Accurate GW0 band gaps and their phonon-induced renormalization in solids

doi:10.1088/1674-1056/ac0041

中国物理B ›› 2021, Vol. 30 ›› Issue (11): 117101-117101.doi: 10.1088/1674-1056/ac0041

Accurate GW₀ band gaps and their phonon-induced renormalization in solids

Tong Shen(申彤)^1,2, Xiao-Wei Zhang(张小伟)^1,3,†, Min-Ye Zhang(张旻烨)⁴, Hong Jiang(蒋鸿)^4,‡, and Xin-Zheng Li(李新征)^1,2,§

1 Interdisciplinary Institute of Light-Element Quantum Materials, Research Center for Light-Element Advanced Materials, and Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China;
2 State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing 100871, China;
3 International Center for Quantum Materials, Collaborative Innovation Center of Quantum Matter, and School of Physics, Peking University, Beijing 100871, China;
4 Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China

收稿日期:2021-03-16 修回日期:2021-04-30 接受日期:2021-05-12 出版日期:2021-10-13 发布日期:2021-10-13
通讯作者: iao-Wei Zhang, Hong Jiang, Xin-Zheng Li E-mail:willzxw@pku.edu.cn;jianghchem@pku.edu.cn;xzli@pku.edu.cn
基金资助:
Project supported by the National Key Research and Development Program of China (Grand Nos. 2016YFA0300900 and 2017YFA0205003), the National Natual Science Foundation of China (Grant Nos. 11934003, 11774003, and 11634001), the Beijing Natural Science Foundation, China (Grant No. Z200004), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33010400). The computational resources were supported by the High-performance Computing Platform of Peking University, China.

Accurate GW₀ band gaps and their phonon-induced renormalization in solids

Tong Shen(申彤)^1,2, Xiao-Wei Zhang(张小伟)^1,3,†, Min-Ye Zhang(张旻烨)⁴, Hong Jiang(蒋鸿)^4,‡, and Xin-Zheng Li(李新征)^1,2,§

1 Interdisciplinary Institute of Light-Element Quantum Materials, Research Center for Light-Element Advanced Materials, and Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China;
2 State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing 100871, China;
3 International Center for Quantum Materials, Collaborative Innovation Center of Quantum Matter, and School of Physics, Peking University, Beijing 100871, China;
4 Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China

Received:2021-03-16 Revised:2021-04-30 Accepted:2021-05-12 Online:2021-10-13 Published:2021-10-13
Contact: iao-Wei Zhang, Hong Jiang, Xin-Zheng Li E-mail:willzxw@pku.edu.cn;jianghchem@pku.edu.cn;xzli@pku.edu.cn
Supported by:
Project supported by the National Key Research and Development Program of China (Grand Nos. 2016YFA0300900 and 2017YFA0205003), the National Natual Science Foundation of China (Grant Nos. 11934003, 11774003, and 11634001), the Beijing Natural Science Foundation, China (Grant No. Z200004), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33010400). The computational resources were supported by the High-performance Computing Platform of Peking University, China.

摘要/Abstract

摘要： Recent years, huge progress of first-principles methods has been witnessed in calculating the quasiparticle band gaps, with many-body perturbation theory in the GW approximation being the standard choice, where G refers to Green's function and W denotes the dynamically screened Coulomb interaction. Numerically, the completeness of the basis set has been extensively discussed, but in practice far from carefully addressed. Beyond the static description of the nuclei, the electron-phonon interactions (EPIs) are ubiquitous, which cause zero-point renormalization (ZPR) of the band gaps. Therefore, to obtain high quality band gaps, one needs both accurate quasiparticle energies and accurate treatments of EPIs. In this article, we review methods on this. The completeness of the basis set is analyzed in the framework of linearized augmented plane waves, by adding high-energy local orbitals (HLOs). The electron-phonon matrix elements and self-energy are discussed, followed by the temperature dependence of the band gaps in both perturbative and non-perturbative methods. Applications of such an analysis on bulk wurtzite BeO and monolayer honeycomb BeO are given. Adding HLOs widens their GW₀ band gaps by ～ 0.4 eV while ZPR narrows them by similar amount. These influences cancel each other, which explains the fortuitous agreement between experiment and theory when the basis set is incomplete and the EPIs are absent. The phonon-induced renormalization, a term often neglected in calculations of the band gaps, is also emphasized by its large magnitude.

