Spin Polarization of the Uniform Three-Dimensional Electron Gas

Author(s)
H. Van Cong

ABSTRACT

A simple-and-analytic form for total energy (or ground-state energy) in the uniform three-dimensional electron gas, expressed as a function of any Wigner-Seitz radius*r*_{s} and relative spin polarization ζ is obtained with a very good accuracy of 0.036% from the Stoner model and our interpolation between high-and-low density limits with use of a two-point approach for the correlation energy and spin stiffness at *r*_{s} = 1 and 70. This suggests a satisfactory desciption of some physical properties such as: paramagnetic-ferromagnetic phase transition and thermodynamic-and-optical phenomena.

A simple-and-analytic form for total energy (or ground-state energy) in the uniform three-dimensional electron gas, expressed as a function of any Wigner-Seitz radius

KEYWORDS

Electron Gas, Correlation Energy; Spin Stiffness, Total Energy, Spin Susceptibility, Paramagnetic-and-Ferromagnetic Phase Transitions, Wigner States

Electron Gas, Correlation Energy; Spin Stiffness, Total Energy, Spin Susceptibility, Paramagnetic-and-Ferromagnetic Phase Transitions, Wigner States

Cite this paper

nullH. Cong, "Spin Polarization of the Uniform Three-Dimensional Electron Gas,"*Journal of Modern Physics*, Vol. 2 No. 9, 2011, pp. 1017-1023. doi: 10.4236/jmp.2011.29122.

nullH. Cong, "Spin Polarization of the Uniform Three-Dimensional Electron Gas,"

References

[1] E. P. Wigner, “On the Interaction of Electrons in Metal,” Physical Review, Vol. 46, No. 11, 1934, pp. 1002-1011. doi:10.1103/PhysRev.46.1002

[2] M. Gell-Mann and K. A. Bruecker, “Correlation Energy of an Electron Gas at High Density,” Physical Review, Vol. 106, No. 2, 1957, pp. 364-368. doi:10.1103/PhysRev.106.364

[3] R. A. Coldwell-Horsfall and A. A. Maradudin, “Zero- Point Energy of an Electron Lattice,” Journal of Mathe-matical Physics, Vol. 1, No.5, 1960, pp. 395-405. doi:10.1063/1.1703670

[4] D. M. Ceperley and B. J. Alder, “Ground State of the Electron Gas by a Stochastic Method,” Physical Review Letters, Vol. 45, No. 7, 1980, pp. 566-569. doi:10.1103/PhysRevLett.45.566

[5] S. H. Vosko, L. Wilk and M. Nusair, “Accurate Spin- Dependent Electron Liquid Correlation Energies for Local Spin Density Calculations: a Critical Analysis,” Canadian Journal of Physics, Vol. 58, 1980, pp. 1200- 1211.

[6] J. P. Perdew and A. Zunger, “Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems,” Physical Review B, Vol. 23, No. 10, 1981, pp. 5048-5079. doi:10.1103/PhysRevB.23.5048

[7] S. Ichimaru, “Strongly Coupled Plasmas: High-Density Classical Plasmas and Degenerate Electron Liquids,” Re-view of Modern Physics, Vol. 54, No. 4, 1982, pp. 1017- 1059.

[8] J. P. Perdew and Y. Wang, “Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy,” Physical Review B, Vol. 45, No. 23, 1992, pp. 13244-13249. doi:10.1103/PhysRevB.45.13244

[9] H. Van Cong, “About a Simple Expression for the Ho-mogeneous Electron Gas Correlation Enery, Accurate at Any Electron Density and Relative Spin Polarization, and Its Applications,” Physica Status Solidi B, Vol. 205, 1998, pp. 543-552. doi:10.1002/(SICI)1521-3951(199802)205:2<543::AID-PSSB543>3.0.CO;2-U

[10] F. H. Zong, C. Lin and D. M. Ceperley, “Spin Polarization of the Low-Density Three-Dimensional Electron Gas,” Physical Review E, Vol. 66, No. 3, 2002, Article ID: 036703. doi:10.1103/PhysRevE.66.036703

[11] J. Sun, J. P. Perdew and M. Seidl, “Correlation Energy of the Uniform Electron Gas from an Interpolation between High- and Low-Density Limits,” Physical Review B, Vol. 81, No. 8, 2010, Article ID: 085123. doi:10.1103/PhysRevB.81.085123

