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, …