A pseudopotential model for Dirac electrons in graphene with line defects

We consider electron transport in a planar fermion model containing various types of line defects modeled by δ-function pseudopotentials with different matrix coefficients. After determining the necessary boundary conditions, the transmission probability for electron transport through the defect line is obtained for various types of pseudopotentials. For the schematic model considered, which may describe a graphene structure with different types of linear defects, the valley polarization is obtained.