Spectroscopy of nanostructures: from optics to transport

Transcription

1 Spectroscopy of nanostructures: from optics to transport Angel Rubio NanoBio Spectroscopy Group, Dpto. Física de Materiales, Universidad del País Vasco, Centro Mixto CSIC UPV/EHU and DIPC Edificio Korta, San Sebastián, Spain bio.ehu.es E mail: angel.rubio@.ehu.es

2 OUTLINE Introduction: Framing the lecture: spectroscopies Excitations; response concepts Application to finite systems: Linear Response applications : small clusters, phenolates and porphyrines Photovoltaic applications: simple hybrid system Electronic transport Concepts in molecular transport

3 Physical Processes: Spectroscopies

4 Physical Processes: Spectroscopies

5 Photoexcitation and relaxation Time-dependent phenomena!

6

7 Electronic properties of a many body system Excited states Scheme Ground state DFT density n(r) yes, LDA, GGA's Corrections to KS eigenvalues? TDDFT n(r,t) and/or j(r,t) Yes, non-linear phenomena and time-resolved spectroscopies MBPT G1, total energy G2 QM See review: yes Disadvantages XC-func. (r,r') (w) dependence Quasiparticle excitations Comput. IP and EA optical absorption yes, in some cases! G. Onida, L. Reining and AR, Rev. Mod. Phys. 74, 601 (2002)

8 Density Functional versus Many body perturbation theory ground state What about excited-state properties: electronion dynamics, spectroscopies

9 Can we calculate spectra with DFT?

10 What is a spectrum?

11 Vinduced = n v + fxc n Hartree

12

13

14 Beyond DFT Im [ ] ~ vc <v D c> 2 (Ec-Ev- ) Im [ ] ~ s vc <v D c>avc S 2 ( S ) Bethe-Salpeter eqn:

15 Time Dependent Density Functional Theory (Runge and Gross 1984): All observables are functionals of the TD density One-to-one correspondence between the time-dependent density and the external potential, v(r,t) <------> (r,t)? Same timedependent density n(r,t) Time-Dependent Density Functional Theory, Lecture Notes in Physics, Vol. 706 (Springer, Berlin, 2006)

16 Time Dependent Density Functional Theory (Runge and Gross 1984): All observables are functionals of the TD density One-to-one correspondence between the time-dependent density and the external potential, v(r,t) <------> (r,t) d i ℏ =H dt 2 d i ℏ i=h KS [ { j } ] i, i=1, N dt? 2 ℏ e H KS = i A Axc V external V hartree V exchange V correlation 2m cℏ Time-Dependent Density Functional Theory, Lecture Notes in Physics, Vol. 706 (Springer, Berlin, 2006)

17

18 Linear Response TDDFT does the job for you!!! Vext however the KS system Veff = 0 0 v f x c 0 r,r ', w = ij f j f i ci r j r i r ' cj r ' i j w V x c r, f xc r, r ', = n r,

19 How to solve the linear response equations (1) Sum over states: 0 r,r ', w = ij f j f i ci r j r i r ' cj r ' i j w = 0 0 v f xc [1 v f xc 0 ] =0 Cassida's approach

20 How to solve the linear response equations (2) Time propagation Propagation Scheme: Apply a perturbation of the form vext (r,t) = z (t) to the ground state of the system + At t = 0 the Kohn-Sham orbitals are (r,t=0+)= eikz (r ) Propagate these KS wave-functions for a (in)finite time. The dynamical polarizability can be obtained from k -1 z

21 How to solve the linear response equations (3) Density Functional Perturbation Theory

22 Optical Spectroscopy optical gap transport gap photoemision (QP) gap

23 Optical response:

24 Absorption Spectra of p Nitrophenolate Ions in Vacuo and in Solution serve as donor acceptor molecules Steen Bronsted Nielsen et al, ChemPhysChem (2009)

25 Absorption Spectra of p Nitrophenolate Ions in Vacuo and in Solution HOMO 1 Absorption / arb. units W avelength / nm LUMO Fluctuations due to planar-non planar geometries ~ ev (2 and 4 are not planar in DFT) CT is slightly favor by torsion of phenyl rings Steen Bronsted Nielsen et al, ChemPhysChem (in press 2009)

