Study of the RPA pair-correlation function in GaAs-AlGaAs parabolic quantum well wires

Abstract

The ground state intrasubband pair-correlation function for a quasi-one-dimensional electron gas confined in a GaAs-Al x Ga 1−x As parabolic quantum well wire within the Random-Phase Approximation (RPA) is calculated. We have considered two wires with subband energies separation Ω = 2.0 meV and Ω = 2.5 meV. The dependence of the pair-correlation function on the electronic density was studied and the regions where the RPA approach cannot be used were precisely determined.Recently much theoretical work has been done to the understanding of the properties of the plasmon collective excitation in quasi-one-dimensional (Q1D) semiconductor quantum well wires (QWW). In such systems, the electronic motion in the plane perpendicular to the wire extension is quantized in subbands. Experiments performed by Demmel et al. [1] have shown that the subband quantization effects are important to the understanding of the collective motion in quantum wires. Various theoretical methods have been utilized to calculate the collective excitations of electron gas in QWW and among them, the most common is the Random Phase Approximation (RPA). This approach, as is well known, does not consider the local field correction (LFC) and such simplification of the calculation can lead to negative values for the pair correlation function. It is a nonphysical result, since the pair correlation function,g(x), give us the probability of a particle can be observed in a position x if other particle is in the origin of the coordinates, thus the acceptable values for this function must be positive.The choice of the better approach to use for the calculation of the collective excitations is strongly dictated by the electronic density of the system. When the electronic density is sufficiently large the RPA approach describes the system properties satisfactorily. The electronic density from which the RPA gives non-negative values for the pair correlation function for small interparticle separation is defined as the critical density. For density values lower than the critical density the LFC must always be used [2][3][4][5].In the present work we calculate the ground state intrasubband pair-correlation function for a Q1D electron gas present in a GaAs-AlGaAs parabolic quantum well wire. The Q1D electron gas in the parabolic QWW has a quasifree motion in the x-direction and a restrict motion in the plane y − z. Here we assumed that the confinement potential V (y, z) can be written as a sum of the one-dimensional potentials V (y) and V (z). We employed a two-subband model at zero temperature. The confinement potential in the z-direction, V (z), was considered much larger than the parabolic confinement potential V (y) = 1 2 mΩy 2 , where m is the electron effective mass of the semiconductor and Ω is the subband energy separation. Since the confinement in the z-direction is higher than the parabolic confinement, the energy separation between the subbands can be neglected and only the lowest subband in the z-direction is considered be occupied by electrons.The pai...

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