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1. Development of a highly accurate
pseudopotential method
2. Practical application of calculations to
silicene grown on a...
Research objectives
 Expand applicability of first-principle electronic
structure calculations based on density-
function...
What is a pseudopotential?
 The pseudopotential method is used
extensively in first-principle calculations
 Inner-shell ...
TM and MBK pseudopotentials
 Only a single reference energy can be used for the TM
pseudopotential: Scattering characteri...
Constructing the MBK pseudopotential
 The MBK pseudopotential is a non-local potential,
and is given as follows:
 Genera...
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 r...
The 2p and 3p orbitals can be
taken together as reference
energies for the MBK
pseudopotential
Only the 2p orbital can be ...
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 si...
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
cond...
Experimental results for silicene grown on ZrB2
Y. Yamada-Takamura et al., Appl. Phys. Lett. 97, 073109 (2010)
STM image S...
Computation conditions
 OpenMX software package for first-principle density-functional
calculations
 Generalized gradien...
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
ZrB2 (mean)
2.124 (Å...
Comparison and correspondence of ARUPS
spectrum and band structure of Si on ZrB2
Calculated band
structure
Band structure ...
Comparison and correspondence of ARUPS
spectrum and band structure of Si on ZrB2
Calculated band
structure
Band structure ...
Comparison and correspondence of ARUPS
spectrum and band structure of Si on ZrB2
Calculated band
structure
Band structure ...
Dirac cones in silicene
 Dirac cones clearly appear in flat silicene
 But in buckled silicene, Dirac cones are broken
Ba...
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
 Core level shift of the 2p orbital
of Si
 Top: From XP...
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...
Summary
 Performed first-principle calculations for silicene grown on
a ZrB2 surface
 Calculations show buckled silicene...
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Development of highly accurate pseudopotential method and its application to a surface system

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

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

  1. 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. 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. 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. 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. 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. 6. Examples of logarithmic derivatives
  7. 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. 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. 9. Practical application Calculations for silicene grown on a ZrB2 surface
  10. 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. 11. silicene on silver surface Boubekeur Lalmi et al., Appl. Phys. Lett. 97 223109 (2010)
  12. 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. 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. 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. 15. Optimal structure of Si on ZrB2 A. Fleurence et al., Phys. Rev. Lett. 108, 245501 (2012)
  16. 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. 17. Comparison and correspondence of ARUPS spectrum and band structure of Si on ZrB2 Calculated band structure Band structure from ARUPS
  18. 18. Comparison and correspondence of ARUPS spectrum and band structure of Si on ZrB2 Calculated band structure Band structure from ARUPS
  19. 19. Comparison and correspondence of ARUPS spectrum and band structure of Si on ZrB2 Calculated band structure Band structure from ARUPS
  20. 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. 21. Position of Dirac cones in Si on ZrB2 Band structure of Si on ZrB2
  22. 22. Position of Dirac cones in Si on ZrB2 Band structure of Si on ZrB2
  23. 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. 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. 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

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