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Construction of Time-And-Angle-Resolved Construction of Time-and-Angle-Resolved Photoelectron Spectroscopy on Correlated Materials Shuolong Yang June 9, 2010 Abstract Angle-Resolved Photoelectron Spectroscopy (ARPES) has been a major experimen- tal technique in studying the electronic band structure of condensed matter systems. The traditional ARPES system resolves binding energies and in-plane electron mo- menta of electronic systems. It is of great scientific interest to further resolve the information of electron dynamics. In this thesis, I give a brief review of the theoretical and experimental backgrounds of the Femtosecond Time-Resolved ARPES technique. I report the construction of such a system, which consists of an ultrafast 1.5 eV pump beam and 6 eV probe beam, and a Scienta SES200 electron analyzer. An optical au- tocorrelator verifies that the duration of the pump laser pulse is 75 fs; An ARPES experiment on an Sb sample demonstrates that the angular resolution of the electron analyzer is less than 0:34◦ and that the energy resolution is less than 50 meV. 1 Contents 1 Acknowledgments5 2 Theoretical Background6 2.1 Introduction to Ultrafast Electron Dynamics..................6 2.1.1 Motivation to Study the Time Evolution of Correlated Materials...6 2.1.2 Time Scales of Different Types of Interactions in Correlated Systems7 2.2 Basic Principles of Ultrafast Laser Setup for Pump-probe Technique.....9 2.2.1 Mode-Locking Scheme for Ultrafast Laser Pulse Generation......9 2.2.2 Group Velocity Dispersion........................ 11 2.2.3 Higher Harmonic Generation....................... 12 2.3 ARPES Basics.................................. 14 2.3.1 ARPES as a Measure of One-electron Spectral Function....... 14 2.3.2 ARPES Instrumentation and Resolution Concerns........... 16 2.3.3 Pump-probe Technique.......................... 19 3 Construction and Characterization of the Ultrafast Laser Output 20 3.1 Complete Ultrafast Laser Setup......................... 20 3.2 Optical Autocorrelation System and Characterization of the Time Profile.. 22 3.2.1 Introduction to Optical Autocorrelation System............ 22 3.2.2 Characterization of the Time Profile of the Ultrafast Laser Pulse... 23 3.3 Spectral Profile of the Probe Beam....................... 24 4 Calibration and Characterization of the Electron Analyzer 25 4.1 Principles of the Angular Test Device...................... 25 4.2 Calibration Results and Analysis........................ 27 5 Testing ARPES Experiment on Sb 29 5.1 Introduction to Rashba Splitting........................ 29 2 5.2 Measurement of the System's Performance................... 31 6 Further Calibration and Optimization 34 7 Conclusion 35 3 List of Figures 1 Time and energy scales for different interactions in correlated materials. .....8 2 a) Ultrafast Gaussian beam profile in the frequency domain; b) ultrafast Gaussian beam profile in the time domain. .......................... 10 3 Physical picture of photoemission process: a) excited photoelectrons; b) diagram of energy conservation in photoemission[11]. ..................... 14 4 a) Working scheme of hemispherical electron analyzer; b) typical ARPES spectrum[19]. 17 5 Pump-probe technique for Time-Resolved ARPES measurement. ......... 19 6 Complete optics setup for pump-probe measurement. ............... 20 7 Flip mirror setup for finding spatial and temporal overlap. ............ 21 8 Optical autocorrelation setup. ........................... 22 9 Autocorrelation results for the Ti-Sapphire output: a) effect of time-bandwidth duality, 17 nm vs 21 nm; b) effect of chirp mirror compensation. ......... 23 10 Spectral profile of the probe beam. ........................ 25 11 Angular test device schematics. .......................... 26 12 ARPES spectrum of the angular test device .................... 27 13 a) Momentum Distribution Curve and fitting; b) Angle-integrated Energy Distri- bution Curve and exponential fitting. ....................... 28 −1 14 Sb band structure at kx = 0:035A˚ : dotted bands represent the split surface states 31 15 ARPES measurement on Sb(111) by our constructed system:a) measured band structure; b) EDC plots .............................. 32 16 Fermi surface mapping of Sb(111): a) Fermi surface mapping using our constructed system; b) comparison with the published data by Chen et al[4]. ......... 