Spin and charge distribution symmetry dependence of stripe phases in two-dimensional electron systems confined to wide quantum wells

When a spin-split $N\le 2$ Landau level is half filled, the two-dimensional electron system (2DES) is expected to break the rotational symmetry by forming a unidirectional charge density wave, the so-called stripe phase. The stripes are known to rotate from the ``normal'' ([110]) direction to the ``abnormal'' ($[1\bar{1}0]$) direction when the 2DES density is raised above a critical density. We report a study of the evolution of the stripe phase orientation near Landau level filling factors $\nu = 13/2$ and 15/2 when $E_F$ lies in the two, spin-split, $N = 2$ Landau levels of the symmetric subband (the S2$\uparrow$ and S2$\downarrow$ levels) while the $N = 0$ Landau levels of the antisymmetric subband are fully occupied. We find that when $E_F$ lies in S2$\downarrow$ the stripes are always formed along the ``normal'' direction. But, when $E_F$ lies in the S2$\uparrow$ level, the orientation of the stripes can rotate to be along the ``abnormal'' direction at high densities. At a density where the stripe phase at $\nu = 13/2$ is along the ``abnormal'' direction, we can rotate it back to the normal direction by making the charge distribution asymmetric while keeping the density fixed.