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大学・研究所にある論文を検索できる 「厳密な励起状態計算のための基礎研究; 全電子混合基底法におけるスピン軌道相互作用&準粒子理論におけるWard恒等式による規格化」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。
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厳密な励起状態計算のための基礎研究; 全電子混合基底法におけるスピン軌道相互作用&準粒子理論におけるWard恒等式による規格化

中嶋 武 横浜国立大学 DOI:info:doi/10.18880/00014614

2022.05.26

概要

At the beginning of the 20th century, quantum mechanics was established and it became possible to make theoretical predictions on various properties of materials. Many theoretical approaches have appeared in order to study physical phenomena. As one of them, the first-principles calculation is the great one which gives the good agreement with various experimental results. This method also has the great advantage that it is applicable to any target calculation compared with other approaches, because the least number of parameters are just needed in its calculation. It is, however, well known that first-principles calculation become more cumbersome with the size of target system. For this reason, it is long-standing subject in first-principles approach to introduce the approximations with reducing the computational cost and still preserving their physical features. This doctoral thesis includes the two studies based on the first-principles calculation, and I tried to introduce new calculation method and theory to solve the above problem in those studies.

Generally, the one-particle effective Schrödinger equation is taken as first-principles in quantum mechanics, and there are several calculation methods relying on the oneparticle picture; especially, this doctoral thesis is based on density functional theory (DFT) and many-body Green’s function which are famous theories[3–8]. DFT is developed by P. Hohenberg, W. Kohn, and L. J. Sham mainly, and their calculation results are widely applied for much more sophisticated calculations including the Green’s function approach (W. Kohn was awarded Nobel Prize in Chemistry in 1998 for developing DFT). These theories have been applied to calculate several physical phenomena such as stable structures, excitation energies, transition matrices related to photo absorptions, direct and inverse photoemission, etc.

Photoemission, inverse photoemission, and photo absorption in optical experiments are useful to obtain information on electronic states of materials (see Fig. 1.1)[9]. In a direct photoemission experiment, the final state on the material has one hole which was originally occupied by a photoelectron. Since the energy and momentum conservation laws are satisfied in the direct photoemission process among the photoelectron, the photoelectron gives the excitation energy and the energy level information of occupied states. On the other hand, in a similar way, inverse photoemission gives the excitation energy and the energy level information of unoccupied (which is called empty) states. (Notice that photoabsorption is a little different from direct and inverse photoemission, and a more complicated process appears because the excited electrons stay in the material interacting with the holes created in that process.) A hole state created in direct photoemission process is affected by surrounding electrons, so its behavior is different from a bare hole. Therefore, the hole affected by other electrons around the hole is called quasi-hole (see Fig. 1.2). For similar reason, an electron created in inverse photoemission process does not exist as a bare electron in the material, but is affected by surrounding electrons. This electron affected by the surrounding electrons is called quasi-electron (see Fig. 1.2). In this doctoral thesis, I call both quasi-hole and quasi-electron as quasiparticle (QP) for simplicity[10–12]. This QP obeys the one-particle effective Schrödinger equation, which is called the Dyson equation for QP or the QP equation. The QP equation is cumbersome and is difficult to solve without approximations, which means this method needs expensive computational cost in the original procedure. So, the development of good approximations and methods is important to improve discrepancies with experimental spectra and calculated ones. In my first study, I developed a new precise method to calculate the spin-orbit coupling with Kohn-Sham (KS) DFT framework, as published in Annalen der Physik, 531. 9 (2019): 1900060. [1] (see section 1.1 and details are given in chapter 3), and in the second one, I elucidated the validity to normalize quasiparticle wave functions (QPWFs) in QP theory, showed that the Dyson equation can be hermitized under Baym-Kadanoff’s conservation law, and gave the interpretation of the extended KS equation, as published in Physical Review B. 104. 20 (2021): L201116. [2] (see section 1.2 and details are given in chapter 4).

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参考文献

[1] Takeru Nakashima and Kaoru Ohno. “Spin-Orbit Coupling in All-Electron Mixed Basis Approach”. In: Annalen der Physik 531.9 (2019), p. 1900060.

[2] Takeru Nakashima, Hannes Raebiger, and Kaoru Ohno. “Normalization of exact quasiparticle wave functions in the Green’s function method guaranteed by the Ward identity”. In: Physical Review B 104.20 (2021), p. L201116.

