Effects of interaction on field-induced resonances in a confined Fermi liquid

We consider the two-dimensional electron gas confined laterally to a narrow channel by a harmonic potential. As the Zeeman splitting matches the intersubband separation, the nonlocal spin polarization develops a minimum as reported by Frolov et al. [Nature (London) 458, 868 (2009)NATUAS0028-083610.1038/nature07873]. This phenomenon, termed ballistic spin resonance, is due to the degeneracy between the nearest oppositely polarized subbands that is lifted by spin-orbit coupling. We showed that the resonance survives the weak and short-range interaction. The latter detunes it, and as a result shifts the Zeeman splitting at which the minimum in spin polarization occurs. Here this shift is attributed to the absence of the Kohn theorem for the spin-sloshing collective mode. We characterized the shift due to weak interaction qualitatively by analyzing the spin-sloshing mode within the Fermi liquid phenomenology.