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

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

• 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

+

Quasiparticle Excitations

Diagrammatic Expansion of the Self Energy in Screened Coulomb Interaction

Hybertsen and Louie (1985)

H = Ho + (H - Ho)

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

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 & LouiePRL,1998.

Optical Absorption Spectrum of SiO2

Chang, Rohlfing& Louie.PRL, 2000.

Exciton bindng energy?

Eg

Rohlfing & LouiePRL (1999)

Exciton bindingenergy ~ 1eV

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

Si (111) 2x1Surface

Ge(111) 2x1 Surface

Rohlfing & Louie,PRL, 1998.

Optical Properties ofCarbon 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

• Metallic tubes -- stretch of bands by ~15%• Semiconductor tubes -- large opening (~ 1eV) of the gap

(8,0) semiconducting SWCNT(3,3) metallic SWCNT

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

• 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

Electron-hole Amplitude (or Exciton Waveunction) in (8,0) Semiconducting Carbon Nanotubes

||)(

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

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

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

(7,0) (8,0)

(10,0) (11,0)

Optical Spectrum of Carbon SWNTs

Exciton binding energy > 2 eV!

Calculated Absorption Spectra of (8,0) BN Nanotube

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

• 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

QQ

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).

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 HybertsenEric ShirleyJohn NorthrupMichael Rohlfing, …

Excitons and optical properties of crystals, surfaces, polymers, and clusters:

Michael RohlfingEric ChangSohrab Ismail-Beigi, …