THz Spectroscopy of Nanoscale Materials

Transcription

1 THz Spectroscopy of Nanoscale Materials Frontiers of THz Science Stanford, Sept. 5, 2012 Tony F. Heinz Columbia University New York, NY

2 Thanks to Fai Mak, Joshua Lui, Hugen Yan, Leandro Malard, Ajay Nahata, Yannis Chatzakis, Zhiqiang Li, Feng Wang, Ernst Knoesel, Euan Hendry, Mischa Bonn (MPI Mainz) Davide Boschetto (ENSTA, France) Jim Hone (graphene), Irving Herman (quantum dots) gps Sample and device preparation Jie Shan and group: Keliang He, Liang Zhao (Case Western Reserve U.) G. Larry Carr (BNL, IR synchrotron)

3 Probing charge transport and dynamics in nanomaterials - Quantum dots (0-D) - Graphene (2-D) Topics Related discussion on graphene in Nuh Gedik s talk on carbon nanotubes in Robert Kaindl s talk

4 Terahertz Time Domain Spectroscopy E-field (a.u.) reference (without sample) with sample Complex dielectric response/conductiv ity Broad spectral range Dynamics of rapidly evolving systems Time (ps) 6 7

5 Introductory Example Probing Conductivity in Wide-Gap Insulators

6 Conductivity in Insulators Intrinsic interest in mechanism of conductivity Important for: - Electrical breakdown - Optical breakdown (micro-machining) - Radiation induced conductivity (detectors) - Solar energy conversion

7 Probing Transport in Wide-Gap Insulators - Very low intrinsic conductivity - No method of doping - Problems with contacts - Short carrier lifetime

8 Model Insulators Crystalline: Sapphire (Al 2 O 3 ) Rutile (TiO 2 ) Amorphous: Liquids - hexane Al 2 O 3 : Phys. Rev. Lett. 90, (2003). TiO 2 : Phys. Rev. B 69, (2004). Liquids: J. Chem. Phys. 121, 394 (2004).

9 Photoinduced THz Response in Sapphire ˆ σ = ( n e 2 * e / m ) γ iω 0 Drude model Scattering rate Carrier density/drude weight

10 Temperature Dependent Scattering Rate in Sapphire Scattering Rate (THz) μ e = 30,000 cm 2 /V-s μ e = 610 cm 2 /V-s Temperature (K)

11 Temperature Dependent Scattering Rate in Sapphire Scattering Rate (THz) m * = 0.27m 0 U def = 21 ev Acoustic phonon scattering ~ T 3/ 2 LO-phonon ω kt e LO Temperature (K) ~

12 Nanoscale Materials Quantum Dots and Quantum Size Effects in 0-D Materials

13 Semiconductor Nanoparticles

14 Charge Transport in CdSe Nanoparticles E 400 nm e h Transport in confined structures: Role of surface scattering Quantum size effects Also: Schmuttenmaer, Yale

15 Photo-Induced THz Response in CdSe Nanoparticles Induced change is a flat increase in real susceptibility

16 Real conductivity Existence of charge carriers Availability of continuum of states with differing momenta?

17 Electronic States of Carriers in CdSe Nanoparticles Efros

18 Single Nanoparticle Response from the Measurement Suspension to a E e h Apply effective medium theory to extract the single nanoparticle response Number of excited nanoparticles given by absorption of pump light ε = C 4π scr n ex C scr : Screening constant n ex : Excitation density α exciton

19 Size Dependence of single Exciton Polarizability in QDs One exciton polarizability ~ 10 4 other electrons!

20 Polarizability of Confined Charge α = 2e 3 2 i ' r i,0 E i,0 2 Perturbation theory: low-frequency limit Estimate: r ~ i,0 R (2π ) E ~ 2 mr 2 2 α ~ R a 4 R ~ V[ B a B ] with a B Bohr of electron radius

21 Size Dependence of the Exciton Polarizability

22 Summary: THz Spectroscopy of CdSe Nanoparticles Colloidal self-assembled CdSe nanoparticles (r = 1-3 nm) excited with a single electron-hole pair - Real, frequency-independent susceptibility - α > 10,000 Ǻ 3 ~ Volume - Very large photo-induced response (polarizability) that is instantaneous up to THz frequencies - Ultrafast transient showing hole trapping and Auger recombination effects for multiple carriers

