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- Development of highly accurate pseudopotential

method and its application to a surface system

1. Development of a highly accurate

pseudopotential method

2. Practical application of calculations to

silicene grown on a ZrB surface

2

@dc1394 - Research objectives

Expand applicability of first-principle electronic

structure calculations based on density-

functional formalism

Develop a novel highly accurate

pseudopotential

Use theoretical calculations to elucidate

recently discovered surface structures - What is a pseudopotential?

The pseudopotential method is used

extensively in first-principle calculations

Inner-shell electrons near the atomic nucleus

are not directly taken into account

Instead, inner-shell electrons are replaced with

simple potential function - TM and MBK pseudopotentials

Only a single reference energy can be used for the TM

pseudopotential: Scattering characteristics cannot be

replicated over a broad energy range

Multiple reference energies can be used for the MBK

pseudopotential: Scattering characteristics can be

replicated over a broad energy range

N. Troullier and J. L. Martins, Phys. Rev. B 43, 1993 (1991)

I. Morrison, D. M. Bylander and L. Kleinman, Phys. Rev. B 47, 6728 (1993) - Constructing the MBK pseudopotential

The MBK pseudopotential is a non-local potential,

and is given as follows:

Generalized norm-conserving conditions are satisfied by

taking Q =0

ij

The equation becomes identical to the general norm-

conserving pseudopotential - Examples of logarithmic derivatives
- Logarithmic

derivatives of TM

4s

5s

and MBK

pseudopotentials

for s state of Zr

Red: All-Electron

Green: TM

The 4s and 5s orbitals can be

Blue: MBK

taken together as reference

energies for the MBK

pseudopotential

Only the 4s orbital can be used

for the TM pseudopotential

Leads to discrepancies in the

approximation at high energies

around the 5s orbital - Logarithmic

derivatives of TM

2p

3p

and MBK

pseudopotentials

Red: All-Electron

for p state of Si

Green: TM

Blue: MBK

The 2p and 3p orbitals can be

taken together as reference

energies for the MBK

pseudopotential

Only the 2p orbital can be used

for the TM pseudopotential

At energies above -1, TM

pseudopotential differs

considerably from all-electron

calculation

The MBK pseudopotential

gives substantial improvement - Practical application

Calculations for silicene grown on a ZrB2

surface - Outline

A highly accurate pseudopotential used to calculate atomic structure

and electronic states of a graphene-like single layer of Si (silicene)

on a ZrB surface

2

A novel structure recently developed in our laboratory

Silicene is structurally similar to graphene: Interesting from both

theoretical and practical perspectives

Electronic states of silicene await clarification

Graphene has characteristic band structures known as Dirac cones

Do Dirac cones also appear in silicene?

Y. Yamada-Takamura et al., Appl. Phys. Lett. 97, 073109 (2010) - silicene on silver surface

Boubekeur Lalmi et al., Appl. Phys. Lett. 97 223109 (2010) - Why ZrB ?

2

Useful properties

High hardness (Mohs scale: 8)

High melting point (2400 ℃) and conductivity (thermal

conductivity: 99 W/mK; electrical resistance: 4.6 μΩ/cm),

comparable with those of metals

Expected applications

Electron emitter

Catalyst

Substrate for growing GaN thin-film crystals (used in

optical devices such as blue LEDs)

ZrB layer grown on Si substrate is excellent matrix for

2

growing GaN thin-film crystals

Si atoms migrate from Si substrate to form Si monolayer on a

ZrB surface

2

J. Tolle et al., Appl. Phys. Lett. 84, 3510 (2004) - Experimental results for silicene grown on ZrB2

Y. Yamada-Takamura et al., Appl. Phys. Lett. 97, 073109 (2010)

STM image

STM image

XPS spectrum of 2p

(magnified)

orbital of Si - Computation conditions

OpenMX software package for first-principle density-functional

calculations

Generalized gradient approximation (GGA-PBE)

A highly accurate norm-conserving pseudopotential

Numerical localized basis (corresponding to DZP)

Structure optimization: Relativistic representation, including

only scalar terms, is introduced through pseudopotentials

XPS calculation: Fully relativistic treatment used to account for

spin-orbit splitting of the 2p orbital in Si - Optimal structure of Si on ZrB2

A. Fleurence et al., Phys. Rev. Lett. 108, 245501 (2012) - Structure of Si on ZrB2

Location of Si atom

A (hollow)

B (bridge)

C (on-top)

Distance from surface of

2.124 (Å)

3.062 (Å)

2.727 (Å)

ZrB (mean)

2

Distance to nearest Zr

2.815 (Å)

3.216 (Å)

2.684 (Å)

atom (mean)

Distance to nearest Si

2.266 (Å)

2.258 (Å)

2.242 (Å)

atom (mean)

Angle formed with

104.1°

109.7°

117.8°

nearest Si atom (mean)

(sp3-like)

(intermediate)

(sp2-like)

Green: A (hollow)

Red: B (bridge)

Blue: C (on-top) - Comparison and correspondence of ARUPS

spectrum and band structure of Si on ZrB2

Band structure from

Calculated band

ARUPS

structure - Comparison and correspondence of ARUPS

spectrum and band structure of Si on ZrB2

Band structure from

Calculated band

ARUPS

structure - Comparison and correspondence of ARUPS

spectrum and band structure of Si on ZrB2

Band structure from

Calculated band

ARUPS

structure - Dirac cones in silicene

Dirac cones clearly appear in flat silicene

But in buckled silicene, Dirac cones are broken

Band structure of flat silicene

Band structure of buckled silicene - Position of Dirac cones in Si on ZrB2

Band structure of Si on ZrB2 - Position of Dirac cones in Si on ZrB2

Band structure of Si on ZrB2 - Computed core level shifts compared with those

obtained from XPS

Green: A (hollow)

Red: B (bridge)

Blue: C (on-top)

Core level shift of the 2p orbital

of Si

Top: From XPS

Bottom: Computed with a highly

accurate pseudopotential taking

into account the 2p orbital of Si

Excellent agreement between

calculated core level shift and

the one obtained from XPS - DOS of flat silicene, buckled silicene and Si on

ZrB2

DOS of flat silicene

DOS of buckled silicene

Green: A (hollow) Red: B (bridge)

Blue: C (on-top)

DOS of Si on ZrB2 - Summary

Performed first-principle calculations for silicene grown on

a ZrB surface

2

Calculations show buckled silicene maintains a stable

structure on the ZrB surface

2

Computed band structure compared with band structure

from ARUPS: State close to the Fermi surface consists of

a mixture of ZrB surface states and Si orbitals

2

Orbital originating from the Dirac cone in silicene splits

due to strong interaction with ZrB and buckling, and

2

resides at ~1 eV below the Fermi level

Computation results compared with experimental XPS

results: Core level shift is explained by a strong

interaction with ZrB and buckling

2