Floquet engineering of phosphorene-based n − p − n junctions for valley-polarized current

A valley filter that can achieve stable and controllable valley-polarized current is a crucial element in valleytronics, yet its implementation is still challenging. Here, using the Floquet theorem, we propose phosphorene-based $n\text{\ensuremath{-}}p\text{\ensuremath{-}}n$ junctions to realize valley-polarized current under light irradiation. By irradiating linearly polarized light, we obtain the phase transition of phosphorene from insulator to Dirac semimetal. Accordingly, valley-polarized tunneling comes into being accompanied by an interesting negative refraction phenomenon and valley-resolved Klein tunneling. In the tight-binding model, we find that the Stark shift disrupts the energy degeneracy of the valleys, which serves as the fundamental mechanism for valley polarization. The frequency of light significantly influences the hopping energies, which can result in valley reversal under high-frequency conditions. By utilizing the scattering matrix and nonequilibrium Green's function methods, we demonstrate that the system remains stable and can achieve nearly $100%$ valley polarization in current. Our Letter provides a strategy for realizing valley polarization in hexagonal lattice materials while significantly relaxing stringent implementation requirements.