Quasiparticle Excitations and Optical Response of Bulk and Reduced-Dimensional Systems
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Transcript of 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 Berkeleyand
Materials Sciences Division, Lawrence Berkeley National Laboratory
Supported by: National Science FoundationU.S. Department of Energy
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• 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
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Quasiparticle Excitations
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Diagrammatic Expansion of the Self Energy in Screened Coulomb Interaction
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Hybertsen and Louie (1985)
H = Ho + (H - Ho)
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Quasiparticle Band Gaps: GW results vs experimental values
Compiled byE. Shirley and S. G. Louie
Materials include:
InSb, InAsGe GaSbSiInPGaAsCdSAlSb, AlAsCdSe, CdTeBPSiCC60
GaPAlPZnTe, ZnSec-GaN, w-GaNInSw-BN, c-BNdiamondw-AlNLiClFluoriteLiF
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Quasiparticle Band Structure of Germanium
Theory: Hybertsen & Louie (1986)
Photoemission: Wachs, et al (1985)
Inverse Photoemission:Himpsel, et al (1992)
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Optical Properties
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M. Rohfling and S. G. Louie, PRL (1998)
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Both terms important!
repulsive
attractive
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Rohlfing & LouiePRL,1998.
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Optical Absorption Spectrum of SiO2
Chang, Rohlfing& Louie.PRL, 2000.
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Exciton bindng energy?
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Eg
Rohlfing & LouiePRL (1999)
Exciton bindingenergy ~ 1eV
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Si(111) 2x1 Surface
Measured values: Bulk-state qp gap 1.2 eV Surface-state qp gap 0.7 eV Surface-state opt. gap 0.4 eV
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Si (111) 2x1Surface
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Ge(111) 2x1 Surface
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Rohlfing & Louie,PRL, 1998.
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Optical Properties ofCarbon and BN Nanotubes
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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
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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
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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
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Absorption Spectrum of (5,0) Carbon Nanotube
• Net repulsive electron-hole interaction• No bound excitons• Suppression of interband oscillator strengths
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Both terms important!
repulsive
attractive
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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)0.0125 eV
Spataru, Ismail-Beigi, Benedict & Louie, PRL (2004)
(Not Frenkel-like)
|(re,rh)|2
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Electron-hole Amplitude (or Exciton Waveunction) in (8,0) Semiconducting Carbon Nanotubes
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||)(
2
z
ezV −=
1D Hydrogen atom
(R. Loudon, Am. J. Phys. 27, 649 (1959))
Ground state:
−∞=−=
=
22
2
0
0
0
1
2
)()(
BeamE
zz
h
δ
⎪⎩
⎪⎨
⎧
Excited states:
22
2 1
2 NamEE
Be
evenN
oddN
h−== ∞= ,1N
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Optical Spectrum of 4.2Nanotubes
Possible helicities are: (5,0), (4,2) and (3,3)
Theory: Spataru, Ismail-Beigi, Benedict & Louie (2003)* E. Chang, et al (2004)
exciton
exciton
interband
2.0 eV*
Theory
Expt.: Li, et al. (2002) Hong Kong group
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Optical Excitations in (8,0) & (11,0) SWCNTs
(8,0) (11,0)
Expta 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)
• 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
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(7,0) (8,0)
(10,0) (11,0)
Optical Spectrum of Carbon SWNTs
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Exciton binding energy > 2 eV!
Calculated Absorption Spectra of (8,0) BN Nanotube
Park, Spataru, and Louie, 2005
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Lowest Bright Exciton in (8,0) Boron-Nitride Nanotube
• Composed of 4 sets of transitions
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Comparison of Lowest Energy Exciton of (8,0) C and BN Tube
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• Momentum conservation: only excitons with energy above the photon line can decay.
• Temperature and dark-exciton effects (statistical averaged):
• Expt: 10-100 ns
Radiative Life Time of Bright Excitons
tube(11,0) for the ps 10)0(
if ,
if ,)(
)(
)0(2)(
int
0
0222
2
222
2
int
≈
⎪⎩
⎪⎨
⎧
>∞
<−=
rad
rad
QQQcQE
QEEeac
Q
τ
μτ
Transition rate (Fermi golden rule):
€
T = 300 K ⇒ τ radT ≈ 10 ns
<<kBT
Q
hcQ
E(Q)
E
Q0
Q
τ
Q0
10 ps
Spataru, Ismail-Beigi, Capaz and Louie, PRL (2005).
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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.
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Collaborators
Bulk and surface quasiparticle studies:
Mark HybertsenEric ShirleyJohn NorthrupMichael Rohlfing, …
Excitons and optical properties of crystals, surfaces, polymers, and clusters:
Michael RohlfingEric ChangSohrab Ismail-Beigi, …
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