Terahertz TimeDomain Spectroscopy THzTDS Principles and Applications to

Terahertz Time-Domain Spectroscopy (THz-TDS) Principles and Applications to Solid State Physics Jae Hoon Kim Optical Spectroscopy Laboratory Department of Physics, Yonsei University POSTECH Colloquium 2017. 09. 13

CONTENTS 1. Optical Spectroscopy 2. Terahertz Time-Domain Spectroscopy 3. Applications to Solid State Physics

1. Optical Spectroscopy Elecromagnetic waves Wavelength Long wavelength Low energy http: //server 2. phys. uniroma 1. it/gr/irs/index. htm Short wavelength High energy http: //www. ces. fau. edu/nasa/module-2/radiation-sun. php

Elecromagnetic Spectrum http: //ds 9. ssl. berkeley. edu/LWS_gems/2/espec. htm

1. Optical Spectroscopy Transmission / Reflectivity T(ω) and/or R(ω) (Transparent/Opaque) IR E r II E i R(ω) = IR / II IT E t T(ω) = IT / II Optical constants Conductivity σ(ω) Dielectric constant ε(ω) Refractive Index N(ω) J(ω) = σ(ω) E(ω) D(ω) = ε(ω) E(ω) q(ω) = (ω/c) N(ω)

Relationship between optical constants Kramers-Kronig relations

Spectrometers 1 THz = 33. 3 cm-1 = 4. 14 me. V 0. 124 me. V 12. 4 me. V 1 cm-1 102 cm-1 0. 03 THz 0. 3 THz 124 me. V 103 cm-1 30 THz 1 e. V 104 cm-1 100 e. V 105 cm-1 106 cm-1 300 THz Cary 5000 0. 4 e. V – 6. 5 e. V 3300 nm – 175 nm Bruker 113 v 10 – 10, 000 cm-1 1 me. V – 1. 25 e. V TPS 3000 2 – 150 cm-1 0. 2 me. V – 19 me. V 0. 05 THz - 5 THz 10 e. V Bruker 120 HR 100 – 20, 000 cm-1 10 me. V – 2. 25 e. V Infrared GES 5 0. 075 e. V – 5. 9 e. V 16500 nm – 200 nm Visible UV/VUV

Fourier Transform Infrared Spectroscopy 1 THz = 33. 3 cm-1 = 4. 14 me. V 0. 124 me. V 12. 4 me. V 1 cm-1 102 cm-1 0. 3 THz 0. 03 THz 103 cm-1 30 THz 1 e. V 104 cm-1 10 e. V 105 cm-1 106 cm-1 300 THz Cary 5 G Fourier Transform 0. 4 e. V – 6. 5 e. V Infrared (FTIR) Spectroscopy 3300 nm – 175 nm Bruker 113 v 10 – 10, 000 cm-1 1 me. V – 1. 25 e. V TPS 3000 2 – 150 cm-1 0. 2 me. V – 19 me. V 0. 05 THz - 5 THz 124 me. V Bruker 120 HR 100 – 20, 000 cm-1 10 me. V – 2. 25 e. V Infrared GES 5 0. 075 e. V – 5. 9 e. V 16500 nm – 200 nm Visible UV/VUV

Terahertz Spectroscopy 1 THz = 33. 3 cm-1 = 4. 14 me. V 0. 124 me. V 12. 4 me. V 1 cm-1 102 cm-1 0. 3 THz 0. 03 THz 124 me. V 103 cm-1 30 THz 1 e. V 104 cm-1 100 e. V 105 cm-1 106 cm-1 300 THz Cary 5000 0. 4 e. V – 6. 5 e. V 3300 nm – 175 nm Bruker 113 v 10 – 10, 000 cm-1 1 me. V – 1. 25 e. V TPS 3000 2 – 150 cm-1 0. 2 me. V – 19 me. V 0. 05 THz - 5 THz 10 e. V Terahertz (THz) Spectroscopy Bruker 120 HR 100 – 20, 000 cm-1 10 me. V – 2. 25 e. V Infrared GES 5 0. 075 e. V – 5. 9 e. V 16500 nm – 200 nm Visible UV/VUV

Spectroscopy - division of light into separate frequencies light source element spectrum angular seperation : dispersive spectroscopy (VUV-VIS) spatial interference : Fourier-transform spectroscopy (IR) temporal pulse : time-domain spectroscopy (THz) detector

detector coherent : both intensity and phase incoherent : only intensity source polychromatic : many frequencies (broad band; pulse) monochromatic : one frequency (narrow band; CW) spectrometer source, element, detector polarizer, filter, modulator, analyzer range, resolution, sensitivity spectroscopy light probe of material properties metals, insulators, semiconductors, polymers, …

Interband Transition Interband optical absorption. Keita Yamaguchi Direct Bandgap Indirect Bandgap

Interband Transition (Direct & Indirect) Si In. As Keita Yamaguchi Direct Bandgap Indirect Bandgap

Interband Transition (Direct & Indirect) In. As Bandgap Si Bandgap Keita Yamaguchi Direct Bandgap Indirect Bandgap

Graphene Universal Transparency 97. 7 % in the visible Exciton Resonance Absorption 4. 6 e. V

