how to use salmon-2...
TRANSCRIPT
ScalableAb-initioLight-MattersimulatorforOpticsandNanoscienceshttp://salmon-tddft.jp/
How to Use SALMON-2:Periodic Systems
Overview
1
Mitsuharu UEMOTOCenter for Computational Sciences, University of Tsukuba
SALMONTUTORIAL,TSUKUBA,2017
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
IntroductionofRT-TDDFTforSolid
SALMONTUTORIAL,TSUKUBA,20172
Real-TimeTDDFTfor“NonlinearOptics”inSolid
• First-principleTDDFT-basedelectrondynamicssimulation• Light-matterinteractionbetween“stronglaserpulse” and“solidcrystal”
Multiscalecalculation
• LightPropagation• Damaging/Ablation• Non-thermallaserprocessing
S.A.Sato,K.Yabana etal,PRB92,1(2015).
P =�(1)E+�(2)E2 + �(3)E3 + · · ·
Real-TimeCalculation
• Linearresponse• DielectricFunction
• Nonlinearresponse:• SHG,THG,Kerreffects
• Lightmatterenergytransfer
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
SolidCrystal
SALMONTUTORIAL,TSUKUBA,20173
Silicon(Wikipedia.org)
~a1
~a2
Si
• SolidCrystal• Periodicstructureofatoms• Resultisunmodifiedtotheshiftbythelatticevector:
R =n1a1 + n2a2 + n3a3
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
PeriodicConditionandBlochWavefunction
SALMONTUTORIAL,TSUKUBA,20174
b,k(r+R) = eikR b,k(r)
V (r+R) = V (r)
k:Blochwavevectorb:BandIndex
TheBlochwavefunction canrewrittenbyusingtheperiodicfunctionubk :
b,k(r) =eikrub,k(r)
! TR
H = ✏
TranslationOperator
[TR,H] = 0
TR = �
• HamiltonianisinvarianttotheshiftbyR
HamiltonianandTranslationoperatorhascommoneigenstate:
Theelectron’swavefuntion inperiodicsystemsatisfy:
Bloch’stheorem
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
Brilliouin ZoneandKpoints
SALMONTUTORIAL,TSUKUBA,20175
k0 = k+
✓2⇡m1
a1,2⇡m2
a2,2⇡m3
a3
◆Thek valueswitharbitraryintegerm correspondstothesameeigenstate
✓� ⇡
a1 k1 ⇡
a1
◆,
✓� ⇡
a2 k2 ⇡
a2
◆,
✓� ⇡
a3 k3 ⇡
a3
◆k-vectorsarerestrictedintheregionofthereciprocalspace
→ Brilliouin Zone(BZ)
Uniformlychoosethek-pointsintheBrilliouin Zone
ZZZdkf(k) !
X
ki
!(ki)f(ki)
ub,k ! ub,ki
DiscretizeBZtofinitenumberofk-points:
ub,keikR $ ub,k0eik
0R
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
GoverningEquationinPeriodicSystem
SALMONTUTORIAL,TSUKUBA,20176
i~ @
@tub,k(r, t) =
1
2m
⇣�i~r+ ~k+
e
cA(t)
⌘2
+ vion + vH + vXC
�ub,k(r, t)
vion
vH vXCub,k
E(t) =� A(t)/cIncidentField J(t)
KSorbit Atomicpotential ElectronInteraction
Time-DependentKohn-Sham(TDKS)equationinPeriodicSystem:
ub,k(r) ! zu(NL,NK,NB)Compute TDKS equation by using Finite Difference Method on Real Space Grid
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
ExampleofRT-TDDFTCalculation
SALMONTUTORIAL,TSUKUBA,20177
0 1 2 3 4 5
Si[110] (Å)
0
1
2
3
4
Si[
001]
(Å)
Si Si
Si
A(t) =A0 cos2 ⇡t
Tsin!1t
• Frequency=1.55[eV]• Intensity=109 [W/cm2]• Length=10[fs]
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience 8
PART 1
Ground State Calculation
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
GroundStateCalculation
SALMONTUTORIAL,TSUKUBA,20179
SolveKohn-ShamEquation
• ElectronSingle-particleEigenenergy Spectra
• ElectronDensityofStates(DoS)
• ChargeDensityProfile
• TotalEnergy
"b,k
n(r) =X
b,k
|ub,k(r)|2fk
⇢(E) =X
b,k
�(E � "b,k)fk
"b,kub,k(r) =
1
2m(�~r+ ~k)2 + vion + vH + vXC
�ub,k(r)
→ InitialStateofthereal-timecalculation
Etot
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
ExampleofGroundStateCalculation
SALMONTUTORIAL,TSUKUBA,201710
SALMON
Ti-layer
S-layer
S-layer
Ti-layer
Ti
S
TopofViewCrystalStructure
DensityofStates
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience 11
PART 2
Linear Response Calculation(Dielectric Function)
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
LinearResponseCalculation
SALMONTUTORIAL,TSUKUBA,201712
SolveTime-dependentKohn-ShamEquation
• Impulseresponse
• DielectricFunction
• Conductivity
• …
(withweakincidentfield:A(t),E(t))
i~ @
@tub,k(r, t) =
1
2m
⇣�i~r+ ~k+
e
cA(t)
⌘2
+ vion + vH + vXC
�ub,k(r, t)
J(t)
✏ij(!)
