The diagrammatic method of Berezinskii for one-dimensional disordered wire with spin-orbit interaction

We extend Berezinskii's diagram technique to the one-dimensional disordered wire containing Rashba and Dresselhaus spin-orbit interactions. The retarded and advanced Green's functions are factorized in coordinates space in the presence of spin-orbit interactions. This factorization allows us to transform all coordinate dependence of the Green's functions from lines to the impurity vertices. Our calculations show that all possible impurity vertices giving a contribution to the correlators do not differ from those given in the conventional technique, except that they are written in a 2 × 2 matrix form and the Fermi velocity v_F^∗ now depends on the spin-orbit coupling constants. The diagrammatic method of Berezinskii with spin-orbit interaction is used to obtain the distribution of the electron density of the localized state p_∞(y) .