  In Zeeman spectra of a GaAs-AlGaAs quantum wire array with superlattice
period lp, the zero-field shift is found to increase in steps of (2 pi hbar/
e)lp^{-2} at the cyclotron radius Rc ~lp, lp/2, and lp/3. This shift, caused by
spin-Landau orbit coupling and quantized in units of the flux quantum 2 pi hbar
/e,is a manifestation of the gauge invariance, and the first observation of the
flux quantization in a non-superconducting material.The quantum interference
associated with the phase difference in the quantum barrier scattering is also
reported.
