Theoretical Studies on Quasiparticle Excitations in Material Systems

1. Quasiparticle Excitations and Optical Response of Bulk and Reduced-Dimensional Systems Steven G. Louie Department of Physics, University of California at Berkeley and Materials Sciences Division, Lawrence Berkeley National Laboratory Supported by: National Science Foundation U.S. Department of Energy

2. + First-principles Study of Spectroscopic Properties • Many-electron interaction effects • Quasiparticles and the GW approximation - Excitonic effects and the Bethe-Salpeter equation • Physical quantities • - Quasiparticle energies and dispersion: band gaps, photoemission & tunneling spectra, … • - Optical response: absorption spectra, exciton binding energies and wavefunctions, radiative lifetime, … • - Forces in the excited-state: photo-induced structural transformations, …

3. Quasiparticle Excitations

5. Diagrammatic Expansion of the Self Energy in Screened Coulomb Interaction

6. H = Ho + (H - Ho) Hybertsen and Louie (1985)

7. Quasiparticle Band Gaps: GW results vs experimental values Materials include: InSb, InAs Ge GaSb Si InP GaAs CdS AlSb, AlAs CdSe, CdTe BP SiC C60 GaP AlP ZnTe, ZnSe c-GaN, w-GaN InS w-BN, c-BN diamond w-AlN LiCl Fluorite LiF Compiled by E. Shirley and S. G. Louie

8. Quasiparticle Band Structure of Germanium Theory: Hybertsen & Louie (1986) Photoemission: Wachs, et al (1985) Inverse Photoemission: Himpsel, et al (1992)

9. Optical Properties

11. M. Rohfling and S. G. Louie, PRL (1998)

12. Both terms important! repulsive attractive

14. Rohlfing & Louie PRL,1998.

17. Optical Absorption Spectrum of SiO2 Chang, Rohlfing& Louie. PRL, 2000.

18. Exciton bindng energy?

19. Eg p1 - p1* p2 - p2* Exciton binding energy ~ 1eV p2 - p1* p1 - p2* Rohlfing & Louie PRL (1999)

20. Si(111) 2x1 Surface Measured values: Bulk-state qp gap 1.2 eV Surface-state qp gap 0.7 eV Surface-state opt. gap 0.4 eV

21. Si (111) 2x1 Surface

24. Ge(111) 2x1 Surface

25. Rohlfing & Louie, PRL, 1998.

26. Optical Properties of Carbon and BN Nanotubes

27. (n,m) carbon nanotube Optical Excitations in Carbon Nanotubes • Recent advances allowed the measurement of optical response of well characterized, individual SWCNTs. [Li, et al., PRL (2001); Connell, et al., Science (2002), …] • Response is quite unusual and cannot be explained by conventional theories. • Many-electron interaction (self-energy and excitonic) effects are very important => interesting new physics

28. Quasiparticle Self-Energy Corrections (3,3) metallic SWCNT (8,0) semiconducting SWCNT • Metallic tubes -- stretch of bands by ~15% • Semiconductor tubes -- large opening (~ 1eV) of the gap

29. Absorption Spectrum of (3,3) Metallic Carbon Nanotube • Existence of a bound exciton (Eb = 86 meV) • Due to 1D, symmetric gap, and net short-range electron-hole attraction

30. Absorption Spectrum of (5,0) Carbon Nanotube • Net repulsive electron-hole interaction • No bound excitons • Suppression of interband oscillator strengths

31. Both terms important! repulsive attractive

32. Absorption Spectrum of (8,0) Carbon Nanotube Absorption spectrum CNT (8,0) d = 0.0125 eV Spataru, Ismail-Beigi, Benedict & Louie, PRL (2004) |(re,rh)|2 (Not Frenkel-like) • Long-range attractive electron-hole interaction • Spectrum dominated by bona fide and resonant excitons • Large binding energies ~ 1eV! • [Verified by 2-photon spectroscopy, F. Wang, T. Heinz, et al. (2005); also, Y. Ma, G. Fleming, et al. (2005)]

33. Electron-hole Amplitude (or Exciton Waveunction) in (8,0) Semiconducting Carbon Nanotubes

34. 1D Hydrogen atom (R. Loudon, Am. J. Phys. 27, 649 (1959)) Ground state: Excited states:

35. Theory 2.0 eV* interband exciton exciton Theory: Spataru, Ismail-Beigi, Benedict & Louie (2003) * E. Chang, et al (2004) Expt.: Li, et al. (2002) Hong Kong group Optical Spectrum of 4.2A Nanotubes Possible helicities are: (5,0), (4,2) and (3,3)

36. Optical Excitations in (8,0) & (11,0) SWCNTs • Photoluminescence excitation ==> measurement of first E11 and second E22 optical transistion of individual tubes [Connell, et al., Science (2002)] • Number of other techniques are now also available aS. Bachilo, et al., Science (2002) bY. Ma, G. Fleming, et al (2004) Important Physical Effects: band structure quasiparticle self energy excitonic Spataru, Ismail-Beigi, Benedict & Louie, PRL (2004)

37. (8,0) (7,0) (11,0) (10,0) Optical Spectrum of Carbon SWNTs

38. Calculated Absorption Spectra of (8,0) BN Nanotube Exciton binding energy > 2 eV! Park, Spataru, and Louie, 2005

39. Lowest Bright Exciton in (8,0) Boron-Nitride Nanotube • Composed of 4 sets of transitions

40. Comparison of Lowest Energy Exciton of (8,0) C and BN Tube

41. E hcQ E(Q) D<<kBT Q Q0  10 ps Q Q0 Radiative Life Time of Bright Excitons Transition rate (Fermi golden rule): • Momentum conservation: only excitons with energy above the photon line can decay. • Temperature and dark-exciton effects (statistical averaged): • Expt: 10-100 ns Spataru, Ismail-Beigi, Capaz and Louie, PRL (2005).

42. Summary • First-principles calculation of the detailed spectroscopic • properties of moderately correlated systems is now possible. • GW approximation yields quite accurate quasiparticle energies for many materials systems, to a level of ~0.1 eV. • Evaluation of the Bethe-Salpeter equation provides ab initio and quantitative results on exciton states, optical response and excited-state forces for crystals and reduced-dimensional systems. • Combination of DFT and MBPT ==> both ground- and excited-state properties of bulk materials and nanostructures.

43. Collaborators • Bulk and surface quasiparticle studies: • Mark Hybertsen • Eric Shirley • John Northrup • Michael Rohlfing, … • Excitons and optical properties of crystals, surfaces, polymers, and clusters: • Michael Rohlfing • Eric Chang • Sohrab Ismail-Beigi, …