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)
Yoshida Laboratory
Yuya Yamada（山田裕也）
1
Contents
 Introduction
 Motivation
 Research method
first-principles calculations
 Lithium -my graduation thesis
 Sodium
 GW-approximation (GWA)
 Aluminum hydride
 Summary and future works
2
Introduction
Pressure
Definition
example
F
P
A
P by DAC:
1000 times
where F is the force, A the area.
Diamond Anvil Cell(DAC):
1011Pa=100GPa
3
http://www.flickr.com/photos/arejay/168460585/
An elephant with high-heeled
shoes : 108 Pa
Introduction
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
4
Motivation
Motivation
 High pressure Phase transition
 Studying elemental substances
 Basic knowledge of phase transition
5
Research method
Study’s flow
First-principles calculation
Parameters are only:
・Atomic number
・Atomic position
Get properties
6
Design
Calculation by means of computer
Research method
Advantage of Computational physics
including first-principles calculations
 We can predict material properties ahead of experiment.
（At a low cost, No danger）
 Properties under almost unrealizable conditions can be
predicted.
7
My study –lithium
Phase diagram of Li
hR1
bcc
Unknown .
Theoretically predicted
to be C2 etc.
cI16
fcc
Not confirmed by Exp
０
8
40
Confirmed by Exp.
70
80
M.Hanflad et al. Nature 2000
Takahiro Matsuoka & Katsuya Shimizu Nature
2009
GPa
My study –lithium
Band structure of Li (C2)
[eV]
７４－９１GPa
Structure
Brillouin Zone
9
I used the parameters in the paper by
Yansun Yao et al. PRL 102, 115503 (2009)
My study –lithium
Band structure of Li (C2)
７４－９１GPa
[eV]
Semiconductor！
Band gap
0.2450[eV]
(indirect gap type)
10
I used the parameters in the paper by
Yansun Yao et al. PRL 102, 115503 (2009)
My calculation
Sodium
Na
Na in hP4 structure at 320GPa
Yanming Ma, et al., Nature 458, 182-185 (2009)
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GW-approximation(GWA)
Approximations used in the first-principles calculations
 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
GW-approximation(GWA)
GW-approximation(GWA)
 Hedin’s GWA gives the self energy
r, r ' ,   
Where
i
0
i '


d

'
G
r,
r
'
,



'
W
(
r,
r
'
,

'
)
e
2 
*

(
r
)

0
i
i (r )
G (r, r',  )  
i    i  i
W   v  (1  v) v
1
1
G0is Green’s
function
W is screened
Coulomb
interaction
Takao Kotani et al. PRB 76 165106 (2007)
13
GW-approximation(GWA)
Difference between GWA and LDA
QSGW
Ge
(GW with Σ computed)
One shot GW
(Diagonal- Σ- only)
LDA
M. van Shilfgaarde et al PRB 74 245125(2006)
14
GW-approximation(GWA)
Improvement of band gaps by the GWA
LDA ,GWA(one-shot GW)
GaAs
Na
eV
QSGW
(quasiparticle self-consistent GW)
LDA
QSGW
15
M. van Shilfgaarde et al PRL 96 226402(2006)
One-shot GW
○：Exp.
GW-approximation(GWA)
Changes of electronic Density of States
Density of States in Ce02
(One-shot GW)
(QSGW)
eV
M. van Shilfgaarde et al PRL 96 226402(2006)
Exp.: E.wuilloud,et al.PRL 53,202(1984)
16
Aluminum hydride
AlH3 Pressure - Volume
Black: volume per H atom
in AlH3
Red curve : volume per
H2 atom in H2
Blue: volume per H
molecule in H2
f.u.= formula unit
17
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
Aluminum hydride
AlH3 resistances
・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)
18
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
Pm-3n (up to 100GPa)
Red: aluminum
Blue: hydrogen
This calculation is done by GGA, so the bandgap probably is
underestimated.
GW approximation ??
Igor Goncharenko et al. PRL 100,045504(2008)
20
Summary and future works
Summary
 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 .
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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 GWapproximation 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.
22
Materials to be studied are: lanthanum hydride and
aluminum hydride ,whose structures under high pressure
is not identified by experiments.
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