Yoshida Laboratory Yuya Yamada（山田裕也）

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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 )

Contents

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IntroductionMotivationResearch method first-principles calculationsLithium -my graduation thesisSodiumGW-approximation (GWA)Aluminum hydrideSummary and future works

　　　　

Pressure

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A

FP

where F is the force, A the area.

An elephant with high-heeled shoes : 108 Pa

http://www.flickr.com/photos/arejay/168460585/Diamond Anvil Cell(DAC):

1011Pa=100GPa

Introduction

Definition example

P by DAC:1000 times

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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

Motivation

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High pressure Phase transition

Studying elemental substances Basic knowledge of phase

transition

Motivation

Study’s flow

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Design

Calculation by means of computer Get properties

First-principles calculation

Parameters are only:・ Atomic number・ Atomic position

Research method

Advantage of Computational physics including first-principles calculations

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We can predict material properties ahead of experiment.（ At a low cost, No danger ）

Properties under almost unrealizable conditions can be predicted.

Research method

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Phase diagram of Li

０ 40 80 GPa

bccfcc

hR1

cI16

Confirmed by Exp.

M.Hanflad et al. Nature 2000Takahiro Matsuoka & Katsuya Shimizu Nature 2009

My study –lithium

Unknown .Theoretically predicted to be C2 etc.

Not confirmed by Exp

Band structure of Li (C2)　

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７４－９１GPa７４－９１GPa

Structure

My study –lithium

Brillouin Zone

I used the parameters in the paper byYansun Yao et al. PRL 102, 115503 (2009)

[eV]

Band structure of Li (C2)

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７４－９１ GPa７４－９１ GPa

My study –lithium

Semiconductor ！(indirect gap type)

Band gap0.2450[eV]

My calculationI used the parameters in the paper byYansun Yao et al. PRL 102, 115503 (2009)

[eV]

Na

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Na in hP4 structure at 320GPa

Yanming Ma, et al., Nature 458, 182-185 (2009)

Sodium

LDA (Local Density Approximation)GGA(Generalized Gradient Approximation )

To get good values of the band gapsGWA (GW-approximation ) G:Green’s function,W:screened coulomb interaction

one-shot GWQuasiparticle self-consistent GW (QSGW) etc.

12Contents I

introduce today

Approximations used in the first-principles calculations

GW-approximation(GWA)

GW-approximation(GWA)

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Hedin’s GWA gives the self energy

Where

'0 )','(',''2

,',

ieWGdi rr,rr,rr

i i

ii

iG

)()(),(

*0 rrr'r,

vvvW 11 )1(

is Green’s functionW is screened Coulomb interaction

0G

Takao Kotani et al. PRB 76 165106 (2007)

GW-approximation(GWA)

Difference between GWA and LDA

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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)

Improvement of band gaps by the GWA

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GaAs Na

QSGWGWA

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)

Changes of electronic Density of States

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Density of States in Ce02

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)

AlH3 Pressure - Volume

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f.u.= formula unit

Igor Goncharenko et al. PRL 100,045504(2008)

Volume per unit formula unit in AlH3 as a function of pressure.

Red curve is from ab initio calculations

Black: volume per H atom in AlH3

Red curve : volume per H2 atom in H2

Blue: volume per H molecule in H2

Aluminum hydride

AlH3 resistances

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・ 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

AlH3 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

AlH3 Band structure and Density of States

20Igor 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

Summary

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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

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.

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Summary and future works

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