1. Yoshida Laboratory Yuya Yamada （山田裕也） 1 Theoretical prediction of structures and properties of simple materials under high pressure ( 高圧下における単純物質の構造と物性の理論的予測 )

2. Contents 2 Introduction Motivation Research method first-principles calculations Lithium -my graduation thesis Sodium GW-approximation (GWA) Aluminum hydride Summary and future works

3. Pressure 3 where F is the force, A the area. An elephant with high-heeled shoes : 10 8 Pa http://www.flickr.com/photos/arejay/168460585/ Diamond Anvil Cell(DAC): 10 11 Pa=100GPa Introduction Definition example P by DAC: 1000 times

4. 4 Characteristic phases of elemental substances at high pressures elemental substances in the 2nd period ・ structures ・ metal   insulator ・ formation of molecules by pressurization ・ molecular dissociation by pressurization Introduction

5. Motivation 5 High pressure  Phase transition Studying elemental substances  Basic knowledge of phase transition Motivation

6. Study’s flow 6 Design Calculation by means of computer Get properties First-principles calculation Parameters are only: ・ Atomic number ・ Atomic position Research method

7. Advantage of Computational physics including first-principles calculations 7 We can predict material properties ahead of experiment. （ At a low cost, No danger ） Properties under almost unrealizable conditions can be predicted. Research method

8. 8 Phase diagram of Li ０ 40 80 GPa bcc fcc hR1 cI16 Confirmed by Exp. M.Hanflad et al. Nature 2000 Takahiro Matsuoka & Katsuya Shimizu Nature 2009 My study –lithium Unknown. Theoretically predicted to be C2 etc. Not confirmed by Exp

9. Band structure of Li (C2) 9 ７４－９１ GPa Structure My study –lithium Brillouin Zone I used the parameters in the paper by Yansun Yao et al. PRL 102, 115503 (2009) [eV]

10. Band structure of Li (C2) 10 ７４－９１ GPa My study –lithium Semiconductor ！ (indirect gap type) Band gap 0.2450[eV] My calculation I used the parameters in the paper by Yansun Yao et al. PRL 102, 115503 (2009) [eV]

11. Na 11 Na in hP4 structure at 320GPa Yanming Ma, et al., Nature 458, 182-185 (2009) Sodium

12. LDA (Local Density Approximation) GGA(Generalized Gradient Approximation ) To get good values of the band gaps GWA (GW-approximation ) G:Green’s function,W:screened coulomb interaction one-shot GW Quasiparticle self-consistent GW (QSGW) etc. 12 Contents I introduce today Approximations used in the first-principles calculations GW-approximation(GWA)

13. 13 Hedin’s GWA gives the self energy Where is Green’s function W is screened Coulomb interaction Takao Kotani et al. PRB 76 165106 (2007) GW-approximation(GWA)

14. Difference between GWA and LDA 14 QSGW (GW with Σ computed) One shot GW (Diagonal- Σ - only) LDA Ge M. van Shilfgaarde et al PRL 96 226402(2006) GW-approximation(GWA)

15. Improvement of band gaps by the GWA 15 GaAsNa QSGW GWA LDA ○ ： Exp. LDA,GWA(one-shot GW) QSGW (quasiparticle self-consistent GW) eV M. van Shilfgaarde et al PRL 96 226402(2006) GW-approximation(GWA)

16. Changes of electronic Density of States 16 Density of States in Ce0 2 eV (One-shot GW) (QSGW) M. van Shilfgaarde et al PRL 96 226402(2006) Exp.: E.wuilloud,et al.PBL 53,202(1984) GW-approximation(GWA)

17. AlH 3 Pressure - Volume 17 f.u.= formula unit Igor Goncharenko et al. PRL 100,045504(2008) Volume per unit formula unit in AlH 3 as a function of pressure. Red curve is from ab initio calculations Black: volume per H atom in AlH 3 Red curve : volume per H 2 atom in H 2 Blue: volume per H molecule in H 2 Aluminum hydride

18. AlH 3 resistances 18 ・ The more the tempereture increases,the more resistances increases. This is the properties of metal. ・ Resistances changes abruptly at around 100 GPa, so we could say that phase transition occurs here. Igor Goncharenko et al. PRL 100,045504(2008) Aluminum hydride

19. AlH 3 Density of States We can see the band gap. Red line is 0GPa, dashed line 50GPa, and black solid line 100GPa. As the pressure is increased, the band gap becomes narrower. So we can expect the insulator-to-metal transition. 19 J.Graetz et al. PRB 74 214114(2006) Aluminum hydride

20. AlH 3 Band structure and Density of States 20 Igor Goncharenko et al. PRL 100,045504(2008) Pm-3m (up to 100GPa) This calculation is done by GGA, so the bandgap probably is underestimated. GW approximation ?? Aluminum hydride

21. Summary 21 Li metal becomes semiconducting when it is under high pressure. First-principles calculation is a powerful method for predicting properties of materials. GW-approximation (GWA)predicts more accurate band gaps than the conventional LDA. Summary and future works

22. Future works I will calculate( by using GW-approximation )the band gaps of scandium hydride and yttrium hydride, which is discovered by experiment. This is because I want to know the predictability of the metalization pressure by the GW- approximation comparing the calculated results and experiments. Next, I will calculate the structure and pressure where insulator-to-metal transition occurs by calculating the band gap and its pressure dependence. Materials to be studied are: lanthanum hydride and aluminum hydride,whose structures under high pressure is not identified by experiments. 22 Summary and future works

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