A Brief Review and Role of Local Field Correction Functions in Condensed Matter Physics

Editorial Board PCSS Journal; А.М. Вора

doi:10.15330/pcss.26.3.500-519

Автор(и)

А.М. Вора Гуджаратський університет, Ахмедабад, Гуджарат, Індія

DOI:

https://doi.org/10.15330/pcss.26.3.500-519

Ключові слова:

однорідний електронний газ, корекції функції локального поля (КЛПФ), дифузійний метод Монте-Карло (DMC), теорія діелектричного екранування

Анотація

У огляді висвітлюється важливість спектру коригувальних функцій локального поля (LFCFs) у фізиці конденсованих станів, які зустрічаються у різних літературних оглядах. Загалом, у літературі виявлено 40 різних форм LFCFs. Наведено основні параметри кожної функції LFCFs разом із коротким описом. Головна мета – виділити різні корекції локального поля, опубліковані в літературі починаючи з 1957 року та надати науковій спільноті повну довідкову інформацію.

Посилання

L. V. Tarasov, Basic Concepts of Quantum Mechanics (Mir Publications, Moscow, 1983).

W. A. Harrison, Elementary Electronic Structure (World Scientific, Singapore, 1999).

W. A. Harrison, Pseudopotentials in the Theory of Metals (W. A. Benjamin, Inc., New York, 1966).

V. Heine and D. Weaire, in Solid State Physics, Vol. 24, Eds. H. Ehrenreich, F. Seitz and D. Turnbull (Academic Press, New York, 1970), p. 249.

L. I. Yastrebov and A. K. Katsnelson, Foundations of One-Electron Theory of Solids (Mir Publications, Moscow, 1987).

D. J. Singh and L. Nordström, Planewaves, Pseudopotentials and the LAPW Method (Springer, USA, 2006).

S. K. Srivastava, Pseudopotential in Physics and Chemistry of Solids (TPI Printers, Allahabad, 1977).

M. Meyer and V. Pontikis, Computer Simulation in Materials Science-Interatomic Potentials, Simulation Techniques and Applications, Eds. (Springer Science+Business Media, B.V., Dordrecht, 1991).

T. E. Faber, Theory of Liquid Metals (Cambridge Univ. Press, Cambridge, 1972).

M. Shimoji, Liquid Metals (Academic Press, London, 1977).

J. Hafner, From Hamiltonians to Phase Diagrams (Springer-Verlag Berlin Heidelberg New York, 1987).

G. Mahan, Many-Particle Physics, 2nd Ed. (Plenum, New York, 1990).

D. Pines and P. Nozières, The Theory of Quantum Liquids, Vol. I (Benjamin, New York, 1966).

L. V. Keldysh, D. A. Kirzhnitz and A. A. Maradudin, The Dielectric Function of Condensed Systems (Elsevier Science Publishers B.V., North-Holland, 1989).

F. J. Rogers and H. E. Dewitt, Strongly Coupled Plasma Physics, NATO ASI Series (Plenum Press, New York and London, 1986).

S. Lundqvist and N. H. March, Theory of the Inhomogeneous Electron Gas (Springer Science+Business Media, LLC, New York, 1983).

H. Smith, The Lindhard Function and the Teaching of Solid State Physics, Phys. Scr., 28(3), 287 (1983); https://doi.org/10.1088/0031-8949/28/3/005.

D. Davis, Thomas-Fermi Screening in One Dimension, Phys. Rev. B, 7(1), 129 (1973); https://doi.org/10.1103/PhysRevB.7.129.

H. Haug and S. W. Koch, Quantum theory of the optical and electronic properties of semiconductors (World Scientific, Singapore, 2004).

J. Lindhard, Kogl. Dan. On The Properties of a Gas of Charged Particles, Mat. Fys. Medd. 28 (8), 1 (1954); https://gymarkiv.sdu.dk/MFM/kdvs/mfm%2020-29/mfm-28-8.pdf.

S. H. Vosko and L. Wilk, A Comparison of Self-Interaction-Corrected Local Correlation Energy Functionals, J. Phys. B: Atom. Mol. Phys., 16 (20), 3687 (1983); https://doi.org/10.1088/0022-3700/16/20/006.

J. Bardeen, Conductivity of Monovalent Metal, Phys. Rev., 52(7), 688 (1937); https://doi.org/10.1103/PhysRev.52.688.

H. Ehrenreich, M. H. Cohen, Self-Consistent Field Approach to the Many-Electron Problem, Phys. Rev. 115, 786 (1959); https://doi.org/10.1098/rspa.1957.0106.

H. Hubbard, The description of collective motions in terms of many-body perturbation theory, Proc. Roy. Soc. A240, 539 (1957); https://doi.org/10.1098/rspa.1957.0106.

