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 ZrB2 surface

@dc1394

Development of highly accurate pseudopotential

method and its application to a surface system

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 TMpseudopotential: Scattering characteristics cannot be replicated over a broad energy range

Multiple reference energies can be used for the MBKpseudopotential: 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 Qij=0

The equation becomes identical to the general norm-conserving pseudopotential

Examples of logarithmic derivatives

Logarithmic

derivatives of TM

and MBK

pseudopotentials

for s state of Zr

The 4s and 5s orbitals can be

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

4s 5s

Red: All-Electron

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

2p 3p

Logarithmic

derivatives of TM

and MBK

pseudopotentials

for p state of Si Red: All-Electron

Green: TM

Blue: MBK

Practical application

Calculations for silicene grown on a ZrB2surface

Outline

A highly accurate pseudopotential used to calculate atomic structure and electronic states of a graphene-like single layer of Si (silicene) on a ZrB2 surface

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 ZrB2?

Useful properties

High hardness (Mohs scale: 8)

High melting point (2400 ) and conductivity (thermal conductivity: 99 W/mK; electrical resistance: 4.6 /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)

ZrB2 layer grown on Si substrate is excellent matrix for growing GaN thin-film crystals

Si atoms migrate from Si substrate to form Si monolayer on a ZrB2 surface

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

(magnified)

XPS spectrum of 2p

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 ZrB2Location of Si atom A (hollow) B (bridge) C (on-top)

Distance from surface of ZrB2 (mean)

2.124 () 3.062 () 2.727 ()

Distance to nearest Zr atom (mean)

2.815 () 3.216 () 2.684 ()

Distance to nearest Si atom (mean)

2.266 () 2.258 () 2.242 ()

Angle formed with nearest Si atom (mean)

104.1(sp3-like)

109.7(intermediate)

117.8(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

Calculated band

structure

Band structure from

ARUPS

Comparison and correspondence of ARUPS

spectrum and band structure of Si on ZrB2

Calculated band

structure

Band structure from

ARUPS

Comparison and correspondence of ARUPS

spectrum and band structure of Si on ZrB2

Calculated band

structure

Band structure from

ARUPS

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 ZrB2Band structure of Si on ZrB2

Position of Dirac cones in Si on ZrB2Band structure of Si on ZrB2

Computed core level shifts compared with those

obtained from XPS

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

Green: A (hollow)

Red: B (bridge)

Blue: C (on-top)

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

Blue: C (on-top)

DOS of flat silicene, buckled silicene and Si on

ZrB2

DOS of Si on ZrB2

DOS of buckled siliceneDOS of flat silicene

Summary

Performed first-principle calculations for silicene grown on

a ZrB2 surface

Calculations show buckled silicene maintains a stable

structure on the ZrB2 surface

Computed band structure compared with band structure

from ARUPS: State close to the Fermi surface consists of

a mixture of ZrB2 surface states and Si orbitals

Orbital originating from the Dirac cone in silicene splits

due to strong interaction with ZrB2 and buckling, and

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 ZrB2 and buckling