33 4 1 Acknowledgments This work has received tremendous help from Prof. Zhi-Xun Shen's research group, De- partment of Physics at Stanford University and Stanford Vice Provost for Undergraduate Education. Special thanks go to Patrick Kirchmann and Jonathan Sobota, whom I have been closely collaborating with and learning from. Photoemission technology has been de- veloping vastly for the past two decades. It took the effort of several generations of scientists and engineers to implement this technology and produce significant scientific data. It was the selfless help from my colleagues that made it possible for me to master the fundamentals and furthermore contribute to this field in only one year. I also attribute this work to the people who have greatly helped me with study and life as an international undergraduate student, among whom are Prof. Douglas Osheroff, Prof. David Goldhaber-Gordon, Prof. Hari Manoharan, Prof. Daniel Bump, Mr. Rick Pam and Ms. Elva Carbajal. 5 2 Theoretical Background Time-Resolved ARPES is a powerful tool in studying the ultrafast electron dynamics in correlated systems. In this section, I will briefly explain how the underlying microscopic interactions and elementary excitations in a complex correlated system can be disentangled in the time-domain due to their distinctively different time scales. It is this interest that drives us to construct a Time-Resolved ARPES system. In the next two sub-sections, I will introduce the basic principles of ultrafast laser and ARPES technologies. 2.1 Introduction to Ultrafast Electron Dynamics 2.1.1 Motivation to Study the Time Evolution of Correlated Materials Quasi-particle excitations exchange energies and momenta through scattering processes, which are defined by the underlying microscopic interactions. One way of studying these interactions is to excite the electronic system with an ultrafast pump laser pulse in the fem- tosecond regime and record by a second time-delayed probe laser pulse, how the electronic band structure evolves as a function of pump-probe delay. In particular, we use a femtosec- ond infrared pump beam to excite the system and a ultraviolet probe beam that photo-emits the electrons. One of the central quantities in such an experiment is the population decay rate Γ of electrons excited above the Fermi level EF . Several scattering schemes contribute to Γ[13]: 1e Γ = Γe−e + Γ + Γe−ph + Γe−def (1) 1e Here Γe−e,Γ ,Γe−ph and Γe−def denote the decay rates of inelastic electron-electron, elastic electron-electron, electron-phonon and electron-defect scatterings, respectively. By studying the decay rate of the excited electron population, which are termed hot electrons since they are not in equilibrium with the lattice, it is possible to retrieve the information about different scattering mechanisms. In particular, the time evolution of hot electrons 6 in metallic materials has been investigated in great detail[6][9]. In general, Γe−e dominates Equation1 for large excitation energies E − EF kBT ;Γe−ph dominates for low excitation energies E − EF kBT . It should be noted that the preceding discussion of interaction disentanglement only concerns metallic materials, for which the Fermi Liquid Theorem is widely applicable. The situation is different for highly-correlated materials such as Mott Insulators or High Tc Superconductors, for which the failure of Fermi Liquid Theorem has been demonstrated by ARPES experiments[7]. The time evolution of electronic states in correlated systems has emerged as a major research field in that it provides a new perspective to evaluate current theoretical models. In particular, as in the example of high Tc superconductivity, the small isotope shift effect in optimally doped samples[1] and the d-wave symmetry of the superconducting gap[7] evidence an argument against the mechanism of phonon-mediated pairing. Dynamical information of electron-phonon interactions shines light on evaluating this type of arguments. 2.1.2 Time Scales of Different Types of Interactions in Correlated Systems The formalism of characterizing the different types of interactions in a electronic system remains valid in the context of correlated materials. In order to reveal the physical picture of ultrafast electron dynamics in correlated materials, it is crucial to survey the time scales of different types of interactions, as illustrated by Figure1[17]. It is evident from Figure1 that different types of interactions generally have different time scales. In particular, the electron-electron thermalization process has a characteristic time varying from a few femtoseconds to hundreds of femtoseconds, and generally happens much faster than the electron-phonon coupling and the coherent phonon interactions. In this regard, if we pump a correlated system using photon absorptions, electrons will be thermal- ized first to a high temperature. These hot electrons reach the peak temperature at the time scale of 100 fs. The electron temperature starts decreasing by means of inelastic electron- 7 Figure 1: Time and energy scales for different interactions in correlated materials. electron scattering and electron-phonon interactions. Some lattice modes are coupled with the hot electrons and thus become hot phonons. At this stage,
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