Magnetic field induced Quasi Helical Liquid state in a disordered 1D electron system with strong spin-orbit interaction

We study the crossover from a Luttinger liquid to a quasi-helical liquid state in a one-dimensional system of interacting electrons with strong spin-orbit interaction in the presence of a transverse magnetic field, which leads to a gap for one-half of the conducting modes. In particular, we study the effect of gap opening by electron localization in the presence of non-magnetic disorder. We show that the localization length has a nonuniform behavior as a function of the magnetic field. With increasing field, the localization length grows from its zero-field Luttinger-liquid value to a maximum, after which it crosses over to again smaller values corresponding to the localization length of spinless fermions.