Examples (Al, Au, Cu, In. Sb) Metals (Al, Au) Aluminium Transition Metal (Cu) Doped Semiconductor (In. Sb)

Exam. Conductor: Drude Model

Conductor: Drude Model

Examples (III-V; Polymer) Semiconductor (In. Sb, Ga. As, Al. Sb) Polycarbonate K-K relation

Insulator: Lorentz Model

Insulator: Lorentz Model

3. THz Time-Domain Spectroscopy Terahertz Wave THz Gap

Terahertz Technology (Applications) http: //www 2. nict. go. jp/advanced_ict/terahz/thz/jp/research. html

Security http: //thznetwork. net/index. php/thz-images

Medical Imaging Quality Assurance Communications http: //thznetwork. net/index. php/thz-images

Generation and Detection of THz Waves Laser-Gated Photoconductive Antenna THz emitter Sample THz receiver I meter

Operation Schematic TPS 3000 computer Spectrum amplitude Temporal Waveform Fast-Fourier Transform Spectrum phase

Single Layer Transmission Ei(ω) L 2 n. L/c pth echo (2 p times reflection)

Relation between T and n, k Ei(ω) Primary Pulse (p=0) L 2 n. L/c

Approximation n, k Ei(ω) L 2 L/v Primary Pulse (n>>k Approx. )

p-Si : Time pulse Spectrum Thickness : 1004 μm p-type ; Dopant : B Orientation : (100) Resistivity : 8 ~ 12 Ohm cm Fast Fourier Transform

p-Si : Transmission Refractive Index n >> k Approximation Full Correction

Thin Film Analysis (Tinkham Formula) d Thin Film Formula Robert A. Kaindl et al. , PRL 88, 027003 (2002)

3. Applications to Solid State Physics : Graphene Universal conductance

Bi 2 Se 3 MBE Films : Terahertz Time-Domain Signal Magnified peaks • Time-domain pulses transmitted through vacuum & Bi 2 Se 3 thin films (2 -8 QL) • The sample pulses are magnified • A systematic time delay & peak reduction relative to the reference: the changes in the film thickness & the absorption

Complex THz Conductance of Bi 2 Se 3 MBE Films • Terahertz complex conductance spectra of a series of Bi 2 Se 3 thin films (2 -8 QL)

Comparison with Theory and ARPES (Bi 2 Se 3 Films) Gapped, but topological Liu, C. X. et al. Phys. Rev. B 81, 041307 (2010). Bi 2 Se 3 on DLG Trivial Nature Phys. 6, 584– 588 (2010) + + − − − ordinary insulator QSH insulator (If EF is in the gap) Tight Binding (TB) model constructed by maximally localized Wannier function (MLWF) from first-principles calculation

d. c. Limit Conductance of Bi 2 Se 3 MBE Films • 2 QL “zero” d. c. limit conductance clear RHEED confirms the proper formation • 3 QL quantum spin Hall phase d. c. limit conductance of 2 G 0 a pair of Dirac hyperbolas 2 D: quantized, plateau 3 D: continuous, linear • 4 QL 2 G 0: a single QWS from both surfaces • 5 QL 6 G 0: 3 QWSs from both surfaces • Above 6 QL additional G from bulk free-carrier states • • • The d. c. limits of the real conductance G 1 in units of the conductance quantum e 2/h The band schematic corresponding to the evolving phase of Bi 2 Se 3 ultrathin films The sequential contributions by the TSSs, QWSs, and bulk free-carrier states 8 G 0

Demonstration of Spin Precession Ø Zeeman Torque Magnetic moment Gyromagnetic ratio Bohr magneton g-factor (electron) Ø Landau – Lifshitz (LL) Equation Dissipation of energy of magnetization oscillation Gurevich, Alexander G. , and Gennadii A. Melkov. Magnetization oscillations and waves. CRC press, 1996.

Spin Precession in Pristine YFe. O 3 Spin configuration of YFe. O 3 Antiferromagnetic resonance modes

Terahertz time signal of YFe. O 3

BCS superconductor (Nb. Ti. N) Nb. Ti. N (Tc=14. 1 K; d=280 nm) Meissner Effect http: //www. sciencedaily. com/releases/2004/08/040824014758. htm Weak-coupling BCS superconductor

Metamaterials LC resonance YBCO on sapphire sub. [Microscopic image] Quadrupole resonance

Nb. N Superconducting Metamaterial

Summary v Solid State Optics - Interaction between solids and electromagnetic waves - Deep insights into electron & phonon systems v THz Spectroscopy - THz-TDS as a new spectroscopic tool - Time domain pulse spectroscopy technique - Conductivity spectra without KK analysis - Complementary to Transport, IR, Ellipsometry - Ideal for Low-Density Correlated System - Superconductor, 2 D Materials, Topological Insulator, Metamaterial, Magnetic Materials 3 D Imaging, Medical Application, Conservation Science, Explosive Detection

Reference Theory Electrodynamics of Solids - Martin Dressel FTIR FOURIER TRANSFORM INFRARED SPECTROMETRY - Peter R. Griffiths Terahertz Introduction to THz Wave Photonics - X. –C Zhang