Spin-resolved correlations at arbitrary spin polarization and ground state of a quasi-one-dimensional electron gas

• Published in: Physica. E, Low-dimensional systems & nanostructures Low-dimensional systems & nanostructures, 2013-01, Vol.47, p.217-223
• Main Authors: Garg, Vinayak, Moudgil, R.K.
• Format: Article
• Language: English
• Subjects: Condensed matter: structure, mechanical and thermal properties; Cross-disciplinary physics: materials science; rheology; Diffusion in nanoscale solids; Diffusion in solids; Equations of state, phase equilibria, and phase transitions; Exact sciences and technology; Materials science; Nanocrystalline materials; Nanoscale materials and structures: fabrication and characterization; Physics; Quantum wires; Specific phase transitions; Structural transitions in nanoscale materials; Transport properties of condensed matter (nonelectronic)
• ISSN: 1386-9477; 1873-1759
• DOI: 10.1016/j.physe.2012.11.010

We study the spin-resolved correlations at arbitrary spin polarization ζ and the ground state of a quasi-one-dimensional electron gas by using the dynamical self-consistent mean-field theory of Singwi et al. Numerical results are presented for the spin-resolved pair-correlation functions, correlation energies, and ground-state energy at selected ζ and a range of electron density rs. Our results agree nicely with the recent lattice regularized diffusion Monte Carlo simulation data at small rs and ζ. With increasing rs and/or ζ, the spin-resolved correlations become less satisfactory, but the spin-summed quantities show a reasonable agreement, thus implying a cancellation among discrepancies in the components. Interestingly, theory predicts that the like-spin correlation energy becomes little positive for rs>1.5. A comparison between the ground-state energies of the unpolarized and fully polarized spin phases reveals that the exchange–correlations may induce a phase transition to the latter above a critical rs, rsc. Importantly, the transition is in agreement with recent experiments on low density electron quantum wires. However, the stability of partially spin-polarized states could not be ascertained due to difficulty in obtaining the self-consistent density response function beyond a certain rs, preceding rsc. Using the static mean-field theory, we find that the spin-polarization transition is abrupt (i.e., the partially spin-polarized states are energetically unstable) and it occurs at nearly the same rs as in the dynamical approach. In agreement with recent experiments, our study predicts an abrupt spin-polarization transition in an electron quantum wire at low density. The figure below shows the ground-state energy Eg(rs,ζ) vs. density rs at selected spin polarization ζ, along with the simulation data. [Display omitted] ► We have studied spin-resolved correlations and ground-state of a quasi-one-dimensional electron gas. ► Our results show a reasonable agreement with the diffusion Monte Carlo Simulations. ► We find, in agreement with experiments, an abrupt polarization transition below a critical density. ► The same-spin correlation energy can become little positive below a critical density.