THEORY OF PHONON SHAKEUP EFFECTS ON PHOTOLUMINESCENCE FROM THE WIGNERCRYSTAL IN A STRONG MAGNETIC-FIELD

We develop a method to compute shakeup effects on photoluminescence fr om a strong-magnetic-field-induced two-dimensional Wigner crystal. Onl y localized holes are considered. Our method treats the lattice electr ons and the tunneling electron on an equal footing, and uses a quantum -mechanical calculation of the collective modes that does not depend i n any way on a harmonic approximation. We find that shakeup produces a series of sidebands that may be identified with maxima in the collect ive-mode density of states, and definitively distinguishes the crystal state from a liquid state in the absence of electron-hole interaction . In the presence of electron-hole interaction, sidebands also appear in the liquid state coming from short-range density fluctuations aroun d the hole. However, the sidebands in the liquid state and the crystal state have different qualitative behaviors. We also find a shift in t he main luminescence peak, that is associated with lattice relaxation in the vicinity of a vacancy. The relationship of the shakeup spectrum with previous mean-field calculations is discussed.