�ij(!) J(!) = �(!)E(!)
P(!) =1
4⇡(✏(!)� I)E(!)
A(t) = �A ✓(t)
E(t) = ��E �(t)
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
LinearResponse(DielectricFunction)
SALMONTUTORIAL,TSUKUBA,201713
Incident Pulse Weakincidentfield
InducedCurrent
J(t) =� e
m
X
b,k
1
⌦
Z
⌦Re u?
b,k(r, t)⇣�i~r+ ~k+
e
cA(t)
⌘2ub,k(r, t) dr+ JNL
Responsetoweakincident
InducedCurrentDensity
A(t) = �A ✓(t)
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
LinearResponse(DielectricFunction)
SALMONTUTORIAL,TSUKUBA,201714
�(!) =
RJ(t)ei!t dtRE(t)ei!t dt
✏(!) =4⇡i
!�(!)
Re[✏(!)] Im[✏(!)]
Conductivity
DielectricConst.
E0
Z�(t)e�i!t dt
(ExperimentalvaluefromD.E.Aspnes etal.Phys.Rev.B,27,2(1983))
Fouriertransformedspectra
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience 15
PART 3
Pulse Response Calculation
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
PulseResponseCalculation
SALMONTUTORIAL,TSUKUBA,201716
SolveTime-dependentKohn-ShamEquation
• InducedCurrent,Polarization
• Nonlinearopticalconstants
• ExcitationEnergy
• ProjectiontoGroundState andNumberofExcitedElectrons:
…withStrongIncidentPulse
i~ @
@tub,k(r, t) =
1
2m
⇣�i~r+ ~k+
e
cA(t)
⌘2
+ vion + vH + vXC
�ub,k(r, t)
A(t)
Eex
(t) = Etot
(t)� Etot
(0)
J(t),P(t) =
ZJ(t) dt
�(2),�(3), · · ·
nex
= Nelec
�X
k
(occ)X
b,b0
��⌦uGS
b,k
��ub0,k(t)↵��2 fk
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
NonlinearResponsesfromSiO2 Crystal
SALMONTUTORIAL,TSUKUBA,201717
Incidentpulse
A(t) =A0 cos2 ⇡t
Tsin!1t
• Centralfrequencyω1 =1.55eVPhaselengthTp =20fs
1.00.50.0
-0.5-1.0
Elec
tric
field
(GV/
m)
0 5 10 15 20Time (fs)
Ez(t)
0.0100.0050.000
-0.005-0.010
Pola
rizat
ion
(C/m
2 )
0 5 10 15 20Time (fs)
Pz(t)
Appliedelectricfield
Calculatedpolarization
• Pulseshapefunction
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
NonlinearResponsesfromSiO2 Crystal
SALMONTUTORIAL,TSUKUBA,201718
↑Linear ↑Second order ↑Third order
p(1)(t)
p(3)(t)
I 1, I 3I 2, I 3Ez(t)
0.15
0
-0.15
p z(1
) (t) (a
u)
0 5 10 15 20Time t (fs)
6
-6
0
p z(3
) (t) (a
u)
0 5 10 15 20Time t (fs)
• NumericallyexpandedtheSiO2 responsestothep(1) andp(3) components
P(t) =p(1)(t)E + p(2)(t)E2 + p(3)(t)E3 + · · ·
PulseintensityI1 =1X1010 W/cm2I2 =5X1010 W/cm2I3 =1X1011 W/cm2
• χ(3)=4.32X10-22 V2/m2 (LDA),• =1.34X10-22 V2/m2 (mGGA)• Experimentχ(3)=2.5X10-22 V2/m2
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
ExcitationEnergyofSiliconCrystal
SALMONTUTORIAL,TSUKUBA,201719
Eex
(t) = Etot
(t)� Etot
(0)
Excitationenergy Z t
J(t0)E(t0) dt0or
S.A.Sato,K.Yabanaetal.J.Chem.Phys.143,(2015).
