Real-time TDDFT simulations within SIESTA. Daniel Sánchez-Portal, Rafi Ullah, Fabiano Corsetti, Miguel Pruneda and Emilio Artacho

Transcription

1 Real-ime TDDFT simulaios wihi SIESTA Daiel Sáchez-Poal, Rafi Ullah, Fabiao Cosei, Miguel Pueda ad Emilio Aacho

2 Mai objecive Apply eal-ime simulaios wihi ime-depede desiy fucioal heoy TDDFT o sudy eleco ad coupled eleco-io dyamics fo solids ad cluses Keywods: TDDFT o follow he eleco dyamics: Sadad appoach fo elecoic espose of solids Simila esuls o RPA wih less sophisicaed omal XC keels Real-ime simulaios as opposie o fequecy domai: Abiay peubaios, i.e., o-liea egime available Need fo vey sable algoihms fo ime evoluio Ehefes dyamics fo he coupled eleco-io dyamics

3 DFT- Koh Sham Idepede paicles i a effecive poeial ] [ ρ xc ex eff V V V Φ V eff ψ ε ψ ψ d ʹ ʹ ʹ Φ 3 ρ Haee poeial ] [ E V xc c x δρ ρ δ Exchage-coelaio poeial 2 e N ψ ρ wih

4 Exesio o ime depede siuaios: Time depede desiy fucioal heoy ˆ 1 0 H d A Ψ Ψ Time depede quaum evoluio ca be obaied fom a saioay poi of he acio A 0, 1 I pacice, TDKS equaios,,,, i V eff ψ ψ ψ ], [,,, j V V V xc ex eff ρ Φ ],,, [ 0 A A Ψ ρ TDDFT E. Ruge ad E. K.U. Goss, PRL 84

5 Sadad appoximaio also i SIESTA So-called adiabaic saic appoximaio fo he exchage-coelaio poeial Depeds o isaaeous desiy

6 Eleco dyamics i SIESTA I TD-KS equaios: i Ψ HΨ SIESTA LCAO: Ψ i, ρ, µ µ,ν c i µ φ µ ρ µν φ µ φ ν c ν H c ν µν µν is i c S 1 Hc

7 Eleco dyamics i SIESTA II Disceizaio of TD-KS equaios: Hc S c i / 1 c H S i c c Δ Fowad popagaio fo d/2 Backwads popagaio fo d/ / 1 Δ c H S i c c Cak-Nicholso c H is H is c Δ Δ Uiay by cosucio Good eegy cosevaio Time evesal symmey 1 O H H Δ

8 Applicaios o calculae opical adsopio A. Tsolakidis, D. Sáchez-Poal, R. M. Mai, PRB2002, adapig a ecipe by Yabaa ad Besch, PRB 1996 E D Low eegy peaks wih TDLDA σ SIESTA Yabaa Exp π D ω α ω E ω

9 TDDDFT vesus Koh-Sham esul No selfcosise Usual shif o highe eegies TDDFT A. Tsolakidis, D. Sáchez-Poal, R. M. Mai, Phys. Rev. B 66,

10 Respose of cabo aoubes o a exeal field pepedicula o he axis Sog depolaizaio effec E ex [ ] 3 ω Ag I α - m1 plasmo Ou calculaio fo he 3,3 ube i vey good ageeme wih he esuls L. Wiz, e al. Elecoic Popeies of Novel Maeials: XVIIh Ieaioal Wieschool, 2003 ad Maiopoulus, Reiig, Rubio,Vas, PRL, 2003

11 Resuls fo SWCNT of lage diamees E ex 3 [ ω ] Ag I α No se puede mosa la image. Puede que su equipo o ega suficiee memoia paa abi la image o que ésa esé dañada. Reiicie el equipo y, a coiuació, aba el achivo de uevo. Si sigue apaeciedo la x oja, puede que ega que boa la image e iseala de uevo. 3 [ ω ] Ag I α gaphee

12 m1 π plasmo as a fucio of he ube adius No se puede mosa la image. Puede que su equipo o ega suficiee memoia paa abi la image o que ésa esé dañada. Reiicie el equipo y, a coiuació, aba el achivo de uevo. Si sigue apaeciedo la x oja, puede que ega que boa la image e iseala de uevo.

13 Key appoximaios fo coupled eleco dyamics µ ψ c φµ Rµ ψ µ µ c µ φ µ c µ v. φ µ µ Basis se moveme gives ise o addiioal ems, depede o velociies, ha ae igoed i ou case. Isead we pefom he eleco dyamics fo saic ios ad pojec he wavefucios fom oe se of aomic posiios o he followig ick by Sakey ad Tomfoh. Isead we use a appoximae uiay pojeco opeao [poposed by Tomfoh ad Sakey, PSSb 2001] o fid he ew coefficies of he wavefucios i he aslaed basis se This woks well whe io velociies ae o vey lage Time sep used fo io dyamics is sufficiely small

14 Applicaio o sudy elecoic soppig powe i solids

15 Compuig he eegy loss TDDFT calculaio of he eegy loss as a fucio of he speed of he pojecile Vey simple fo a localized age: Add a peubaio ad.. 1 Displace he peubaio wih cosa velociy ad ecod he oal eegy 2 Compue he foce o pojecile ad iegae ΔE Eegy và 0 ΔE ~0 Localized scaee posiio Will somehig simila wok fo a solid?

16 Solids? Peiodic bouday codiios: fiie size effecs Iiially saic peubaio: asie effecs? Achievig a saioay egime is ecessay fo a meaigful defiiio of he soppig powe i solids: de dx 1 v de d

17 Mai esul Real-ime TDDFT simulaios seem o wok o sudy elecoic soppig i solids Peiodic bouday codiios/fiie size effecs do o seems o affec fo supecells of easoable size, a leas a low velociies < 0.5 a.u. Vey bief asies Saioay icease of he eegy achieved, allowig fo he defiiio of a elecoic soppig powe

18 H i Gemaium 96 aoms supecell up o 144 i checks ΔE elec. o. ev Δν0.05 a.u a.u. [001] chael a.u z Boh R Ullah, F Cosei, D Sachez-Poal & E Aacho PRB 2015

19 H i Gemaium Expeimeal daa: D. Roh, D. Goebl, D. Pimezhofe, ad P. Baue, NIMB v h v h exp ~ 0.03 a.u. v h [001] ~0.05 a.u. v h [111] ~0.03 a.u. v h [011] ~0.03 a.u. Elecoic soppig powe vs velociy R Ullah, F Cosei, D Sachez-Poal & E Aacho PRB 2015

20 H i gemaium: Small-gap semicoduco Adiabaic sceeig Dyamic v 0.5 a.u. sceeig R Ullah, F Cosei, D Sachez-Poal & E Aacho, PRB 2015

21 Elecoic soppig of H ad He i gold Exp-Th compaiso A Zeb, J Kohaoff, D Sachez-Poal, A Aau, JI Juaisi & E Aacho PRL 2012

22 Coclusio RT-TDDFT comig soo ex SIESTA elease, aleady i uk vesio ad available i lauchpad Alhough somewha less opimized ha he goud sae calculaios i allows sudyig he opical popeies ad he espose of he sysem o peubaios beyod he liea egime fo sysems coaiig up o hudeds aoms So fa i has bee successfully esed o sudy he opical popeies of aosucues ad he elecoic ficio i he pocess of ieacio of fas ios wih solids.