Critical Densities for the RPA Approach in Quasi-One-Dimensional Electronic Systems

Abstract

73.21.Hb The intrasubband pair-correlation function, gðxÞ, for a quasi-one-dimensional electron gas confined in a GaAs-Al x Ga 1Àx As rectangular quantum wire within the random-phase approximation (RPA) is calculated for several values of the potential barrier height and wire width. We have studied the dependence of the pair-correlation function on the electronic density, and delimited the regions where the RPA approach gives physically acceptable results, i.e. the electronic density values where gðxÞ possesses positive values for small interparticle separations. The critical density increases with increasing potential barrier height or decreasing wire width. IntroductionIn the last few years, the advent of modern semiconductor growth techniques, such as molecular beam epitaxy (MBE), made possible the fabrication of submicrometre devices. The development of such devices has led to the requirement for more accurate theoretical models for the understanding of their electronic properties. Ultrathin semiconducting wires, namely, quantum well wires (QWW), have been intensively studied. In such systems the electron gas is confined by a quasi-one-dimensional (Q1D) potential barrier that leads the electrons to have a quasi-free motion along the length of the wire, while the motion normal to the wire is quantized in two directions. The first QWW was a GaAs surrounded by Al x Ga 1Àx As fabricated by Petroff et al. [1] following a suggestion of Sakaki [2]. Recent progress in the growth of semiconductor nanostructures has made available wires of good quality. Several effects on the properties of the quasi-one-dimensional electronic gas were studied experimentally from photoluminescence and excitation photoluminescence spectroscopy [3][4][5][6].The many-body effects of the Q1D electron gas present in a QWW structure have motivated a significant number of experimental and theoretical works. Quantum wires in the two-subband limit have been studied experimentally [7], and these results are in agreement with the theoretical conclusions [8]. The collective excitation has been theoretically calculated within different approximation methods, taking into account important effects such as the cross-section geometry of the wire [9, 10], the potential barrier height [11], the multisubband effects [12], etc. The most common method used in the calculations has been the random-phase approximation (RPA), which gives good results when the electronic density is sufficiently high.