[12] N. H. March, “Kinetic and Potential Energies of an Elec-tron Gas,” Physical Review, Vol. 110, No. 3, 1958, pp. 604-605. doi:10.1103/PhysRev.110.604

[13] H. Van Cong, “Bandgap Changes in Excited Intrinsic (Heavily Doped) Si and Ge,” Physica B, Vol. 405, No. 4, 2010, pp. 1139-1149. doi:10.1016/j.physb.2009.11.016

[14] H. Stupp, M. Hornung, M. Lakner, O. Madel and H. V. L?hneysen, “Possible Solution of the Conductibility Ex-ponent Puzzle for the Metal-Insulator Transition in Heavily Doped Uncompensated Semiconductors,” Physical Review Letters, Vol. 71, No. 16, 1993, pp. 2634-2637. doi:10.1103/PhysRevLett.71.2634

[1] E. P. Wigner, “On the Interaction of Electrons in Metal,” Physical Review, Vol. 46, No. 11, 1934, pp. 1002-1011. doi:10.1103/PhysRev.46.1002

[2] M. Gell-Mann and K. A. Bruecker, “Correlation Energy of an Electron Gas at High Density,” Physical Review, Vol. 106, No. 2, 1957, pp. 364-368. doi:10.1103/PhysRev.106.364

[3] R. A. Coldwell-Horsfall and A. A. Maradudin, “Zero- Point Energy of an Electron Lattice,” Journal of Mathe-matical Physics, Vol. 1, No.5, 1960, pp. 395-405. doi:10.1063/1.1703670

[4] D. M. Ceperley and B. J. Alder, “Ground State of the Electron Gas by a Stochastic Method,” Physical Review Letters, Vol. 45, No. 7, 1980, pp. 566-569. doi:10.1103/PhysRevLett.45.566

[5] S. H. Vosko, L. Wilk and M. Nusair, “Accurate Spin- Dependent Electron Liquid Correlation Energies for Local Spin Density Calculations: a Critical Analysis,” Canadian Journal of Physics, Vol. 58, 1980, pp. 1200- 1211.

[6] J. P. Perdew and A. Zunger, “Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems,” Physical Review B, Vol. 23, No. 10, 1981, pp. 5048-5079. doi:10.1103/PhysRevB.23.5048

[7] S. Ichimaru, “Strongly Coupled Plasmas: High-Density Classical Plasmas and Degenerate Electron Liquids,” Re-view of Modern Physics, Vol. 54, No. 4, 1982, pp. 1017- 1059.

[8] J. P. Perdew and Y. Wang, “Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy,” Physical Review B, Vol. 45, No. 23, 1992, pp. 13244-13249. doi:10.1103/PhysRevB.45.13244

[9] H. Van Cong, “About a Simple Expression for the Ho-mogeneous Electron Gas Correlation Enery, Accurate at Any Electron Density and Relative Spin Polarization, and Its Applications,” Physica Status Solidi B, Vol. 205, 1998, pp. 543-552. doi:10.1002/(SICI)1521-3951(199802)205:2<543::AID-PSSB543>3.0.CO;2-U

[10] F. H. Zong, C. Lin and D. M. Ceperley, “Spin Polarization of the Low-Density Three-Dimensional Electron Gas,” Physical Review E, Vol. 66, No. 3, 2002, Article ID: 036703. doi:10.1103/PhysRevE.66.036703

[11] J. Sun, J. P. Perdew and M. Seidl, “Correlation Energy of the Uniform Electron Gas from an Interpolation between High- and Low-Density Limits,” Physical Review B, Vol. 81, No. 8, 2010, Article ID: 085123. doi:10.1103/PhysRevB.81.085123

[12] N. H. March, “Kinetic and Potential Energies of an Elec-tron Gas,” Physical Review, Vol. 110, No. 3, 1958, pp. 604-605. doi:10.1103/PhysRev.110.604

[13] H. Van Cong, “Bandgap Changes in Excited Intrinsic (Heavily Doped) Si and Ge,” Physica B, Vol. 405, No. 4, 2010, pp. 1139-1149. doi:10.1016/j.physb.2009.11.016

[14] H. Stupp, M. Hornung, M. Lakner, O. Madel and H. V. L?hneysen, “Possible Solution of the Conductibility Ex-ponent Puzzle for the Metal-Insulator Transition in Heavily Doped Uncompensated Semiconductors,” Physical Review Letters, Vol. 71, No. 16, 1993, pp. 2634-2637. doi:10.1103/PhysRevLett.71.2634