[3] Pierre Hohenberg and Walter Kohn. “Inhomogeneous electron gas”. In: Physical review 136.3B (1964), B864.

[4] Walter Kohn and Lu Jeu Sham. “Self-consistent equations including exchange and correlation effects”. In: Physical review 140.4A (1965), A1133.

[5] Ulf Von Barth and Lars Hedin. “A local exchange-correlation potential for the spin polarized case. i”. In: Journal of Physics C: Solid State Physics 5.13 (1972), p. 1629.

[6] Lars Hedin. “New method for calculating the one-particle Green’s function with application to the electron-gas problem”. In: Physical Review 139.3A (1965), A796.

[7] Giancarlo Strinati. “Application of the Green’s functions method to the study of the optical properties of semiconductors”. In: La Rivista del Nuovo Cimento (1978-1999) 11.12 (1988), pp. 1–86.

[8] Gy Csanak, HS Taylor, and Robert Yaris. “Green’s function technique in atomic and molecular physics”. In: Advances in atomic and molecular physics. Vol. 7. Elsevier, 1971, pp. 287–361.

[9] Giovanni Onida, Lucia Reining, and Angel Rubio. “Electronic excitations: density-functional versus many-body Green’s-function approaches”. In: Reviews of modern physics 74.2 (2002), p. 601.

[10] Lev Davidovich Landau. “The theory of a Fermi liquid”. In: Soviet Physics Jetp-Ussr 3.6 (1957), pp. 920–925.

[11] LD Landau. “SOV PHYS JETP”. In: Sov. Phys. JETP 5 (1957), p. 101.

[12] Lev Davidovich Landau and Evgenii Mikhailovich Lifshitz. Course of theoretical physics. Elsevier, 2013.

[13] Leslie L Foldy and Siegfried A Wouthuysen. “On the Dirac theory of spin 1/2 particles and its non-relativistic limit”. In: Physical Review 78.1 (1950), p. 29.

[14] Mark S Hybertsen and Steven G Louie. “Electron correlation and the band gap in ionic crystals”. In: Physical Review B 32.10 (1985), p. 7005.

[15] Mark S Hybertsen and Steven G Louie. “Spin-orbit splitting in semiconductors and insulators from the ab initio pseudopotential”. In: Physical Review B 34.4 (1986), p. 2920.

[16] Giovanni B Bachelet and M Schlüter. “Relativistic norm-conserving pseudopotentials”. In: Physical Review B 25.4 (1982), p. 2103.

[17] Shota Ono et al. “TOMBO: All-electron mixed-basis approach to condensed matter physics”. In: Computer physics communications 189 (2015), pp. 20–30.

[18] Mark S Hybertsen and Steven G Louie. “First-principles theory of quasiparticles: calculation of band gaps in semiconductors and insulators”. In: Physical review letters 55.13 (1985), p. 1418.

[19] RW Godby, M Schlüter, and LJ Sham. “Accurate exchange-correlation potential for silicon and its discontinuity on addition of an electron”. In: Physical review letters 56.22 (1986), p. 2415.

[20] Rex W Godby, Michael Schlüter, and LJ Sham. “Self-energy operators and exchange-correlation potentials in semiconductors”. In: Physical Review B 37.17 (1988), p. 10159.

[21] Patrick Rinke et al. “Combining GW calculations with exact-exchange densityfunctional theory: an analysis of valence-band photoemission for compound semiconductors”. In: New Journal of Physics 7.1 (2005), p. 126.

[22] John Clive Ward. “An identity in quantum electrodynamics”. In: Physical Review 78.2 (1950), p. 182.

[23] Yasushi Takahashi. “On the generalized Ward identity”. In: Il Nuovo Cimento (1955-1965) 6.2 (1957), pp. 371–375.

[24] G Strinati, HJ Mattausch, and W Hanke. “Dynamical aspects of correlation corrections in a covalent crystal”. In: Physical Review B 25.4 (1982), p. 2867.

[25] Robert O Jones and Olle Gunnarsson. “The density functional formalism, its applications and prospects”. In: Reviews of Modern Physics 61.3 (1989), p. 689.

[26] L. J. Sham and W. Kohn. “One-particle properties of an inhomogeneous interacting electron gas”. In: Physical Review 145.2 (1966), pp. 561–567. ISSN: 0031899X. DOI: 10.1103/PhysRev.145.561.

[27] Lu J Sham and Michael Schlüter. “Density-functional theory of the energy gap”. In: Physical Review Letters 51.20 (1983), p. 1888.

