  The Harper-Hofstadter problem for two-dimensional electron gas with Rashba
spin-orbit coupling subject to periodic potential and perpendicular magnetic
field is studied analytically and numerically. The butterfly-like energy
spectrum, spinor wave functions as well as the spin density and average spin
polarization are calculated for actual parameters of semiconductor structure.
Our calculations show that in two-dimensional electron gas subject to periodic
potential and uniform magnetic field the effects of energy spectrum splitting
caused by large spin-orbit Rashba coupling can be observed experimentally.
