Time-Dependent Density Functional Theory in Condensed Matter Physics

Size: px

Start display at page:

Download "Time-Dependent Density Functional Theory in Condensed Matter Physics"

Pamela Todd
6 years ago
Views:

Exenal Revew on Cene fo Compuaonal Scences Unvesy of Tsukuba 013..18-0 Tme-Dependen Densy Funconal Theoy n Condensed Mae Physcs K.

1 Exenal Revew on Cene fo Compuaonal Scences Unvesy of Tsukuba Tme-Dependen Densy Funconal Theoy n Condensed Mae Physcs K. YABANA Cene fo Compuaonal Scences Unvesy of Tsukuba Collaboaos: G.F. Besch Unv. Washngon T. Oobe JAEA J.-I. Iwaa Unv. Tokyo S. Shnohaa Unv. Tsukuba/MPI T. Sugyama Unv. Tsukuba S.A. Sao Unv. Tsukuba

1MeV 1eV Tme 10-3 s 10-17 s Mass 10 9 ev 5x10 5 ev

2 poon neuon Nucle Nucleon many-body sysem Aoms Molecules Solds Elecon many-body sysems Sze m m Enegy 1MeV 1eV Tme 10-3 s s Mass 10 9 ev 5x10 5 ev Ineacon Nuclea foce Coulomb foce (Song neacon) Sascs Femon Femon

3 Tme-Dependen Densy Funconal Theoy Successful fo quanave descpon of many-femon dynamcs Nucle (nucleon dynamcs) Aoms Molecules Solds (elecon dynamcs) Lnea esponse egme - Gan esonances ( (Q)RPA ) - Eleconc excaons n molecules - Opcal esponse of molecules and solds Nonlnea egme Inal value poblem - Heavy on collson - Lase scence (Inense and ula-sho lase pulse)

4 4 We ae developng eal-me TDDFT compuaonal mehod. K. Yabana G.F. Besch Phys. Rev. B (1996). ( ) ) ( ) ( )) ( ( ' ) ' ( ' ) ( V n n d e R V m a ex xc a on ψ ψ µ = = n ) ( ) ( ψ Hamlonan fo elecons n Fs-pncples DFT We poneeed he mehod combnng nuclea mehod developed n TDHF calculaon wh fs-pncples densy funconal Hamlonan n condensed mae physcs. ( ) l k j m z y x ψ - Hgh-ode fne dffeence appoxmaon fo dffeenal opeaos - Taylo expanson mehod fo me evoluon

Na 147 Assume Icosahedal shape L 147 Densy change nduced by mpulsve foce 30

5 Elecon dynamcs n meallc cluses by TDDFT K. Yabana G.F. Besch Phys. Rev. B (1996). Na 147 Assume Icosahedal shape L 147 Densy change nduced by mpulsve foce Dpole momen Dpole momen Tme [ev -1 ] Dpole momen as funcon of me 10 0 Tme [ev -1 ]

6 Real-me calculaon fo opcal absopon specum of L 147 K. Yabana G.F. Besch Phys. Rev. B (1996). Real-me calculaon fo auocoelaon funcon zˆ ( ) zˆ ( 0) [ev -1 ] Exp:L 139 TDDFT Foue ansfomaon oscllao sengh dsbuon σ 1 k ω ( ω) d e zˆ ( ) zˆ ( 0)

7 Phooabsopon of molecules by TDDFT (LB94 funconal) Connuum RPA calculaon fo defomed sysem K. Yabana Y. Kawasha T. Nakasukasa J.-I. Iwaa Chaged Pacle and Phoon Ineacons wh Mae: Recen Advances Applcaons and Inefaces Chape 4 Taylo & Fancs 010. N H O C 6 H 6 C 60

Elecon dynamcs n bulk S unde song lase pulse I= 3.

8 Elecon dynamcs n bulk S unde song lase pulse I= W/cm T=50 fs ħω=0.5 ev Lase phoon enegy s much lowe han dec bandgap. Elecc Feld (a.u.) Tme (fs) 40 Densy change fom he gound sae (110) Gound sae densy (110) Red Geen 0 Blue - 8

9 Tme-dependen exenson of Bloch s band heoy ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ' ' ' 1 = = nk nk nk xc nk u n u n n e d A c e k p m u µ ( ) ( ) u a u nk nk = Compuaonal aspecs - 3D unfom gd fo space hgh-ode fne dffeence fo dffeenaon - Taylo expanson fo me evoluon Elecon dynamcs n cysallne sold (aomc posons ae fxed)

10 Delecc funcon of S fom eal-me TDDFT-ALDA Insananeous kck a =0 hen calculae cuen J() σ 1 = k ω ( ω) d e J ( ) ε ( ω) = 1 4 ( ω) ω π σ J ( ) τ fs 10 No vey good n qualy howeve.

