Development of highly accurate pseudopotential method and its application to a surface system
Transcript of Development of highly accurate pseudopotential method and its application to a surface system
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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
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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
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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
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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)
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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
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Examples of logarithmic derivatives
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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
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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
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Practical application
Calculations for silicene grown on a ZrB2surface
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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)
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silicene on silver surface
Boubekeur Lalmi et al., Appl. Phys. Lett. 97 223109 (2010)
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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)
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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
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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
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Optimal structure of Si on ZrB2
A. Fleurence et al., Phys. Rev. Lett. 108, 245501 (2012)
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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)
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Comparison and correspondence of ARUPS
spectrum and band structure of Si on ZrB2
Calculated band
structure
Band structure from
ARUPS
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Comparison and correspondence of ARUPS
spectrum and band structure of Si on ZrB2
Calculated band
structure
Band structure from
ARUPS
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Comparison and correspondence of ARUPS
spectrum and band structure of Si on ZrB2
Calculated band
structure
Band structure from
ARUPS
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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
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Position of Dirac cones in Si on ZrB2Band structure of Si on ZrB2
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Position of Dirac cones in Si on ZrB2Band structure of Si on ZrB2
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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)
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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
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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