We observe discrete plasmons in layered 2D electron gases with a large, but finte, number of periods, The twofold degeneracy of plasmon modes with wave numbers in the first Brillouin zone of the infinite system is lifted by the loss of complete periodicity in the finite system. These characteristic discrete plasmon doublets are measured in inelastic-light-scattering spectra of multilayer GaAs/(AlGa)As heterostructures. PACS numbers: 71.45.Gm, 72.15.Nj, 73.40.Lq The charge-density excitations of layered twodimensional electron systems are the subject of current theories that consider plasma modes in semifinite 1,2 and finite 3 systems. Remarkable new effects are predicted for semiconductor superlattices. Giuliani and Quinn 1 proposed a new class of surface plasmons. They are free of Landau damping because quantization of electron motion along the superiattice axis prevents their decay into electron-hole pairs. Wu, Hawrylak, and Quinn 2 have calculated the anisotropy of chargedensity excitations on the lateral surface of a semiconductor superiattice. Jain and Allen 3 have investigated the discrete plasmon spectrum of layered films. Inelastic light scattering, widely used to probe collective excitations in semiconductor superiattice, 4 " 9 has been suggested 1,310 as the experimental method to study the new charge-density excitations. This Letter reports the observation and interpretation of discrete plasmons in inelastic-light-scattering spectra of GaAs/(AlGa)As heterostructures. 11 The discrete modes are observed in multilayers with relatively large number of periods (N == 15), which demonstrates that these effects are essential to plasma oscillations in semiconductor superlattices. In the spectra we measure characteristic plasmon doublets. They are explained by the lifting of the degeneracy of pairs of modes with wave numbers q@ and lirld -q^ in the first Brillouin zone of the superiattice with period d. In the infinite superiattice these modes are degenerate because each 2D electron gas is at a plane of mirror symmetry. The lifting of the degeneracy in finite multilayers is due to the loss of these symmetries.A superiattice of 2D electron gases each with an areal density n embedded in a material with dielectric constant e$ has a plasma frequency 12 " 16 <»p(q,
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