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience 20
PART 4
Multiscale Maxwell+TDDFTCalculation
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
LightPropagationinSolidStateMaterial
SALMONTUTORIAL,TSUKUBA,201721
Weakintensitylight
Strongintensitylight
• Lightpropagationinthesolidmedia→Maxwell’swaveequation.
E(t)IncidentEMfield
+++
- - -P(t)
Considerthelightirradiationintothesolidmaterial,E(t):AppliedElectricFieldP(t):InducedPolarization
• Dielectricresponsetoappliedfield→ LinearResponse
P = �(1)E = ("� 1)/4⇡ ·E
�r⇥r⇥A(r, t)� "
c2@2
@t2A(r, t) =0
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
LightPropagationinSolidStateMaterial
SALMONTUTORIAL,TSUKUBA,201722
J(t) =� e
m
X
b,k
1
⌦
Z
⌦Re u?
b,k(r, t)⇣�i~r+ ~k+
e
cA(t)
⌘2ub,k(r, t) dr+ JNL
J =J[A(t)]
• “ConstitutionRelation”ofElectromagnetics:(CurrentdensitycanbedescribedasthefunctionaloftheEMfield)
Inducedcurrentdensityinmatter
�r⇥r⇥A� 1
c2@
@t2A =� 4⇡
cJ
• GoverningequationofEMfield(Maxwell’swaveeq.)Couple
Lightpropagationinthemedia
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
MultiscaleMaxwell-TDDFTcalculation
SALMONTUTORIAL,TSUKUBA,201723
SolveTD-KSEq.inMicroscopicGrid
RT-TDDFTcalculation:
Macroscopicsystem(EMfield)
SolveMaxwell’sEq.inMacroscopicgrid:
Microscopicsystem(Electrondynamics)
FDTD-basedEMcalculation:
r⇥r⇥A+1
c2@2A
@t2=4⇡
cJ
A(t��ti) ! J(t)J(t��ti) ! A(t)
ExchangeJandAateverytimestep
Eunk = H(k)unk
�x ⇠ 10 nm
�x ⇠ 0.05 nm
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
ExampleofMultiscaleCalculation
SALMONTUTORIAL,TSUKUBA,201724
Computationmodel
Incidentpulse
Vacuumregion VacuumregionMatter region
• Considerthelaserpulseirradiationtothin-film(d~7μm)Siliconcrystal
• Incidentpulse• Frequency:1.55eV• Pulselength:16fs• Azimuthpolarizedbeam• I=1012 W/cm2
7um
Si
0°
45°
90°
135°
180°
225°
270°
315°
2040
6080
MartinKrausetal,OpEx,18,.21
2Dimensionalproblem
• Cylindricalsymmetriccase• Lightpropagationtothinfilmsemiconductor
• Application• SimulationofLaserProcessingbyCylindricalVectorBeam
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
ExampleofMultiscaleCalculation
SALMONTUTORIAL,TSUKUBA,201725
EMFieldVacuum MatterRegion Vacuum
PenetrationDepth(nm)
ElectronicExcitationEnergy
PenetrationDepth(nm)
Energyabsorptionbythemulti-photonexcitationprocess
• 512X64=32768macroscopicpoints
http://salmon-tddft.jp/ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
Conclusion
SALMONTUTORIAL,TSUKUBA,201726
ScalableAb-initioLight-MattersimulatorforOpticsandNanoscience
IsolatedSystem(Molecule) PeriodicSystem(Solidmaterial)
GroundStateCalculation: Totalenergy,DoS,Chargedensityprofile…
LinearResponseCalculation: Dielectricfunction,Oscillatorstrength…
PulseReponseCalculation: Nonlinearexcitation,Energytransfer...
Maxwell+TDDFT MultiscaleCalculation
Let’s enjoy your research life with SALMON !