We have studied the effect of confinement and correlations on the plasmon dispersion in an atom-scale metallic wire by determining the electron density response function. The wire electrons are modelled as comprising a quasi-one-dimensional homogeneous gas, with different transverse confinement models. The response function is calculated by including electron correlations beyond the random-phase approximation within the self-consistent mean-field approach of Singwi et al (1968 Phys. Rev. 176 589). The plasmon dispersion results are found to be in very good agreement with the recent electron-energy-loss spectroscopy measurements by Nagao et al (2006 Phys. Rev. Lett. 97 116802). However, our predictions are found to depend strongly on the nature of the confinement model, the structure of the one-dimensional electronic band and the electron effective mass, implying a crucial role for the wire structure.

The ground-state properties of the quasi-one-dimensional electron gas are determined theoretically within the quantum/dynamical version of the self-consistent mean-field approximation of Singwi, Tosi, Land, and Sjölander ͑the so-called qSTLS approach͒. The transverse motion of electrons is assumed to be confined by a harmonic potential. The calculated static structure factor, pair-correlation function, and correlation energy are compared directly with the recent findings of lattice regularized diffusion Monte Carlo simulation study due to Casula et al. It has been found that the qSTLS results are overall in better agreement with the simulation data than the predictions based upon static mean-field theories. Results for the dynamic local-field correction, dynamic structure factor, and plasmon excitation energy are also reported. The qSTLS approach is found to yield an inadequate description of the dynamic properties; for instance, the dynamic structure factor was seen to become negative over a range of frequencies. Our theoretical predictions, seen in conjunction with similar studies on the three-and two-dimensional electron systems, lead us to conclude that the correlation effects are relatively more pronounced in one-dimensional electron gas.

We have studied correlational properties of quasi-one-dimensional electron gas at finite temperature T by incorporating the dynamics of electron correlations within the quantum version of the self-consistent mean-field approach of Singwi, Tosi, Land, and Sjölander. Static structure factor, pair-correlation function, static density susceptibility, excess kinetic energy, and free correlation energy are calculated covering a wide range of temperature and electron number density. As at absolute zero temperature, the inclusion of dynamics of correlations results in stronger spatial electron correlations, with a pronounced peak in the static structure factor at wave vector q ∼ 3.5k F , which grows further with decreasing electron density. Below a critical density, the static density susceptibility seems to diverge at this value of q, signaling a transition from liquid to the Wigner crystal state-a prediction in qualitative agreement with recent simulations and experiment. However, thermal effects tend to impede crystallization with the consequence that the critical density decreases significantly with rising T. On the other hand, the pair-correlation function at short range exhibits a non-monotonic dependence on T, initially becoming somewhat stronger with rising T and then weakening continuously above a sufficiently high T. The calculated free correlation energy shows a noticeable dependence on T, with its magnitude increasing with increase in T. Further, we have looked into the effect of temperature on the frequency-dependence of dynamic local-field correction factor and the plasmon dispersion. It is found that with rising T the dynamics of correlations weakens, and the plasmon frequency exhibits a blue shift. Wherever interesting, we have compared our results with the lower-order approximate calculations and zero-T quantum Monte Carlo simulations.

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