay France

T1 T2 k=K+q

Hamiltonian can be rotated into a diagonal form

Graphene- Electromagnetic field Interaction

NonLinear Optical Excitations Matrix Density ρ = Mele et al 2002

Time evolution of the particle density matrix H=Ho+Hint The density matrix is expanded in the excited fields

The second-order terms ρ2 include the lowest-order changes Δ=2 vF q

Polar asymmetry of the photocurrent

SPIN ORBIT INTERACTION IN GRAPHENE H=H π +H σ +H so H so =Δ L s 4x4 spinor H=Δ int [τ z σ z s z ]+Δ R [σ x s y +τ z σ y s x ] Δ int =0.01K Δ R =0.07K +0.2 K Rasbah Electric field Curvature Guinea et al 2006

Effect of Δint Eigenvalues

Δint=Ω β = z.qxA

Δ*=2

Effect of ΔR