J. Hubbard, The description of collective motions in terms of many-body perturbation theory. II. The correlation energy of a free-electron gas, Proc. R. Soc. (London) A243, 336 (1958); https://doi.org/10.1098/rspa.1958.0003.

L. J. Sham, A calculation of the phonon frequencies in sodium, Proc. R. Soc. (London) A283, 33 (1965); https://doi.org/10.1098/rspa.1965.0005.

D. J. Geldert, S. H. Vosko, The screening function of an interacting electron gas, Can. J. Phys. 44, 2137 (1966); https://doi.org/10.1139/p66-174.

W. Kohn, L. J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev. 140, A1133 (1965); https://doi.org/10.1103/PhysRev.140.A1133.

L. Kleinman, New Approximation for Screened Exchange and the Dielectric Constant of Metals, Phys. Rev. 160, 585 (1967); https://doi.org/10.1103/PhysRev.160.585.

L. Kleinman, Exchange and the Dielectric Screening Function, Phys. Rev. 172, 383 (1968); https://doi.org/10.1103/PhysRev.172.383.

N. W. Ashcroft, Electron-ion pseudopotentials in the alkali metals, J. Phys. C: Solid State Phys. 1, 232 (1968); https://doi.org/10.1088/0022-3719/1/1/326.

K.S. Singwi, M. P. Tosi, A. Sjölander, R. H. Land, Electron Correlations at Metallic Densities, Phys. Rev. 176, 589 (1968); https://doi.org/10.1103/PhysRev.176.589.

D. C. Langreth, Approximate Screening Functions in Metals, Phys. Rev. 181, 753 (1969); https://doi.org/10.1103/PhysRev.181.753.

R. W. Shaw, R. Pynn, Optimized model potential: exchange and correlation corrections and calculation of magnesium phonon spectrum, J. Phys. C: Solid State Phys. 2, 2071 (1969); https://doi.org/10.1088/0022-3719/2/11/321.

K.S. Singwi, A. Sjölander, M.P. Tosi, R.H. Land, Electron Correlations at Metallic Densities. IV, Phys. Rev. B1, 1044 (1970); https://doi.org/10.1103/PhysRevB.1.1044.

R. W. Shaw, Exchange and correlation in the theory of simple metals, J. Phys. C: Solid State Phys. 3, 1140 (1970); https://doi.org/10.1088/0022-3719/3/5/027.

R. W. Shaw, in Solid State Physics: Advances in Research and Application, Eds. H. Ehrenreich, F. Seitz, D. Turnbull, Vol. 24, Academic Press, New York (1970).

F. Toigo, T. O. Woodruff, Calculation of the Dielectric Function for a Degenerate Electron Gas with Interactions. I. Static Limit, Phys. Rev. B2, 3958 (1970); https://doi.org/10.1103/PhysRevB.2.3958.

W. F. King, P. H. Cutter, A first principle pseudopotential calculation of the elastic shear constants of magnesium, J. Phys. Chem. Sol. 32, 761 (1971); https://doi.org/10.1016/0022-3697(71)90038-2.

W. F. King, P. H. Cutter, Lattice Dynamics of Beryllium from a First-Principles Nonlocal Pseudopotential Approach, Phys. Rev. B2, 1733 (1970); https://doi.org/10.1103/PhysRevB.2.1733.

W. F. King, P. H. Cutter, Lattice Dynamics of Magnesium from a First-Principles Nonlocal Pseudopotential Approach, Phys. Rev. B3, 2485 (1971); https://doi.org/10.1103/PhysRevB.3.2485.

A. W. Overhouser, Simplified Theory of Electron Correlations in Metals, Phys. Rev. B3, 1888 (1971); https://doi.org/10.1103/PhysRevB.3.1888.

S. D. Mahanti, T. P. Das, Theory of Knight Shifts and Relaxation Times in Alkali Metals-Role of Exchange Core Polarization and Exchange-Enhancement Effects, Phys. Rev. B3, 1599 (1971); https://doi.org/10.1103/PhysRevB.3.1599.

P. Vashishta, K. S. Singwi, Electron Correlations at Metallic Densities. V, Phys. Rev. B6, 875 (1972); https://doi.org/10.1103/PhysRevB.6.875.

S. C. Jain, M. Jain, On the calculation of the dielectric function of an interacting electron gas, Phys. Lett. A44, 49 (1973); https://doi.org/10.1016/0375-9601(73)90955-9.

K. N. Pathak and P. Vashishta, Electron Correlations and Moment Sum Rules, Phys. Rev. B7, 3649 (1973); https://doi.org/10.1103/PhysRevB.7.3649.

A. A. Kugler, Theory of the local field correction in an electron gas, J. Stat. Phys. 12, 35 (1975); https://doi.org/10.1007/BF01024183.

