Static and dynamic correlation functions of a two-dimensional quantum electron fluid

Abstract

In this paper we study the static and dynamic electron density and spin-density correlation functions of a two-dimensional electron fluid in the quantum Singwi-Tosi-Land-Sjölander theory. The static density and spin-density structure factors S(q) and S^~(q) and their corresponding pair-correlation functions g(r) and g^~(r) have been calculated and compared with the available Monte Carlo (MC) simulation data. It is found that the results for S(q) are in good agreement with the MC data except at large values of q for the larger electron density parameter r_s. The pair-correlation function g(r) remains positive in the density range examined (1≤r_s≤8) and matches closely with the MC data except at small separations. The spin-dependent pair-correlation functions g_↑↓(r) and g_↑↑(r) also satisfy the positive-definite condition. The behavior of the dynamic properties studied is found to be qualitatively similar to the three-dimensional case except for the important difference in the behavior of the dynamic structure factor S(q,ω). It is seen that S(q,ω) exhibits a double-peak structure in the intermediate wave-vector region beyond the plasmon cutoff wave vector. We have also calculated the spin-dependent effective dynamic potentials by combining the spin-symmetric and spin-antisymmetric effective dynamic potentials. The results are compared with the classical Singwi-Tosi-Land-Sjölander theory wherever possible.