Development of highly accurate pseudopotential method and its application to a surface system

1. 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

2. 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

3. 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

4. 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)

5. 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

6. Examples of logarithmic derivatives

7. 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

8. 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 SiRed: All-Electron
Green: TM
Blue: MBK

9. Practical application
Calculations for silicene grown on a ZrB2
surface

10. 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)

11. silicene on silver surface
Boubekeur Lalmi et al., Appl. Phys. Lett. 97 223109 (2010)

12. Why ZrB2?
 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)
 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)

13. 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

14. 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

15. Optimal structure of Si on ZrB2
A. Fleurence et al., Phys. Rev. Lett. 108, 245501 (2012)

16. Structure of Si on ZrB2
Location of Si atom A (hollow) B (bridge) C (on-top)
Distance from surface of
ZrB2 (mean)
2.124 (Å) 3.062 (Å) 2.727 (Å)
Distance to nearest Zr
atom (mean)
2.815 (Å) 3.216 (Å) 2.684 (Å)
Distance to nearest Si
atom (mean)
2.266 (Å) 2.258 (Å) 2.242 (Å)
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)

17. Comparison and correspondence of ARUPS
spectrum and band structure of Si on ZrB2
Calculated band
structure
Band structure from
ARUPS

18. Comparison and correspondence of ARUPS
spectrum and band structure of Si on ZrB2
Calculated band
structure
Band structure from
ARUPS

19. Comparison and correspondence of ARUPS
spectrum and band structure of Si on ZrB2
Calculated band
structure
Band structure from
ARUPS

20. 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

21. Position of Dirac cones in Si on ZrB2
Band structure of Si on ZrB2

22. Position of Dirac cones in Si on ZrB2
Band structure of Si on ZrB2

23. 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)

24. 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

25. 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