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We report the observations of inelastic light scattering by the elementary excitations of the one-dimensional electron gas. The quantum wires are fabricated from a modulation-doped single GaAs/Al Gai, As quantum well by electron-beam lithography and shallow electron-cyclotronresonance reactive-ion etching. In spectra of intersubband excitations we observe a clear separation of spin-density and charge-density collective modes. The splitting associated with the lateral potential of the wires is also seen in transitions to states of the first excited level of the parent quantum well. Determinations of electron-electron interactions in intersubband excitations of the one-dimensional electron gas show large corrections due to the exchange terms (or vertex corrections) that represent the excitonic binding of the particle-hole pairs. Narrow quantum wires of width less than 100 nm are currently obtained by state-of-the-art semiconductor nanofabrication technologies. ' The behavior of free carriers in such nanostructures presents fundamental characteristics due to their motional confinement to one dimension. Electron-electron interactions in one dimension are expected to change drastically both elementary excitations and screening, and the question of whether the onedimensional (1D) electron system is better described as a Fermi liquid or as a Luttinger liquid is still open. ' Intersubband transitions and elementary excitations of the 1D electron gas have been studied by far-infrared (FIR) optical absorption ' and inelastic light scattering. ' FIR measurements can detect charge-density excitations (CDE's), if they carry an electrical dipole moment. s s io In contrast, inelastic light scattering experiments are specially well suited to observe CDE's, ' spin-density excitations (SDE's), ' and single-particle excitations (SPE's), r s i2 which can be identified by simple polarization selection rules.The observation of spin-density excitations that are well separated from the single-particle continuum reveals the strength of vertex corrections (or excitonic shifts) due to exchange terms of the Coulomb interaction in 2D systems. ' These terms represent the excitonic binding of the particle-hole pair states in intersubband excitations.The strength of the exchange interaction depends strongly on the confinement of the electron gas and on its density. In two dimensions and at very low densities exchange eÃects are predominant over the Hartree terms, whereas in the high-density regime with more than one subband occupied by electrons, SDE's are suppressed.Recent light scattering work in semiconductor quantum wires found indications for an enhancement of excitonic shifts in one dimension.However, in these experiments well-defined intersubband spin-density excitations were not observed in the absence of an external magnetic field and the strength of vertex corrections in one dimension could not be assessed.In this paper we report observations of excitations of the one-dimensional electron gas in GaAs quantum wires by resonant inelast...

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