Time-resolved photoelectron spectroscopy: An ultrafast clock to study electron dynamics at surfaces, interfaces and condensed matter

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University of Kaiserslautern, Erwin-Schroedinger-Strasse 46, 67663 Kaiserslautern, Germany Graduate

1 Time-resolved photoelectron spectroscopy: An ultrafast clock to study electron dynamics at surfaces, interfaces and condensed matter Benjamin Stadtmüller Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, Erwin-Schroedinger-Strasse 46, Kaiserslautern, Germany Graduate School of Excellence Materials Science in Mainz, Erwin Schroedinger Straße 46, Kaiserslautern, Germany

2 Outline Introduction: Ultrafast phenomena in atoms and solids Band structure of solids and angle resolved photoemission Time and Angle Resolved 2 Photon Photoemission: Lifetime of electrons in condensed matter Time and Angle Resolved Photoemission: Optically excited phase transitions in Outlook: Challenges and Perspectives of time resolved ARPES

3 Characteristic Timescales in Matter 1 sec (1 s) Clock tick 1 millisecond (10-3 s) Camera shutter 1 microsecond (10-6 s) Camera flash 1 nanosecond (10-9 s) Processor speed Data storage 1 picosecond (10-12 s) 1 femtosecond (10-15 s) 1 attosecond (10-18 s) Chemical reactions 1 st steps in vision, photosynthesis Electron dynamics in atoms, molecules and materials

1 picosecond (10-12 s) femtosecond (10-15 s)

reactions 1 st steps in vision, photosynthesis

between electrons in atoms and molecules

4 1 picosecond (10-12 s) femtosecond (10-15 s) Characteristic Timescales in Matter Chemical reactions 1 st steps in vision, photosynthesis Electron dynamics in atoms, molecules and materials O 1 τ = ω = k m r C s attosecond (10-18 s) Correlation effects between electrons in atoms and molecules Double ionization of helium Sansone et al. ChemPhysChem (2012) 13, 661

5 1 picosecond (10-12 s) femtosecond (10-15 s) Characteristic Timescales in Matter Chemical reactions 1 st steps in vision, photosynthesis Electron dynamics in atoms, molecules and materials O 1 τ = ω = k m r C s attosecond (10-18 s) Correlation effects between electrons in atoms and molecules Double ionization of helium Fundamental phenomena in matter happen Sansone on et ps al. to ChemPhysChem as timescale (2012) 13, 661

$Detector: Probe- Pulse Gas jet - Absorption spectroscopy - High harmonic generation - Electrons - Electron diffraction -.$

6 Ultrafast phenomena in atoms and molecules Investigation of isolated, non-interacting particles Atoms in gas phase Ultrafast Detector: Probe- Pulse Gas jet - Absorption spectroscopy - High harmonic generation - Electrons - Electron diffraction -. Pump- Pulse

Ultrafast electron dynamics in atoms Atomic wave

dynamics in condensed matter systems? Calegari et al.

7 Ultrafast phenomena in atoms and molecules Investigation of isolated, non-interacting particles Ultrafast electron dynamics in atoms Atomic wave functions V(r) r²* Ψ 100 (r) ² Why study ultrafast dynamics in condensed matter systems? Calegari et al. J. Phys. B 49 (2016) Meckel M et al 2008 Science

8 On the route to nanoscale devices

9 Ultrafast phenomena in atoms, molecules and solids Ultrafast electron dynamics in atoms and molecules Ultrafast dynamics in condensed matter Probe- Pulse - Isolated systems - Dynamics of local atomic and molecular wave functions

10 Ultrafast phenomena in atoms, molecules and solids Ultrafast electron dynamics in atoms and molecules Ultrafast dynamics in condensed matter Probe- Pulse - Isolated systems - Dynamics of local atomic and molecular wave functions Pump- Pulse - Coupled system - Dynamic is determined by ensemble of all electrons and atoms

11 Ultrafast phenomena in solids In a condensed matter system: Periodic arrangement and chemical bonding lead to collective phenomena: - Valence electrons can delocalize - Collective vibrational modes Phonon modes - Collective spin-phenomena Magnetism, Rashba-effect Spins Spin-Orbit Coupling R(T)

12 Ultrafast phenomena in solids In a condensed matter system: Separation into three sub-systems Periodic arrangement and chemical bonding lead to collective phenomena: Electrons Spins Lattice - Valence electrons can delocalize - Collective vibrational modes Phonon modes Spin-Orbit Coupling - Collective spin-phenomena Magnetism, Rashba-effect R(T) Fundamental interactions and excitations of each sub-system are reflected in the others

