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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 subband, and a finite spin splitting is found to significantly increase the magnitude of the quasiparticle-mass suppression (by upto 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 new 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.