Quasiparticle Excitations and Optical Response of Bulk and Reduced-Dimensional Systems
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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

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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


+ Reduced-Dimensional Systems

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 Reduced-Dimensional Systems


Diagrammatic Expansion of the Self Energy Reduced-Dimensional Systems

in Screened Coulomb Interaction


H = H Reduced-Dimensional Systemso + (H - Ho)

Hybertsen and Louie (1985)


Quasiparticle band gaps gw results vs experimental values
Quasiparticle Band Gaps: GW results vs experimental values Reduced-Dimensional Systems

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 Reduced-Dimensional Systems

Theory:

Hybertsen & Louie (1986)

Photoemission:

Wachs, et al (1985)

Inverse Photoemission:

Himpsel, et al (1992)


Optical Properties Reduced-Dimensional Systems


M. Rohfling and S. G. Louie, PRL (1998) Reduced-Dimensional Systems


Both terms important! Reduced-Dimensional Systems

repulsive

attractive


Rohlfing & Louie Reduced-Dimensional Systems

PRL,1998.


Optical Absorption Spectrum of SiO2 Reduced-Dimensional Systems

Chang, Rohlfing& Louie.

PRL, 2000.


Exciton bindng energy? Reduced-Dimensional Systems


E Reduced-Dimensional Systemsg

p1 - p1*

p2 - p2*

Exciton binding

energy ~ 1eV

p2 - p1*

p1 - p2*

Rohlfing & Louie

PRL (1999)


Si(111) 2x1 Surface Reduced-Dimensional Systems

Measured values: Bulk-state qp gap 1.2 eV

Surface-state qp gap 0.7 eV

Surface-state opt. gap 0.4 eV


Si (111) 2x1 Reduced-Dimensional Systems

Surface


Ge(111) 2x1 Surface Reduced-Dimensional Systems


Rohlfing & Louie, Reduced-Dimensional Systems

PRL, 1998.


Optical Properties of Reduced-Dimensional Systems

Carbon and BN Nanotubes


Optical excitations in carbon nanotubes

(n,m) carbon nanotube Reduced-Dimensional Systems

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


Quasiparticle self energy corrections
Quasiparticle Self-Energy Corrections Reduced-Dimensional Systems

(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 Reduced-Dimensional Systems

  • 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 Reduced-Dimensional Systems

  • Net repulsive electron-hole interaction

  • No bound excitons

  • Suppression of interband oscillator strengths


Both terms important! Reduced-Dimensional Systems

repulsive

attractive


Absorption Spectrum of (8,0) Carbon Nanotube Reduced-Dimensional Systems

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 Reduced-Dimensional Systems

(8,0) Semiconducting Carbon Nanotubes


1D Hydrogen atom Reduced-Dimensional Systems

(R. Loudon, Am. J. Phys. 27, 649 (1959))

Ground state:

Excited states:


Theory Reduced-Dimensional Systems

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)


Optical excitations in 8 0 11 0 swcnts
Optical Excitations in (8,0) & (11,0) SWCNTs Reduced-Dimensional Systems

  • 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)


(8,0) Reduced-Dimensional Systems

(7,0)

(11,0)

(10,0)

Optical Spectrum of Carbon SWNTs


Calculated Absorption Spectra of (8,0) BN Nanotube Reduced-Dimensional Systems

Exciton binding energy > 2 eV!

Park, Spataru, and Louie, 2005


Lowest Bright Exciton in (8,0) Boron-Nitride Nanotube Reduced-Dimensional Systems

  • Composed of 4 sets of transitions



E Reduced-Dimensional Systems

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).


  • 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.


  • 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, …


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