关键词: quasiparticle band gaps, electron-phonon interactions, basis-set completeness, Beryllium oxide

Abstract: Recent years, huge progress of first-principles methods has been witnessed in calculating the quasiparticle band gaps, with many-body perturbation theory in the GW approximation being the standard choice, where G refers to Green's function and W denotes the dynamically screened Coulomb interaction. Numerically, the completeness of the basis set has been extensively discussed, but in practice far from carefully addressed. Beyond the static description of the nuclei, the electron-phonon interactions (EPIs) are ubiquitous, which cause zero-point renormalization (ZPR) of the band gaps. Therefore, to obtain high quality band gaps, one needs both accurate quasiparticle energies and accurate treatments of EPIs. In this article, we review methods on this. The completeness of the basis set is analyzed in the framework of linearized augmented plane waves, by adding high-energy local orbitals (HLOs). The electron-phonon matrix elements and self-energy are discussed, followed by the temperature dependence of the band gaps in both perturbative and non-perturbative methods. Applications of such an analysis on bulk wurtzite BeO and monolayer honeycomb BeO are given. Adding HLOs widens their GW₀ band gaps by ～ 0.4 eV while ZPR narrows them by similar amount. These influences cancel each other, which explains the fortuitous agreement between experiment and theory when the basis set is incomplete and the EPIs are absent. The phonon-induced renormalization, a term often neglected in calculations of the band gaps, is also emphasized by its large magnitude.

Key words: quasiparticle band gaps, electron-phonon interactions, basis-set completeness, Beryllium oxide

中图分类号: (Methods of electronic structure calculations)

71.15.-m

63.20.kd (Phonon-electron interactions) 31.15.A- (Ab initio calculations)

Tong Shen(申彤), Xiao-Wei Zhang(张小伟), Min-Ye Zhang(张旻烨), Hong Jiang(蒋鸿), and Xin-Zheng Li(李新征). Accurate GW₀ band gaps and their phonon-induced renormalization in solids[J]. 中国物理B, 2021, 30(11): 117101-117101.