26 Absorption Spectra of p Nitrophenolate Ions in Vacuo and in Solution O NO2 S1 h O S0 O NO 2 NO2 From blue to red: in vacuo they cover the full visible whereas in solution they absorb in a narrow energy region The solvent shift is mainly due to counter ion and H-bond interactions, then the results do not correlate with solvent polarity

27 Towards the color of plants:

28 Towards the color of plants: The real Chlorophyll molecule

29 Towards the color of plants: The real Chlorophyll molecule

30 Towards the color of plants: The real Chlorophyll molecule

31 Photovoltaics Hybrids Grätzel cells

32 CT: Photo-excitation of the lightharvesting carotenoid-porphyrin-c60? N. Spallanzine et al, J. Phys. Chem. B, 2009, 113 (2009)

33 Photo-excitation of the light-harvesting carotenoid-porphyrin-c60

34 Carotenoid-porphyrin-C60 photodynamics Charge on the C60 Dynamical ions Clamped ions Clamped ions

35 35 Quantum Transport Ab-initio model Non-equilibrium Quantum Mechanics Many-body problem Thanks to R. Godby I(t)=I([U]); Conductance G=I/U for steady state

36 Applying a bias voltage Current: (Landauer)! Molecular DOS The bias can affect the HOMO-LUMO gap The bias can affect the resonance width These effects must be taken into account to describe the IV

37 37 Experiments & modelling Experiments: Octanedithiol/Au: R 900 MΩ [X. D. Cui et al., Science (2001).] Benzene-di-amin/Au: R 2 MΩ [Quek, Nano Lett. (2007).] Benzene-di-thiol/Au: R 18±12 MΩ [M. A. Reed et al. Science (1997).] H2/Pt: G 0.95 G0 ( 1/(13 kω)) [R.H.M.Smit et al. Nature (2002).] Theory Density Functional Theory + NEGF: for G G0 generally good for G << G0 poor e.g. G G0 for Benzene-di-amin/Au [Quek, Nano Lett. (2007).] X. D. Cui et al. Science, Vol 294, (2001)

38 LEVEL ALIGNMENT, Dispersion forces VdW Supramolecular chemistry Biophysics... Aromatic molecules on Cu(110) Molecular Transport N. Atodiresei, S.Blugel et al, PRL 102, (2009) See the talk of P. Rinke for CO on surfaces

39 MOLECULAR TRANSPORT : LEVEL ALIGNMENT

40

41

42 Molecular Transport in TDDFT G. Stefanucci, S. Kurth, AR and E.K.U Gross "Molecular electronics: analysis, design, and simulation", J. Seminario, ed(s), Elsevier Series on Theoretical and Computational Chemistry (2007); PRB (2005)

43

44

45 Example: Electron pumping Device which generates a net current between two electrodes (with NO static bias) by applying a timedependent potential in the device region Recent experimental realization : Pumping through carbon nanotube by surface acoustic waves on piezoelectric surface (Leek et al, PRL 95, (2005)) G. Stefanuci, S. Kurth, AR and E.K.U. Gross; PRB (2008)

46 Example: Electron pumping net current in the device by applying a TD potential to the device region Realisation: pumping in C nanotubes using surface acustic waves (Archimidean screw, ca. 250 bc) G. Stefanuci, S. Kurth, AR and E.K.U. Gross; PRB (2007)

47 OUTLOOK/PERSPECTIVE TDDFT is a powerful tool to handle the combined dynamics of electron/ion in response to external electromagnetic fields of nanostructures, biological molecules and extended systems. Ehrenfest dynamics provides valuable insight but with limitations Speed-up using a new Lagrangian formulation similar to CP The optics of low-dimensional structures is dominated by excitons Environment and T effects are important Work to be done: Memory effects l Dissipation ; lifetimes ; de-coherence Spatial non-locality: Charge-transfer excitations; Non-adiabatic effects in excite state ion dynamics (related to geometrical phases)

48 !!!! yo u k an Th For more details see: