Coulomb-exchange effects in nanowires with spin splitting due to a radial electric field

We present a theoretical study of Coulomb-exchange interaction for electrons confined in a cylindrical quantum wire and subject to a Rashba-type spin-orbit coupling with radial electric field. The effect of spin splitting on the single-particle band dispersions, the quasiparticle effective mass, and the system's total exchange energy per particle are discussed. Exchange interaction generally suppresses the quasiparticle effective mass in the lowest nanowire sub-band, and a finite spin splitting is found to significantly increase the magnitude of the quasiparticle-mass suppression (by up to 15% in the experimentally relevant parameter regime). In contrast, spin-orbit coupling causes a modest (1%-level) reduction of the magnitude of the exchange energy per particle. Our results shed light on the interplay of spin-orbit coupling and Coulomb interaction in quantum-confined systems, including those that are expected to host exotic quasiparticle excitations.