[28] RW Godby, M Schlüter, and LJ Sham. “Trends in self-energy operators and their corresponding exchange-correlation potentials”. In: Physical Review B 36.12 (1987), p. 6497.

[29] Mark S Hybertsen and Steven G Louie. “Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies”. In: Physical Review B 34.8 (1986), p. 5390.

[30] CS Wang and WE Pickett. “Density-functional theory of excitation spectra of semiconductors: application to Si”. In: Physical review letters 51.7 (1983), p. 597.

[31] WE Pickett and CS Wang. “Local-density approximation for dynamical correlation corrections to single-particle excitations in insulators”. In: Physical Review B 30.8 (1984), p. 4719.

[32] Klaus Capelle and Vivaldo L Campo Jr. “Density functionals and model Hamiltonians: Pillars of many-particle physics”. In: Physics Reports 528.3 (2013), pp. 91–159.

[33] Victor L Moruzzi, James F Janak, and Arthur R Williams. Calculated electronic properties of metals. Elsevier, 2013.

[34] Leonard Kleinman. “Exchange density-functional gradient expansion”. In: Physical Review B 30.4 (1984), p. 2223.

[35] Axel D Becke. “Density-functional exchange-energy approximation with correct asymptotic behavior”. In: Physical review A 38.6 (1988), p. 3098.

[36] DM Bylander, Leonard Kleinman, and Seongbok Lee. “Self-consistent calculations of the energy bands and bonding properties of B 12 C 3”. In: Physical Review B 42.2 (1990), p. 1394.

[37] A Seidl et al. “Generalized Kohn-Sham schemes and the band-gap problem”. In: Physical Review B 53.7 (1996), p. 3764.

[38] Paul Adrien Maurice Dirac. “The quantum theory of the electron”. In: Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 117.778 (1928), pp. 610–624.

[39] Steven G Louie, Kai-Ming Ho, and Marvin L Cohen. “Self-consistent mixedbasis approach to the electronic structure of solids”. In: Physical Review B 19.4 (1979), p. 1774.

[40] Tsubasa Aoki and Kaoru Ohno. “Accurate quasiparticle calculation of x-ray photoelectron spectra of solids”. In: Journal of Physics: Condensed Matter 30.21 (2018), 21LT01.

[41] Riichi Kuwahara and Kaoru Ohno. “Linearized self-consistent GW approach satisfying the Ward identity”. In: Physical Review A 90.3 (2014), p. 032506.

[42] Riichi Kuwahara, Yoshifumi Noguchi, and Kaoru Ohno. “GW Γ+ Bethe-Salpeter equation approach for photoabsorption spectra: Importance of self-consistent GW Γ calculations in small atomic systems”. In: Physical Review B 94.12 (2016), p. 121116.

[43] Kaoru Ohno, Francesco Mauri, and Steven G Louie. “Magnetic susceptibility of semiconductors by an all-electron first-principles approach”. In: Physical Review B 56.3 (1997), p. 1009.

[44] Kaoru Ohno, Shota Ono, and Tomoharu Isobe. “A simple derivation of the exact quasiparticle theory and its extension to arbitrary initial excited eigenstates”. In: The Journal of chemical physics 146.8 (2017), p. 084108.

[45] Kaoru Ohno, Keivan Esfarjani, and Yoshiyuki Kawazoe. Computational materials science: from ab initio to Monte Carlo methods. Springer, 2018.

[46] Richard Phillips Feynman. “Space-time approach to non-relativistic quantum mechanics”. In: Feynman’s Thesis—A New Approach To Quantum Theory (2005), pp. 71–109.

[47] Julian Schwinger. “On the Green’s functions of quantized fields. I”. In: Proceedings of the National Academy of Sciences 37.7 (1951), pp. 452–455.

[48] Viktor Mikhailovich Galitskii and Arkadii Beinusovich Migdal. “Application of quantum field theory methods to the many body problem”. In: Sov. Phys. JETP 7.96 (1958), p. 18.

[49] Joaquin Mazdak Luttinger and John Clive Ward. “Ground-state energy of a many-fermion system. II”. In: Physical Review 118.5 (1960), p. 1417.

[50] Philippe Nozieres. Theory of interacting Fermi systems. CRC Press, 2018.

[51] Jeffrey Goldstone. “Derivation of the Brueckner many-body theory”. In: Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 239.1217 (1957), pp. 267–279.

