Strain-Tunable Harmonic Responses in Valley-Polarized Bilayer Graphene

We theoretically investigate the linear and second-order nonlinear optical responses of valley-polarized bilayer graphene under uniaxial strain. Employing a low-energy effective Hamiltonian that incorporates trigonal warping and strain-induced anisotropy, we calculate the optical susceptibilities within the quantum kinetic formalism. We show that, while the second-order response vanishes in valley-balanced bilayer graphene owing to the cancellation of contributions from opposite valleys, a finite valley polarization lifts this cancellation and enables a net second-harmonic generation (SHG) signal. Uniaxial strain substantially modifies the nonlinear response by distorting the low-energy electronic structure and altering the pseudospin texture, producing a highly anisotropic SHG spectrum. Pronounced resonant enhancements occur at photon energies $\hbar\omega \approx E_f$ and $\hbar\omega \approx 2E_f$, associated with two-photon and one-photon interband resonances, respectively. Remarkably, changing the sign of the strain parameter reverses the direction of the induced second-harmonic current, providing a mechanically controlled switching mechanism for nonlinear optical transport. These results establish strain engineering as an effective route for manipulating valley-dependent nonlinear optical phenomena in bilayer graphene and suggest new opportunities for tunable mid-infrared photonic and valley-optoelectronic applications.