参考文献

[1] Hybertsen M S and Louie S G 1986 Phys. Rev. B 34 5390
[2] Godby R W, Schlüter M and Sham L 1988 Phys. Rev. B 37 10159
[3] Onida G, Reining L and Rubio A 2002 Rev. Mod. Phys. 74 601
[4] Blaha P, Schwarz K, Tran F, Laskowski R, Madsen G K H and Marks L D 2020 J. Chem. Phys. 152 074101
[5] Jiang H and Blaha P 2016 Phys. Rev. B 93 115203
[6] Nabok D, Gulans A and Draxl C 2016 Phys. Rev. B 94 035118
[7] Shen T, Zhang X W, Shang H, Zhang M Y, Wang X, Wang E G, Jiang H and Li X Z 2020 Phys. Rev. B 102 045117
[8] Giustino F 2017 Rev. Mod. Phys. 89 015003
[9] Zacharias M, Patrick C E and Giustino F 2015 Phys. Rev. Lett. 115 177401
[10] Zacharias M and Giustino F 2016 Phys. Rev. B 94 075125
[11] Giustino F, Louie S G and Cohen M L 2010 Phys. Rev. Lett. 105 265501
[12] Antonius G, Poncé S, Boulanger P, Côté M and Gonze X 2014 Phys. Rev. Lett. 112 215501
[13] Poncé S, Margine E R and Giustino F 2018 Phys. Rev. B 97 121201
[14] McMillan W 1968 Phys. Rev. 167 331
[15] Allen P B and Dynes R 1975 Phys. Rev. B 12 905
[16] Kittel C 2004 Introduction to Solid State Physics 8th edn (Hoboken, NJ: Wiley)
[17] Baroni S, Giannozzi P and Testa A 1987 Phys. Rev. Lett. 58 1861
[18] Gonze X, Allan D C and Teter M P 1992 Phys. Rev. Lett. 68 3603
[19] Savrasov S Y 1992 Phys. Rev. Lett. 69 2819
[20] Capaz R B, Spataru C D, Tangney P, Cohen M L and Louie S G 2005 Phys. Rev. Lett. 94 036801
[21] Marini A 2008 Phys. Rev. Lett. 101 106405
[22] Giustino F, Cohen M L and Louie S G 2007 Phys. Rev. B 76 165108
[23] Marini A, Hogan C, Grüning M and Varsano D 2009 Comput. Phys. Commun. 180 1392
[24] Cannuccia E and Marini A 2012 Eur. Phys. J. B 85 1
[25] Ponce S, Antonius G, Gillet Y, Boulanger P, Janssen J L, Marini A, Cote M and Gonze X 2014 Phys. Rev. B 90 214304
[26] Ponce S, Antonius G, Boulanger P, Cannuccia E, Marini A, Cote M and Gonze X 2014 Comput. Mater. Sci. 83 341
[27] Kawai H, Yamashita K, Cannuccia E and Marini A 2014 Phys. Rev. B 89 085202
[28] Lloyd-Williams J H and Monserrat B 2015 Phys. Rev. B 92 184301
[29] Antonius G, Poncé S, Lantagne-Hurtubise E, Auclair G, Gonze X and Côté M 2015 Phys. Rev. B 92 085137
[30] Ponce S, Gillet Y, Janssen J L, Marini A, Verstraete M and Gonze X 2015 J. Chem. Phys. 143 102813
[31] Villegas C E P, Rocha A R and Marini A 2016 Phys. Rev. B 94 134306
[32] Jin C H, Kim J, Suh J, Shi Z W, Chen B, Fan X, Kam M, Watanabe K, Taniguchi T, Tongay S, Zettl A, Wu J Q and Wang F 2017 Nat. Phys. 13 127
[33] Sangalli D, Ferretti A, Miranda H, Attaccalite C, Marri I, Cannuccia E, Melo P, Marsili M, Paleari F, Marrazzo A, Prandini G, Bonfa P, Atambo M O, Affinito F, Palummo M, Molina-Sanchez A, Hogan C, Gruning M, Varsano D and Marini A 2019 J. Phys.: Condens. Matter 31 325902
[34] Hinuma Y, Grüneis A, Kresse G and Oba F 2014 Phys. Rev. B 90 155405
[35] Klimeš J, Kaltak M and Kresse G 2014 Phys. Rev. B 90 075125
[36] Gómez-Abal R, Li X, Scheffler M and Ambrosch-Draxl C 2008 Phys. Rev. Lett. 101 106404
[37] Li X Z, Gomez-Abal R, Jiang H, Ambrosch-Draxl C and Scheffler M 2012 New J. Phys. 14 023006
[38] Tiago M L, Ismail-Beigi S and Louie S G 2004 Phys. Rev. B 69 125212
[39] Arnaud B, Lebegue S, Rabiller P and Alouani M 2006 Phys. Rev. Lett. 96 026402
[40] Shishkin M, Marsman M and Kresse G 2007 Phys. Rev. Lett. 99 246403
[41] Jiang H, Gomez-Abal R I, Rinke P and Scheffler M 2010 Phys. Rev. B 82 045108
[42] Madsen G K, Blaha P, Schwarz K, Sjöstedt E and Nordström L 2001 Phys. Rev. B 64 195134
[43] Schwarz K, Blaha P and Madsen G K H 2002 Comput. Phys. Commun. 147 71
[44] Sjöstedt E, Nordström L and Singh D 2000 Solid State Commun. 114 15
[45] Rohlfing M, Krüger P and Pollmann J 1998 Phys. Rev. B 57 6485
