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

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, … First-principles Study of Spectroscopic Properties +

Quasiparticle Excitations

Diagrammatic Expansion of the Self Energy in Screened Coulomb Interaction

Hybertsen and Louie (1985) H = H o + (H - H o )

Quasiparticle Band Gaps: GW results vs experimental values Compiled by E. Shirley and S. G. Louie Materials include: InSb, InAs Ge GaSb Si InP GaAs CdS AlSb, AlAs CdSe, CdTe BP SiC C 60 GaP AlP ZnTe, ZnSe c-GaN, w-GaN InS w-BN, c-BN diamond w-AlN LiCl Fluorite LiF

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

Optical Properties

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

Both terms important! repulsive attractive

Rohlfing & Louie PRL,1998.

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

Exciton bindng energy?

EgEg                     Rohlfing & Louie PRL (1999) Exciton binding energy ~ 1eV

Si(111) 2x1 Surface Measured values: Bulk-state qp gap 1.2 eV Surface-state qp gap0.7 eV Surface-state opt. gap0.4 eV

Si (111) 2x1 Surface

Ge(111) 2x1 Surface

Rohlfing & Louie, PRL, 1998.

Optical Properties of Carbon and BN Nanotubes

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 (n,m) carbon nanotube

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

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

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

Both terms important! repulsive attractive

Absorption Spectrum of (8,0) Carbon Nanotube 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)] Absorption spectrum CNT (8,0)  eV Spataru, Ismail-Beigi, Benedict & Louie, PRL (2004) (Not Frenkel-like) |  (r e,r h )| 2

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

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

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

Optical Excitations in (8,0) & (11,0) SWCNTs (8,0)(11,0) Expt a TheoryExpt b Theory E eV1.55 eV1.20 eV 1.21 eV E eV1.80 eV1.67 eV 1.74 eV E 22 /E a S. Bachilo, et al., Science (2002) b Y. Ma, G. Fleming, et al (2004) Important Physical Effects: band structure quasiparticle self energy excitonic Spataru, Ismail-Beigi, Benedict & Louie, PRL (2004) Photoluminescence excitation ==> measurement of first E 11 and second E 22 optical transistion of individual tubes [Connell, et al., Science (2002)] Number of other techniques are now also available

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

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

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

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

Momentum conservation: only excitons with energy above the photon line can decay. Temperature and dark-exciton effects (statistical averaged): Expt: ns Radiative Life Time of Bright Excitons Transition rate (Fermi golden rule):  <<k B T Q hcQ E(Q)E(Q) E Q0Q0 Q  Q0Q0 10 ps Spataru, Ismail-Beigi, Capaz and Louie, PRL (2005).

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.

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, …