Magnetoplasmon excitations and spin density instabilities in an integer quantum Hall system with a tilted magnetic field

We study the magnetoplasmon collective-mode excitations of integer quantum Hall systems in a parabolically confined quantum well nanostructure in the presence of a tilted magnetic field by using the time-dependent Hartree-Fock approximation. For even integer filling, we find that the dispersion of a spin density mode has a magnetoroton minimum at finite wave vectors, at a few times ${10}^6{\mathrm{cm}}^{-1}$ for parallel fields of order 1–10 T, only in the direction perpendicular to the in-plane magnetic field, while the mode energy increases monotonously with wave vector parallel to the in-plane magnetic field. When the in-plane magnetic field is strong enough (well above 10 T),we speculate that this roton minimum may reach zero energy, suggesting a possible second-order phase transition to a state with broken translational and spin symmetries. We discuss the possibility for observing such parallel field-induced quantum phase transitions. We also derive an expression for the dielectric function within the time-dependent Hartree-Fock approximation and include screening effects in our magnetoplasmon calculation. We discuss several exotic symmetry-broken phases that may be stable in finite parallel fields, and propose that the transport anisotropy, observed recently in parallel field experiments, may be due to the formation of a skyrmion stripe phase predicted in our theory. Our predicted anisotropic finite wave-vector suppression, perhaps even a mode softening leading to the quantum phase transition to the anisotropic phase, in the collective spin excitation mode of the wide well system in the direction transverse to the applied parallel magnetic field should be directly experimentally observable via the inelastic light-scattering spectroscopy.