The Hofstadter Spectrum and Photoluminescence

The observability of the Hofstadter spectrum generated by a Wigner crystal using photoluminescence techniques is studied. Itinerant hole geometries are examined, in which a hole may combine directly with electrons in the lattice. It is found that when the effect of lattice distortions of the WC due to interactions with the hole are accounted for, only the largest Hofstadter gaps are observable. To overcome the problems of lattice distortion, a novel geometry is proposed, involving a two layer system with electrons in one layer forming a WC and in the other a full Landau level. It is found that recombination of electrons in the full Landau level with {\it localized} holes reflects the full Hofstadter spectrum of the lattice.