[52] John Hubbard. “The description of collective motions in terms of many-body perturbation theory”. In: Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 240.1223 (1957), pp. 539–560.

[53] David Pines. The many-body problem: a lecture note and reprint volume. WA Benjamin, 1962.

[54] Lars Hedin and Stig Lundqvist. “Effects of electron-electron and electronphonon interactions on the one-electron states of solids”. In: Solid state physics. Vol. 23. Elsevier, 1970, pp. 1–181.

[55] DNA Zubarev. “Double-time Green functions in statistical physics”. In: Soviet Physics Uspekhi 3.3 (1960), p. 320.

[56] Gian-Carlo Wick. “The evaluation of the collision matrix”. In: Physical review 80.2 (1950), p. 268.

[57] Bengt Holm and Ulf von Barth. “Fully self-consistent GW self-energy of the electron gas”. In: Physical Review B 57.4 (1998), p. 2108.

[58] Ferdi Aryasetiawan and Olle Gunnarsson. “The GW method”. In: Reports on Progress in Physics 61.3 (1998), p. 237.

[59] Murray Gell-Mann and Francis Low. “Bound states in quantum field theory”. In: Physical Review 84.2 (1951), p. 350.

[60] C Bloch and C De Dominicis. “A DEVELOPMENT OF THE GIBBS POTENTIAL OF A QUANTIC SYSTEM COMPOSED OF A LARGE NUMBER OF PARTICLES”. In: Nuclear Phys. 7 (1958).

[61] M Gaudin. “A SIMPLIFIED DEMONSTRATION OF WICK’S THEOREM IN STATISTICAL MECHANICS”. In: Nuclear Phys. 15 (1960).

[62] Alexander L Fetter and John Dirk Walecka. Quantum theory of many-particle systems. Courier Corporation, 2012.

[63] Abraham Klein and Richard Prange. “Perturbation Theory for an Infinite Medium of Fermions”. In: Physical Review 112.3 (1958), p. 994.

[64] Stephen L Adler. “Quantum theory of the dielectric constant in real solids”. In: Physical Review 126.2 (1962), p. 413.

[65] Nathan Wiser. “Dielectric constant with local field effects included”. In: Physical Review 129.1 (1963), p. 62.

[66] Xia Leng et al. “GW method and Bethe–Salpeter equation for calculating electronic excitations”. In: Wiley Interdisciplinary Reviews: Computational Molecular Science 6.5 (2016), pp. 532–550.

[67] Gordon Baym and Leo P Kadanoff. “Conservation laws and correlation functions”. In: Physical Review 124.2 (1961), p. 287.

[68] Gordon Baym. “Self-consistent approximations in many-body systems”. In: Physical review 127.4 (1962), p. 1391.

[69] JM Luttinger. “Fermi surface and some simple equilibrium properties of a system of interacting fermions”. In: Physical Review 119.4 (1960), p. 1153.

[70] Abraham Klein. “Perturbation theory for an infinite medium of fermions. II”. In: Physical Review 121.4 (1961), p. 950.

[71] AJ Layzer. “Properties of the One-Particle Green’s Function for Nonuniform Many-Fermion Systems”. In: Physical Review 129.2 (1963), p. 897.

[72] David Awschalom and Nitin Samarth. “Spintronics without magnetism”. In: Physics 2 (2009), p. 50.

[73] B Merabet et al. “Spin-orbit coupling effect on the electronic structure of Sr2FeHfO6 alloy for spintronics application”. In: Journal of Magnetism and Magnetic Materials 518 (2021), p. 167374.

[74] Charlotte Emma Moore. Atomic energy levels as derived from the analyses of optical spectra. Vol. 1. US Department of Commerce, National Bureau of Standards, 1949.

[75] B Vincent Crist. “Argon implanted into graphite, by XPS”. In: Surface Science Spectra 1.4 (1992), pp. 376–380.

[76] PH Citrin and DR Hamann. “Measurement and calculation of polarization and potential-energy effects on core-electron binding energies in solids: X-ray photoemission of rare gases implanted in noble metals”. In: Physical Review B 10.12 (1974), p. 4948.

[77] Edward B Saloman. “Energy levels and observed spectral lines of ionized argon, Ar II through Ar XVIII”. In: Journal of Physical and Chemical Reference Data 39.3 (2010), p. 033101.

[78] Edward B Saloman. “Energy levels and observed spectral lines of krypton, Kr I through Kr XXXVI”. In: Journal of physical and chemical reference data 36.1 (2007), pp. 215–386.