11 Fones of Lase Scence - Nonlnea elecon dynamcs nduced by song lase pulse - Ulafas elecon dynamcs femo o aosecon - 11

12 Fones of Opcal Scences: Inense lase pulse on sold Lase nensy W/cm 10 W/cm Nonlnea opcs Coheen phonon HHG Elecon-hole plasma Opcal beakdown Lase machnng Lase acceleaon Vacuum beakdown Nonelavsc Quamum mechancs Relavsc Classcal mechancs ee()z z Exenal elecc feld by lase pulse Inenal elecc feld by nucle

Fones n Opcal Scences: Ula-sho dynamcs Pcosecond 10 1 s Femosecond 10 15 s Aosecond 10 18 s 10 3 s Tme Peod of Opcal phonon (S 64 fs) Peod of elecon obal n Hydogen

13 Fones n Opcal Scences: Ula-sho dynamcs Pcosecond 10 1 s Femosecond s Aosecond s 10 3 s Tme Peod of Opcal phonon (S 64 fs) Peod of elecon obal n Hydogen 150as Nucleon moon n nucleus Peod of T-sapphe lase pulse Shoes lase pulse 80 as (008) Real-me obsevaon of valence elecon moon E. Goulelmaks e.al Naue (010). 13

Nonhemal Lase Machney Melng ablaon flamenaon on bulk suface

Mcomachnng wavegude- Nanosugey Opcal mcoscope mage of

14 Nonhemal Lase Machney Melng ablaon flamenaon on bulk suface R.R. Gaass E. Mazu Naue Phooncs 0 (008). Mcomachnng wavegude- Nanosugey Opcal mcoscope mage of wavegudes wen nsde bulk glass by a 5-MHz an of 5-nJ sub-100-fs pulses C.B. Schaffe e.al OPTICS LETTERS 6 93 (001) Ablaon of a sngle mochondon n a lvng cell. N. Shen e.al Mech. Chem. Bosysems 17 (005). 14

15 Queson: How o descbe song lase pulse popagaon n solds? Assume consan delecc funcon λ = 800nm ω = 1.55eV (below dec band gap) A/c Vacuum ε=1 S ε=16 Macoscopc Maxwell eq. ε c ( z) z A = ( z ) A( z ) 0 [µm] Weak feld Descbed solely by delecc funcon (lnea esponse) Exemely song feld Mcoscopcally nonlnea elecon dynamcs nsde sold. Macoscopcally elecomagnesm need modfcaon. How?

16 Queson: How o descbe song lase pulse popagaon n solds? Ou answe I s necessay o combne elecomagnesm and quanum mechancs by lage scale compung Real-me TDDFT fo mcoscopc elecon dynamcs Macoscopc Maxwell equaon 16

17 Peubaon heoy sepaaes macoscopc elecomagnesm (EM) and quanum mechancs (QM) hough Consuve Relaon. D α = α α ( ) E ( ) 4πP ( ) = d' ε ( ' ) E ( ' ) αβ β Elecomagnesm: Maxwell equaon fo macoscopc felds E D B H Lnea consuve elaon D = [ ] = ε ( ω)e D E Quanum Mechancs: Peubaon heoy o calculae lnea suscepbles ε(ω) D α As he feld sengh becomes lage nonlnea opcs becomes mpoan. = αβ β ( ( ) ( ) ( ) ) d' ε ' E ' 4π d' d'' χ ( ' '' ) E ( ' ) E ( '' ) αβγ β γ A exeme nense lm EM and QM no moe sepaae.

18 Mulscale smulaon ( ) ( ) ( ) J c A A c 4 1 π = Macoscopc gd pons(μm) o descbe macoscopc veco poenal { } e on xc en en n E e A c e m 4 1 = = π φ ψ δ δ φ ψ ψ ψ ( ) A n c e m j j d J e e e * * 4 ) ( π ψ ψ ψ ψ = = Ω A each macoscopc pons Kohn-Sham obals ae pepaed and descbed n mcoscopc gds. Exchange of nfomaon by macoscopc cuen and macoscopc veco poenal. ( ) A ( ) J ψ A each macoscopc gd pon We consde a un cell and pepae mcoscopc gd. K. Yabana T. Sugyama Y. Shnohaa T. Oobe G.F. Besch Phys. Rev. B (01).

19 Popagaon of weak pulse Odnay elecomagnesm s OK. A/c Lase fequency:1.55ev: lowe han dec bandgap.4ev(lda) I=10 10 W/cm Vacuum S [µm] =0 [µm] =0.8 [µm] =1.6 [µm] Coupled Maxwell TDDFT smulaon 19

20 Moe nense lase pulse Dynamcs of elecons and macoscopc EM felds ae no moe sepaable. I =5 x 10 1 W/cm Vacuum S [µm] =0 [µm] =0.8 [µm] =1.6 [µm] 0

21 Compuaonally challengng mulscale smulaon A pesen 1-dm popagaon (macoscopc gd) S damond: 1000 coes 10 hous 0000 coes 0 mn (K-compue Kobe) SO (α-quaz) coes hous Oblque ncdence -dm 50 3-dm - Self focusng - Ccula polazaon A mllon of maco-gd pons 1000 need o wa nex geneaon supecompues

22 Compuaonally scalable smulaon 1000 coes 10 hous coes 0 mn (K-compue Kobe) Pefomance a K-Compue n Kobe (n ealy access) We ae ganed 4M node-hous a K-compue fo 014 yea.

23 Concluson TDDFT s a useful unvesal heoy fo many-femon dynamcs. Nuclea Physcs Aoms Molecules Solds Lneaa esponse Gan esonances Phooabsopon Delecc funcon Inal value poblem Heavy on collsons Song lase scences Ineacon of song lase pulse and solds eque connecon of wo basc physcs: Macoscopc elecomagnesm and quanum mechancs We have developed a new mulscale smulaon Maxwell TDDFT scheme whch uns only a he lages supecompues avalable oday. 3

Time-Dependent Density Functional Theory in Optical Sciences

Time-Dependent Density Functional Theory in Optical Sciences Exenal Revew on Cene fo Compuaonal Scences Unvesy of Tsuuba 013..18-0 Tme-Dependen Densy Funconal Theoy n Opcal Scences K. YABANA Cene fo Compuaonal Scences Unvesy of Tsuuba Collaboaos: G.F. Besch Unv.