S. K. Srivastava, Pseudopotential in metals and alloys, J. Phys. Chem. Sol. 38, 451 (1977); https://doi.org/10.1016/0022-3697(77)90177-9.

D. N. Tripathy and S. S. Mandal, Calculation of the dielectric function for an electron liquid, Phys. Rev. B16, 231 (1977); https://doi.org/10.1103/PhysRevB.16.231.

R. Taylor, A simple, useful analytical form of the static electron gas dielectric function, J. Phys. F: Metal Phys. 8, 1699 (1978); https://doi.org/10.1088/0305-4608/8/8/011.

K. Utsumi, S. Ichimaru, Dielectric formulation of strongly coupled electron liquids at metallic densities. IV. Static properties in the low-density domain and the Wigner crystallization, Phys. Rev. B24, 3220 (1981); https://doi.org/10.1103/PhysRevB.24.3220.

J. E. Alvarellos, F. Flores, Local field corrections for the dielectric function of an electron liquid, J. Phys. F: Met. Phys. 14, 1673 (1984); https://doi.org/10.1088/0305-4608/14/7/015.

A. B. Bhatia, R. N. Singh, Phonon dispersion in metallic glasses: A simple model, Phys. Rev. B31, 4751 (1985); https://doi.org/10.1103/PhysRevB.31.4751.

I. Nagy, Analytic expression for the static local field correlation function, J. Phys. C: Solid State Phys. 19, L481 (1986); https://doi.org/10.1088/0022-3719/19/22/002.

B. Farid, V. Heine, G. E. Engel, I. S. Robertson, Phys. Rev. B48, 11602 (1993); https://doi.org/10.1103/PhysRevB.48.11602.

A. Gold and L. Calmels, Correlation in Fermi liquids: Analytical results for the local-field correction in two and three dimensions, Phys. Rev. B48, 11622 (1993); https://doi.org/10.1103/PhysRevB.48.11622.

A. Gold, Local-field correction for the electron gas: Effects of the valley degeneracy, Phys. Rev. B50, 4297 (1994); https://doi.org/10.1103/PhysRevB.50.4297.

A. Gold, The local-field correction for the interacting electron gas: many-body effects for unpolarized and polarized electrons, Z. Phys. B 103, 491 (1997); https://doi.org/10.1007/s002570050404.

G. Ortiz, P. Ballone, Correlation energy, structure factor, radial distribution function, and momentum distribution of the spin-polarized uniform electron gas, Phys. Rev. B50, 1391 (1994); https://doi.org/10.1103/PhysRevB.50.1391.

S. Moroni, D. M. Ceperley, G. Senatore, Static Response and Local Field Factor of the Electron Gas Phys. Rev. Lett. 75, 689 (1995); https://doi.org/10.1103/PhysRevLett.75.689.

J. L. Bretonnet and M. Boulahbak, Semianalytical form for the local-field correction, Phys. Rev. B53, 6859 (1996); https://doi.org/10.1103/PhysRevB.53.6859.

A. Sarkar, D.S. Sen, S. Haldar, D. Roy, Static Local Field Factor for Dielectric Screening Function of Electron Gas at Metallic and Lower Densities, Mod. Phys. Lett. B12, 639 (1998); https://doi.org/10.1142/S0217984998000755.

S. Hellal, J. G. Gasser, A. Issolah, Phys. Rev. B68, 094204 (2003); https://doi.org/10.1103/PhysRevB.68.094204.

A. Sarkar, S. Haldar, D. Roy, D. Sen, Static Local Field Factor and Ground State Properties of Interacting Electron Gas, Acta Phys. Pol. A106, 497 (2004).

T. Dornheim, J. Vorberger, S. Groth, N. Hoffmann, Zh. A. Moldabekov and M. Bonitz, The static local field correction of the warm dense electron gas: An ab initio path integral Monte Carlo study and machine learning representation, J. Chem. Phys. 151, 194104 (2019); https://doi.org/10.1063/1.5123013.

T. Dornheim, M. Böhme, B. Militzer and J. Vorberger, Ab initio path integral Monte Carlo approach to the momentum distribution of the uniform electron gas at finite temperature without fixed nodes, arXiv:2103.08206 (2021).

T. Dornheim, A. Cangi, K. Ramakrishna and M. Böhme, Effective Static Approximation: A Fast and Reliable Tool for Warm-Dense Matter Theory, Phys. Rev. Lett. 125, 235001 (2020); https://doi.org/10.1103/PhysRevLett.125.235001.

