Finite-temperature correlations in a two-dimensional electron gas within a dynamical self-consistent mean-field approximation

• Published in: Physica. E, Low-dimensional systems & nanostructures Low-dimensional systems & nanostructures, 2019-02, Vol.106, p.133-139
• Main Authors: Bhukal, Nisha, Garg, Vinayak, Moudgil, R.K.
• Format: Article
• Language: English
• Subjects: Dynamic exchange-correlation effects; Plasmons; Two-dimensional electron gas
• ISSN: 1386-9477; 1873-1759
• DOI: 10.1016/j.physe.2018.10.016

We have studied the effect of temperature on density-density correlations in a two-dimensional quantum electron gas by using the dynamical Singwi-Tosi-Land-Sjölander (STLS) theory. Static correlation functions viz. structure factor S(q; T), pair-correlation function g(r; T), and static density susceptibility χ(q, 0; T) are calculated over a wide range of temperature and electron density. The inclusion of the dynamics of correlations is found to cause a strong peak in S(q; T) at q ∼ 2.5kF for low densities. Correspondingly, there develops a sharp peak in χ(q, 0; T) that diverges below a critical density. This divergence is interpreted as a precursor of transition to finite-temperature Wigner crystal state. Rise in temperature tends to oppose the crystallization, with critical transition density decreasing with temperature. It is rather found that the dynamical correction to the conventional (static) STLS theory becomes small at a sufficiently high temperature. We have also calculated the plasmon dispersion for the GaAs quantum well based electron system and found that, except at ultra-low densities, agreement with the experimental data of Hirjibehedin et al. is reasonably good. Our results show a red shift in plasmon frequency over the predictions of the STLS and dynamical Hubbard approaches. [Display omitted] •Inclusion of dynamical electron correlations introduces quantitative as well as qualitative changes in the properties of finite-T 2DEG.•Below a critical density, the static density susceptibility diverges at q around 2.5kF, which signals a transition to the finite-T Wigner crystal.•Rising temperature opposes Wigner crystallization, with the critical transition density decreasing fast with temperature.•Above a sufficiently high T, the correction due to dynamical correlations becomes small, and our results approach the static mean-field theory.•Except for the ultra-low densities, the plasmon dispersion agrees nicely with the experimental data of Hirijibehedin et al.•There is seen to be a red shift in plasmon frequency over the predictions of the STLS and dynamical Hubbard approaches.