Softening of magnetorotons in a semi-infinite Fibonacci superlattice

Calculations of interlayer and intralayer screening of the Coulomb interaction on the softening of bulk and surface magnetoroton modes are presented for density and position modulations of the two-dimensional (2D) electron gas (EG) layers of a semi-infinite quasiperiodic superlattice. It is shown that the softening of these modes is due to an increase in the screening by all other layers of the effective intralayer Coulomb interaction. Numerical results are obtained for variable thickness of a 2DEG layer, the separation between layers and the distance between the surface layer and the top metal gate. The critical values of the structure parameters, determining the interlayer and intralayer screening of the Coulomb interaction, are obtained and used in constructing the phase diagrams showing the separation between the quantum fluid and charge-density wave phases.