Response function of a two-dimensional electron gas in a unidirectional periodic potential

The dynamical density-response function of a periodically modulated two-dimensional electron gas under a perpendicular magnetic field is calculated within the random-phase approximation. It is found that the response function is not only broadened by the periodic potential, it also contains a series of subsingularities at the band edges. The maximum number of subsingularities is 2${\mathit{n}}_{\max }$, where ${\mathit{n}}_{\max }$ is the number of occupied Landau levels (the last level may be partially filled). It is further proposed that light-scattering or electromagnetic absorption experiments can be performed to study these predicted structures.