[46] Krasovskii E E, Yaresko A N and Antonov V N 1994 J. Electron Spectrosc. Relat. Phemon. 68 157
[47] Friedrich C, Schindlmayr A, Blügel S and Kotani T 2006 Phys. Rev. B 74 045104
[48] Friedrich C, Müller M C and Blügel S 2011 Phys. Rev. B 83 081101
[49] Jiang H 2018 Phys. Rev. B 97 245132
[50] Zhang M Y and Jiang H 2019 Phys. Rev. B 100 205123
[51] Ashcroft N W and Mermin N D 1976 Solid State Physics (New York: Harcourt College Publishers)
[52] Mahan G D 1993 Many-Particle Physics (New York: Plenum)
[53] Fan H 1951 Phys. Rev. 82 900
[54] Migdal A B 1958 Sov. Phys. JETP 7 996
[55] Antončík E 1955 Czech. J. Phys. 5 449
[56] Allen P B and Heine V 1976 J. Phys. C: Solid State Phys. 9 2305
[57] Allen P B and Cardona M 1981 Phys. Rev. B 23 1495
[58] Baroni S, De Gironcoli S, Dal Corso A and Giannozzi P 2001 Rev. Mod. Phys. 73 515
[59] Wannier G H 1937 Phys. Rev. 52 191
[60] Dacorogna M M, Cohen M L and Lam P K 1985 Phys. Rev. Lett. 55 837
[61] Lam P K, Dacorogna M M and Cohen M L 1986 Phys. Rev. B 34 5065
[62] Zhang X W, Wang E G and Li X Z 2018 Phys. Rev. B 98
[63] Weast R C 1986 CRC Handbook of Chemistry and Physics 67th edn (Boca Raton: CRC Press)
[64] Roessler D, Walker W and Loh E 1969 J. Phys. Chem. Solids 30 157
[65] Chang K J and Cohen M L 1984 Solid State Commun. 50 487
[66] Weber M J 1986 Handbook of Laser Science and Technology (Boca Raton: CRC Press) Vol. 3
[67] Slack G A and Austerman S 1971 J. Appl. Phys. 42 4713
[68] Jaccodine R, Jackson K A and Sundahl R C 1988 Electronic Packaging Materials Science (I!I!I) Symposium, November 30-December 4, 1987, Boston, Massachusetts, USA (PA: Materials Research Society)
[69] Loh E 1968 Phys. Rev. 166 673
[70] Jephcoat A, Hemley R, Mao H, Cohen R and Mehl M 1988 Phys. Rev. B 37 4727
[71] Chang K J, Froyen S and Cohen M 1983 J. Phys. C: Solid State Phys. 16 3475
[72] Van Camp P and Van Doren V 1996 J. Phys.: Condens. Matter 8 3385
[73] Shahrokhi M and Leonard C 2016 J. Alloys Compd. 682 254
[74] Wyckoff R W G 1963 Crystal Structures (New York: Wiley)
[75] Hazen R M and Finger L W 1986 J. Appl. Phys. 59 3728
[76] Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[77] Kresse G and Furthmuller J 1996 Phys. Rev. B 54 11169
[78] Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti G L, Cococcioni M, Dabo I and Dal Corso A 2009 J. Phys.: Condens. Matter 21 395502
[79] Amrani B, Hassan F E H and Akbarzadeh H 2007 J. Phys.: Condens. Matter 19 436216
[80] Jiang H, Gomez-Abal R I, Li X Z, Meisenbichler C, Ambrosch-Draxl C and Scheffler M 2013 Comput. Phys. Commun. 184 348
[81] Karsai F, Engel M, Flage-Larsen E and Kresse G 2018 New J. Phys. 20 123008
[82] Continenza A, Wentzcovitch R M and Freeman A J 1990 Phys. Rev. B 41 3540
[83] Lichanot A, Baraille I, Larrieu C and Chaillet M 1995 Phys. Rev. B 52 17480
[84] Freeman C L, Claeyssens F, Allan N L and Harding J H 2006 Phys. Rev. Lett. 96 066102
[85] Zhuang H L and Hennig R G 2013 Appl. Phys. Lett. 103 212102
[86] Zheng H, Li X B, Chen N K, Xie S Y, Tian W Q, Chen Y, Xia H, Zhang S and Sun H B 2015 Phys. Rev. B 92 115307
[87] Zhang H, Holbrook M, Cheng F, Nam H, Liu M, Pan C R, West D, Zhang S, Chou M Y and Shih C K 2021 ACS Nano 15 2497
[88] Kresse G and Joubert D 1999 Phys. Rev. B 59 1758
[89] Ge Y, Wan W, Ren Y, Li F and Liu Y 2020 Appl. Phys. Lett. 117 123101
[90] Wu W, Lu P, Zhang Z and Guo W 2011 ACS Appl. Mater. Interfaces 3 4787
[91] Valedbagi S, Jalilian J, Elahi S, Majidi S, Fathalian A and Dalouji V 2014 Electron. Mater. Lett. 10 5

Accurate GW₀ band gaps and their phonon-induced renormalization in solids

Accurate GW₀ band gaps and their phonon-induced renormalization in solids

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