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 $vF\ast$ 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 $p\infty (y)$.