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Spin polarization anisotropy in a narrow spin-orbit-coupled nanowire quantum dot

One and two-electron systems confined in a single and coupled quantum dots defined within a nanowire with a finite radius are studied in the context of spin-orbit coupling effects. Anisotropy of the spin-orbit interaction is discussed in terms of the system geometry and orientation of the external magnetic field vector. We find that there are easy and hard spin polarization axes and in the quantum dot with strong lateral confinement electron spin becomes well defined in spite of the presence of spin-orbit coupling. We present an analytical solution for the one-dimensional limit and study its validity for nanowires of finite radii by comparing the results with a full three-dimensional calculation. The results are also confronted with the recent measurements of the effective Lande factor and avoided crossing width anisotropy in InSb nanowire quantum dots [S. Nadj-Perge et al., Phys. Rev. Lett. 108, 166801 (2012)].