Quasiparticle Excitations and Optical Response of Bulk and

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: In. Sb, In. As Ge Ga. Sb Si In. P Ga. As Cd. S Al. Sb, Al. As Cd. Se, Cd. Te BP Si. C C 60 Ga. P Al. P Zn. Te, Zn. Se c-Ga. N, w-Ga. N In. S w-BN, c-BN diamond w-Al. N Li. Cl Fluorite Li. F 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 Si. O 2 Chang, Rohlfing& Louie. PRL, 2000.

Exciton bindng energy?

Eg p 1 - p 1* p 2 - p 2* Exciton binding energy ~ 1 e. V p 2 - p 1* p 1 - p 2* Rohlfing & Louie PRL (1999)

Si(111) 2 x 1 Surface Measured values: Bulk-state qp gap Surface-state opt. gap 1. 2 e. V 0. 7 e. V 0. 4 e. V

Si (111) 2 x 1 Surface

Ge(111) 2 x 1 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 (~ 1 e. V) of the gap

Absorption Spectrum of (3, 3) Metallic Carbon Nanotube • Existence of a bound exciton (Eb = 86 me. V) • Due to 1 D, 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 e. V 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 ~ 1 e. V! [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

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

Optical Spectrum of 4. 2 A Nanotubes Possible helicities are: (5, 0), (4, 2) and (3, 3) Theory interband exciton 2. 0 e. V* 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 E 11 and second E 22 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 E 11 1. 60 e. V 1. 55 e. V 1. 20 e. V 1. 21 e. V E 22 1. 88 e. V 1. 80 e. V 1. 67 e. V 1. 74 e. V E 22/E 11 1. 17 1. 16 1. 40 1. 44 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)

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 e. V! 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 hc. Q E(Q) D<<k. BT • 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). Q 0 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 e. V. • 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, …