23 Bridging the Large and the Small Free electrons: Drude behavior Surface scattering, Quantum-size effects,... Small, isolated quantum dots Discrete levels: Polarizability Bulk Real σ in large quantum dots by Bonn et al. 2 nm

24

25 Nanoscale Materials Graphene - Model 2-D System

26 Graphene Electronic Structure Massless Fermion Dispersion

27 Optical Spectroscopy of Graphene Convenient, non-contact materials characterization Microscopy to identify graphene flakes, domains, thickness Raman characterization of layer thickness, defects, doping Probe of excited states and band structure of graphene Spectroscopy of electronic transitions: Single layers, bilayers, and few-layers Role of stacking order Probe of ultrafast dynamics in graphene Spectroscopic and real-time probse: Electron-Electron interactions, electron-phonon interactions cooling, phonon-phonon coupling, heat diffusion, etc.

28 Interband Transitions: Optical Conductivity Click to edit Master title style Interband transitions for ideal linearly dispersing bands Optical (sheet) conductivity: = (π/4) G 0 Optical absorption: Ando et al. J Phys. Soc. Jpn 71, 1310 (2002) Gusynin et al., PRL 96, (2006) Ryu et al., PRB 75, (2007) Abergel et al., PRB 75, (2007) A(ω) =

29 Experimental Measurement of Graphene Optical Conductivity K. F. Mak, TFH, et al,prl 101, (2008)] [Also Manchester grp, Science 320, 5881 (2008)]

30 IR Conductivity Spectra Pauli blocking of interband absorption Also: D. N. Basov, F. Wang, P. Avouris

31 Exfoliated Graphene

32 CVD Grown Graphene by the meter Bae et al, Nature Nanotech 2010

33 Intraband Transitions in Graphene Free Carrier Response Ando et al., Tokyo Institute of Tech.

34 IR Conductivity Spectra Pauli blocking of interband absorption Also: D. N. Basov, F. Wang, P. Avouris

35 Far IR Conductivity Spectra Free-carrier contribution dominates Strong monolayer response! Direct non-contact determination of carrier scattering rates Also: D. N. Basov, F. Wang, P. Avouris

36 Carrier Scattering Rates Coulomb impurities: n -1/2 Short range scatterers: n 1/2 Independent of T S. Das Sarma, M. S. Fuhrer, D. S. Novikov

37 IR Conductivity Spectra

38 Many-body Effects on Drude Weight (preliminary data) D D VF = 0.017α V 0 F 0 α ~ 0.18 for graphene on HfO 2 Drude weight decreases with doping due to screening of Coulomb interactions A. H. MacDonald, F. Wang

39 Far-Infrared Spectroscopy of Graphene Direct, non-contact determination of scattering rates and variation with carrier density Examination of accuracy of single-particle picture through experimental and theoretical Drude weights Fundamental optical response for graphene collective EM response needed for plasmonics With pump beam - new approach to probing carrier dynamics in graphene

40 Also: Kaindl et al (LBL), Rana et al. (Cornell), Norris et al. (Michigan) on epitaxial SiC samples Nuh Gedik (MIT) Transient Behavior after Excitation with a fs Pulse Time-resolved THz spectroscopy

41 Transient Behavior after Excitation with a fs Pulse Time-resolved THz spectroscopy

42 Bilayer Graphene: Massive Carriers E E E p p p Graphene Interlayer coupling Graphene Bilayer (hyperbolic, splitting ~0.35 ev)

43 Graphene Bilayer Oscillator Restoring force exerted by atomic interactions shearing mode

44 Real-time Observation of Shearing Mode in Few-Layer Graphene

45 Graphene Shearing Mode: Dependence on Layer Number

46 Graphene Shearing Mode: Environmental Effects Connection between phonons and nanomechanics, friction Strong driving of shearing mode phonons with intense THz radiation

47 Click to edit Master title style + Noncontact measurement of conductivity + Scattering rates and mechanisms from spectroscopy + Photoexcited materials and dynamics Insulators Quantum dots Graphene