C. A. Kukkonen and K. Chen, Insights into the Electron-Electron Interaction from Quantum Monte Carlo Calculations, arXiv:2101.10508v1 (2021); https://doi.org/10.48550/arXiv.2101.10508

C.R. Leavens, A.H. MacDonald, R. Taylor, A. Ferraz and N. H. March, Finite Mean-Free-Paths and the Electrical Resistivity of Liquid Simple Metals, Phys. Chem. Liq. 11, 115 (1981); https://doi.org/10.1080/00319108108079103.

Z. H. Levine and S. G. Louie, New model dielectric function and exchange-correlation potential for semiconductors and insulators, Phys. Rev. B25, 6310 (1982); https://doi.org/10.1103/PhysRevB.25.6310.

N. Singh and S. Prakash, Phonon Frequencies and Cohesive Energies of Copper, Silver, and Gold, Phys. Rev. B8, 5532 (1973); https://doi.org/10.1103/PhysRevB.8.5532.

K. S. Singwi, K. Skold and M. P. Tosi, Collective Motions in Classical Liquids, Phys. Rev. A1, 454 (1970); https://doi.org/10.1103/PhysRevA.1.454.

L. Hedin, B. I. Lundquist and S. Lundquist, Beyond the One-Electron Approximation: Density of States for Interacting Electrons, Nat. Bur. Stand. (US) Spec. Publ. 323, 246 (1971); https://doi.org/10.6028/jres.074A.032.

D. J. W. Geldart and R. Taylor, Wave-number dependence of the static screening function of an interacting electron gas. II. Higher-order exchange and correlation effects, Can. J. Phys. 48, 167 (1970); https://doi.org/10.1139/p70-023.

D. Ceperley and B. J. Alder, The low density phases of the electron gas, J. de Physique C7, 295 (1980); http://dx.doi.org/10.1051/jphyscol:1980744.

D. Ceperley and B. J. Alder, Ground State of the Electron Gas by a Stochastic Method, Phys. Rev. Lett. 45, 566 (1980); https://doi.org/10.1103/PhysRevLett.45.566.

G.G. Spink, R.J. Needs and N.D. Drummond, Quantum Monte Carlo study of the three-dimensional spin-polarized homogeneous electron gas, Phys. Rev. B88, 085121 (2013); https://doi.org/10.1103/PhysRevB.88.085121.

G. R. Schleder, A. C. M. Padilha, C. M. Acosta, M. Costa and A. Fazzio, From DFT to machine learning: recent approaches to materials science–a review, NPJ Comp. Mater. 5, 1 (2019); https://doi.org/10.1088/2515-7639/ab084b.

G. Onida, L. Reining, and A. Rubio, Electronic excitations: density-functional versus many-body Green’s-function approaches, Rev. Mod. Phys. 74, 601 (2002); https://doi.org/10.1103/RevModPhys.74.601.

Z. Qian and G. Vignale, Lifetime of a quasiparticle in an electron liquid, Phys. Rev. B71, 075112 (2005); https://doi.org/10.1103/PhysRevB.71.075112.

C. A. Ullrich, Time-Dependent Density-Functional Theory: Concepts and Applications, Oxford University Press, UK (2012); https://doi.org/10.1093/acprof:oso/9780199563029.001.0001.

A. Jain, S. Ping Ong,, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder and K. A. Persson, Commentary: The Materials Project: A materials genome approach to accelerating materials innovation, APL Mater. 1, 011002 (2013); https://doi.org/10.1063/1.4812323.

M. Shishkin and G. Kresse, Implementation and performance of the frequency-dependent GW method within the PAW framework, Phys. Rev. B74, 035101 (2006); https://doi.org/10.1103/PhysRevB.74.035101.

M. Ceriotti, C. Clementi and O. A. von Lilienfeld, Machine learning meets chemical physics, J. Chem. Phys. 154, 160401 (2021); https://doi.org/10.1063/5.0051418.

I. Timrov, N. Marzari and M. Cococcioni, Self-consistent Hubbard parameters from density-functional perturbation theory in the ultrasoft and projector-augmented wave formulations, Phys. Rev. B100, 045141 (2021); https://doi.org/10.1103/PhysRevB.103.045141.

A. Marini, C. Hogan, M. Grüning and D. Varsano, yambo: An ab initio tool for excited state calculations, Comp. Phys. Commun. 180, 1392 (2009); https://doi.org/10.1016/j.cpc.2009.02.003.

C. A. Draxl and J. O. Sofo, Linear optical properties of solids within the full-potential linearized augmented planewave method, Comp. Phys. Commun. 175, 1 (2006); https://doi.org/10.1016/j.cpc.2006.03.005.

S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson and M. C. Payne, First principles methods using CASTEP, Zeitschrift für Kristallographie 220, 567 (2005); https://10.1524_zkri.220.5.567.65075.pdf, https://doi.org/10.1524/zkri.220.5.567.65075.