Analytical calculation of scattering from spin impurity and entanglement generation for edge states of Kane–Mele model

In this paper, the scattering from a spin impurity for the edge state of the Kane–Mele model has been calculated via the Lippmann–Schwinger approach. To solve this problem analytically, we first approximately calculate the edge states of the Kane–Mele model and use it to obtain Green’s function. We then calculate the scattering matrix of an electron from a spin impurity with Heisenberg interaction. Finally, we generalize this method to a double impurity model and use it to calculate the entanglement between two spins of two impurities. •The transmission and reflection coefficients by spin impurities of the edge states of Kane–Mele model are calculated in a 2D topological insulator.•The entanglement between impurities is investigated.•The scattering of electrons from two kondo impurities by Concurrence gauge is studied.