#### Transcript Ab Initio Study of Surfaces and Nanostructures: DFT, GW and Beyond

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 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, … Quasiparticle Excitations Diagrammatic Expansion of the Self Energy in Screened Coulomb Interaction H = Ho + (H - Ho) Hybertsen and Louie (1985) 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 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? Eg p1 - p1* p2 - p2* Exciton binding energy ~ 1eV p2 - p1* p1 - p2* Rohlfing & Louie PRL (1999) Si(111) 2x1 Surface Measured values: Bulk-state qp gap Surface-state qp gap Surface-state opt. gap 1.2 eV 0.7 eV 0.4 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 (3,3) metallic SWCNT • • (8,0) semiconducting SWCNT Metallic tubes -- stretch of bands by ~15% Semiconductor tubes -- large opening (~ 1eV) of the gap 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 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 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)] Electron-hole Amplitude (or Exciton Waveunction) in (8,0) Semiconducting Carbon Nanotubes 1D Hydrogen atom (R. Loudon, Am. J. Phys. 27, 649 (1959)) e2 V ( z) = |z| Ground state: 0 ( z ) = d ( z ) 2 1 E0 = - 2m a 2 0 2 = - e B Excited states: E odd N =E even N 2 1 =2me aB2 N 2 N = 1, Optical Spectrum of 4.2A Nanotubes Possible helicities are: (5,0), (4,2) and (3,3) Theory interband exciton 2.0 eV* exciton Theory: Spataru, Ismail-Beigi, Benedict & Louie (2003) * E. Chang, et al (2004) Expt.: Li, et al. (2002) Hong Kong group 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 (8,0) Expta (11,0) Theory Exptb Theory E11 1.60 eV 1.55 eV 1.20 eV 1.21 eV E22 1.88 eV 1.80 eV 1.67 eV 1.74 eV E22/E11 1.17 1.16 1.40 1.44 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) Optical Spectrum of Carbon SWNTs (7,0) (10,0) (8,0) (11,0) Calculated Absorption Spectra of (8,0) BN Nanotube Exciton binding energy > 2 eV! 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 Radiative Life Time of Bright Excitons Transition rate (Fermi golden rule): E hcQ E(Q) c2a E 2 (Q) , if Q Q0 2 2 2 2 2 2 int rad (Q) = 2pe E (0) E (Q) - c Q , if Q Q 0 int rad D<<kBT (0) 10 ps for the(11,0)tube • Momentum conservation: only excitons with energy above the photon line can decay. • Temperature and dark-exciton effects (statistical averaged): T = 300 K Trad 10 ns • Expt: 10-100 ns Spataru, Ismail-Beigi, Capaz and Louie, PRL (2005). Q0 Q Q0 Q 10 ps 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, …