[79] CD Wagner et al. “Handbook of X-ray photoelectron spectroscopy, PerkinElmer Corp”. In: Eden Prairie, MN 38 (1979).

[80] E Lundgren et al. “Layer dependent core level binding energy shifts: Na, K, Rb and Cs on Al (111)”. In: Surface science 281.1-2 (1993), pp. 83–90.

[81] PM Th M Van Attekum and JM Trooster. “The resolution obtainable in x-ray photoelectron spectroscopy with unmonochromatized Mg Kα radiation”. In: Journal of Electron Spectroscopy and Related Phenomena 18.1 (1980), pp. 135–143.

[82] W Theis and K Horn. “Temperature-dependent line broadening in core-level photoemission spectra from aluminum”. In: Physical Review B 47.23 (1993), p. 16060.

[83] SBM Hagström et al. “Oxidation of aluminum surfaces studied by synchrotron radiation photoelectron spectroscopy”. In: Physica Scripta 16.5-6 (1977), p. 414.

[84] L Ley et al. “Initial stages in the formation of PtSi on Si (111) as followed by photoemission and spectroscopic ellipsometry”. In: Thin Solid Films 270.1-2 (1995), pp. 561–566.

[85] GM Ingo et al. “X-ray photoelectron spectroscopy investigation on the chemical structure of amorphous silicon nitride (a-SiN x)”. In: Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films 7.5 (1989), pp. 3048–3055.

[86] M Taniguchi et al. “Valence band and core-level photoemission spectra of black phosphorus single crystals”. In: Solid State Communications 45.2 (1983), pp. 59–61.

[87] A Barrie, IW Drummond, and QC Herd. “Correlation of calculated and measured 2p spin-orbit splitting by electron spectroscopy using monochromatic x-radiation”. In: Journal of Electron Spectroscopy and Related Phenomena 5.1 (1974), pp. 217–225.

[88] RF Lake and Harold Warris Thompson. “The photoelectron spectra of some molecules containing the C≡ N group”. In: Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 317.1529 (1970), pp. 187–198.

[89] AB Cornford et al. “Photoelectron spectra of the halogens”. In: The Journal of Chemical Physics 54.6 (1971), pp. 2651–2657.

[90] RA Pollak et al. “Evolution of Core States from Energy Bands in the 4 d 5 s 5 p Region from Pd to Xe”. In: Physical Review Letters 29.5 (1972), p. 274.

[91] Russell D Johnson III et al. “NIST Computational Chemistry Comparison and Benchmark Database, NIST Standard Reference Database Number 101, Release 19, April 2018”. In: URL http://cccbdb. nist. gov/. Accessed March 05th (2019).

[92] Bernd A Heß et al. “A mean-field spin-orbit method applicable to correlated wavefunctions”. In: Chemical Physics Letters 251.5-6 (1996), pp. 365–371.

[93] Ulf von Barth and Bengt Holm. “Self-consistent GW 0 results for the electron gas: Fixed screened potential W 0 within the random-phase approximation”. In: Physical Review B 54.12 (1996), p. 8411.

[94] F Bechstedt et al. “Compensation of dynamical quasiparticle and vertex corrections in optical spectra”. In: Physical review letters 78.8 (1997), p. 1528.

[95] R Del Sole and Raffaello Girlanda. “Optical properties of solids within the independent-quasiparticle approximation: Dynamical effects”. In: Physical Review B 54.20 (1996), p. 14376.

[96] AB Migdal. “The momentum distribution of interacting Fermi particles”. In: Soviet Phys. JETP 5 (1957).

[97] Falco Hüser, Thomas Olsen, and Kristian S Thygesen. “Quasiparticle GW calculations for solids, molecules, and two-dimensional materials”. In: Physical Review B 87.23 (2013), p. 235132.

[98] Takao Kotani, Mark Van Schilfgaarde, and Sergey V Faleev. “Quasiparticle self-consistent G W method: A basis for the independent-particle approximation”. In: Physical Review B 76.16 (2007), p. 165106.

[99] Fabio Caruso et al. “Self-consistent G W: All-electron implementation with localized basis functions”. In: Physical Review B 88.7 (2013), p. 075105.

[100] John Robert Schrieffer. Theory of superconductivity. CRC press, 2018.

[101] Philip M Morse and Herman Feshbach. “Methods of theoretical physics”. In: American Journal of Physics 22.6 (1954), pp. 410–413.

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