Plasmonics and non-local interactions from TDDFT: graphene and metal surfaces

Transcription

1 Plasmonics and non-local inteactions fom TDDFT: gaphene and metal sufaces Thomas Olsen Cente fo Atomic-scale Mateials Design CAMD Depatment of Physics Technical Univesity of Denmak

2 Outline Linea esponse theoy and excited states Plasmons on metal sufaces and influence of adsobates Plasmons in gaphene coupled to substates Total enegies fom RPA: gaphene at metal sufaces

3 Linea density esponse function ] ˆ ˆ [ V T n n n eff ϕ ϕ ε + Eigenvalues and wave functions do not epesent physical excitations! Single-paticle DFT equation: Excited state popeties can be obtained fom the linea density esponse function defined by. ' ', ' ', ;, ', t V t t d t n δ fo some extenal petubation V,t ' ', ' ', ;, ', t V t t d t n δ Non-inteacting esponse function follows fom 1. ode petubation theoy on DFT states: m n m n n i m m i n m n i e e f f, ', η ε ε ϕ ϕ ϕ ϕ G q G q GG' q

4 Linea density esponse function The inteacting esponse function can be calculated fom the Dyson equation: + f Hxc The Hatee-exchange-coelation kenel is defined as δv Hxc[ n], t f Hxc, t ; ', t ' δ ', t' We use the fequency independent appoximations: RPA f Hxc 1 ', f ALDA Hxc f RPA Hxc + d 2 E dn LDA xc 2 [ n] n n All calculations have been pefomed with the code GPAW, which uses the Pojecto Augmented Wave method to implicitly epesent all-electon wavefunctions J. Enkovaaa et al, J. Phys.: Condens. Matte. 22,

5 Dielectic constants of simple semiconductos Micoscopic dynamical dielectic function: ε RPA GG' q, δ GG' 4π, 2 GG' q q + G Imε M Si Macoscopic dielectic constant εm q, -1 ε 1 q, Calculated dielectic optical constants: ε ε M q, Reε M

6 Dielectic constants of simple semiconductos Micoscopic dynamical dielectic function: ε RPA GG' q, δ GG' 4π, 2 GG' q q + G Imε M Si Macoscopic dielectic constant εm q, -1 ε 1 q, Calculated dielectic optical constants: ε ε M q, In the following we focus on the Electon Enegy Loss Spectum: Reε M EELS Im ε M 1 q,

7 Suface plasmons on Mg1 The suface plasmon enegy is accuately epoduced at the level of ALDA J. Yan, J. J. Motensen, K. W. Jacobsen, and K. S. Thygesen Phys. Rev. B 83,

8 Suface plasmons on Ag111 Calculated band stuctue fo 1 ML Ag111 slab Photoemission expeiments on Ag111 1ML film Coect alignment of the Ag d-band is accomplished by using a non-standad exchange-coelation potential GLLB. O. Gitsenko, R. van Leeuwen, E. van Lenthe, and E. J. Baeends, Phys. Rev. A 51, M. Kuisma, J. Ojanen, J. Enkovaaa, and T. T. Rantala, Phys. Rev. B 82,

9 Suface plasmons on Ag111 Calculated band stuctue fo 1 ML Ag111 slab Calculated electon enegy loss spectum Too high position of Ag d-band leads to ovesceening of the plasmon. The poblem is almost solved by the GLLB potential J. Yan, K. W. Jacobsen, and K. S. Thygesen Phys. Rev. B 84,

10 Suface plasmons on Ag111 Calculated EELS specta at diffeent q vectos. Suface plasmon dispesion How can we tune the suface plasmon? Nanostuctuing of the suface Nano clustes of vaious shapes Doping in the bulk to change electon density Chemical functionalization/doping of the suface itself Ageement with expeiments within.1 ev.

11 Influence of adsobed hydogen Low enegy peak in EELS spectum. This peak is due to inteband tansitions fom occupied H states blue to empty Ag d-states ed.

12 Gaphene plasmonics Gaphene suppots π-plasmons with popagation length ~µm and velocity ~1 6 m/s. Upon doping 2D metallic plasmons ae intoduced. What is the influence of substate on the gaphene plasmon? J. Yan, K. S. Thygesen, and K. W. Jacobsen Phys. Rev. Lett 16,

13 Gaphene plasmonics Electon Enegy Loss Spectum π-plasmon in fee standing gaphene Stong damping of π- plasmon by e-h pais in SiC substate Metallic sheet plasmon natual doping by substate E F

14 Gaphene plasmonics Electon Enegy Loss Spectum Gaphene π-plasmon Al111 suface plasmon The gaphene π-plasmon couples stongly to the metallic suface plasmon. J. Yan, J. J. Motensen, K. W. Jacobsen, and K. S. Thygesen Phys. Rev. B 83,

15 Gaphene plasmonics Model fo non-local coupling of plasmons Defining the coupled individual density esponses: [ ] s δv V δn g g δ n ext + [ ] g δv V δn s s δ n ext + c c We obtain a model fo the puely nonlocal esponse g eff δn δv g eff [ ] s 1+ V g c g s 1 V V c c The esults ae nealy identical to the calculation of the full system J. Yan, K. S. Thygesen, and K. W. Jacobsen Phys. Rev. Lett 16,

16 Plasmon outlook Tailoing suface plasmons on noble and simple metal sufaces by chemical functionalization/doping Atomic-scale undestanding of the elation between metalmolecule inteaction and plasmon enegy chemical sensing Appoaching plasmonics: Micoscopic dielectic function + Maxwell equations Intoduce mateial dimension in plasmonics easeach

17 Total enegies fom RPA The adiabatic connection and fluctuation-dissipation theoem gives the coelation enegy in tems of the esponse function: [ ] 1 T 2 1 λ π λ i v i v d d E c Fom TDDFT we have λ λ λ f Hxc + [ ] + ln 1 T 2 π i v i v d E RPA c Fo fxc, one obtains the RPA esult:

18 Total enegies fom RPA RPA potential enegy sufaces Chemisoption Physisoption T. Olsen, J. Yan, J. J. Motensen, and K. S. Thygesen Phys. Rev. Lett. 17,

19 Total enegies fom RPA RPA potential enegy sufaces Semi-local and vdw functionals account well fo eithe dispesive o covalent inteactions RPA seems to captue both effects T. Olsen, J. Yan, J. J. Motensen, and K. S. Thygesen Phys. Rev. Lett. 17,

20 Total enegies fom RPA RPA potential enegy sufaces The binding mechanisms ae athe diffeent fo the thee metals Fo Ni111, the chemisoption minimum is due to exchange, while fo Cu and Co the binding is due to coelation T. Olsen, J. Yan, J. J. Motensen, and K. S. Thygesen Phys. Rev. Lett. 17,

21 Outlook: RPA total enegies RPA does not in geneal impove the desciption of covalent bonds, but pefoms much bette that semi-local functionals when vdw inteactions ae impotant and bette that vdw appoximations when covalent bonds ae impotant RPA becomes pohibitly expensive fo lage systems. Appoximations could be intoduced fo The sum ove high lying unoccupied bands in the esponse functions Bette extapolation schemes beyond E cut -1.5 scaling Lage self-coelation eo. The RPA coelation enegy of the H atom is -.57 ev! Cancel the self-coelation eo by Many-body petubation theoy - Second ode sceened exchange TDDFT - fxc.

22 Acknowledgements People: Jun Yan Jens J. Motensen Kistian S. Thygesen Kasten W. Jacobsen Funding: The Lundbeck Foundation Danish Agency fo Science Technology and Innovation Danish Cente fo Scientific Computing