THE HOFSTADTER SPECTRUM OF THE WIGNER CRYSTAL

The Hofstadter spectrum generated by a Wigner crystal (WC), as could b e observed using photoluminescence techniques, is studied. Itinerant h ole 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 particular geometry is proposed tha t involves 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 localized holes reflects th e full Hofstadter spectrum of the lattice.