13 E B [ev] Electrons in condensed matter Electronic wave functions in a solid: Description as periodic lattice V(r) Valence states Periodic wave functions Bloch states z Core levels Atomic levels Electronic band structure Band gap k= 2π z a 0 Lattice constant Hψ i r = Eψ i r 2π a 0 0 2π a 0

14 E B [ev] Electrons in condensed matter Electronic wave functions in a solid: Description as periodic lattice V(r) Valence states Periodic wave functions Bloch states z Core levels Atomic levels Electronic band structure Band gap k= 2π z a 0 Lattice constant Size of Brillouin zone reflects periodicity in real space 2π a 0 0 2π a 0 2π/a Brillouin zone For Electronic simple metals: band structure is experimental observable of electronic wave Electron wave functions functions without strong in momentum correlations space with other sub-systems

15 Angle Resolved Photoemission (ARPES) hν Solid hν hν Energy conservation E f (k f ) E B (k i ) hν

16 The band structure approach Angle resolved photoelectron spectroscopy Excitation in momentum space E Vac E E F k E Momentum conservation k f k k i k hν 0 G

17 Basics of time resolved spectroscopy Pump-Probe Photoemission Experiment Probe Pulse Sensor Pump Pulse Trigger (Angle resolved) photoemission Δ t [fs] ultrafast clock Sensor for electron and spin system Time resolution determined by pulse duration of pump and probe pulse

18 The Two Limits of Time-Resolved PES Single Excitation Limit Collective Excitation Limit Stanford Shen Lab - Low excitation density - Access to unoccupied states - Quasi-particle lifetime Tr-2Photon Photoemission - High excitation density - Access to occupied/unoccupied states - Ensemble dynamics Tr-Pump-Probe ARPES

19 The Two Limits of Time-Resolved PES Single Excitation Limit Collective Excitation Limit Stanford Shen Lab - Low excitation density - Access to unoccupied states - Quasi-particle lifetime - High excitation density - Access to occupied/unoccupied states - Ensemble dynamics

20 Excitation scheme: Electron lifetime in metals Electron/Hole transport in metals t E Vac E F v Drift E k 1. What are the fundamental scattering mechanisms of electrons in matter? 2. How do these scattering mechanism change electron dynamics?

Electron lifetime in metals Excitation scheme: Fundamental scattering mechanisms: t E Vac Defects Excited electrons Plasmons E E F Cold electrons Phonons k 1.

21 Electron lifetime in metals Excitation scheme: Fundamental scattering mechanisms: t E Vac Defects Excited electrons Plasmons E E F Cold electrons Phonons k 1. What are the fundamental scattering mechanisms of electrons in matter? 2. How do these scattering mechanism change electron dynamics? Cold electrons: Phonons: Defect: inelastic scattering (ΔE 0.5*E i ) quasi-elastic scattering (ΔE 10meV) elastic scattering

22 2PPE yield Time-resolved 2PPE E Vac 2PPE detector 1,0 Autocorrelation trace Δt 0,9 t ee 0,8 E F 0, delay t [fs] FWHM lifetime pump probe exp(-t/τ)

23 Time-resolved 2PPE 2f 30fs, 1.55eV Ti:Sa fs- laser - 800nm - 80MHz - nj/pulse Delay-line 30fs, 3.1eV Δt t ee Δd E F Intensity I(E kin, k, Δt) Mach-Zehnder Interferometer Sample Detector

24 Electron dynamics in solids Lifetime of excited electrons in bulk bands PPE Data t 0 E Vac t 0 20 fs lifetime [fs] E F 20 Ag thin film Progress in Surface Science 90 (2015) E-E F [ev]

Electron dynamics in solids Energy dependent lifetime and Fermi-Liquid-Behavior 100 80 2PPE Data lifetime [fs] 60

25 Electron dynamics in solids Energy dependent lifetime and Fermi-Liquid-Behavior PPE Data lifetime [fs] τ ~ M ² ρ s 3 (E EF)² Progress in Surface Science 90 (2015) E-E F [ev]

26 Electron dynamics in solids 120 lifetime t [fs] Ag Co Ni Fe E* - E F [ev] Progress in Surface Science 90 (2015)

E-E F [ev] Electron dynamics at interfaces The

electron-electron scattering - Correlation

27 E-E F [ev] Electron dynamics at interfaces The Pb/Cu interface Lifetime map T 1 =t 0 T 2 =t 0 +Dt 3.0 T 2 =t 0 +2Dt 2.5 E 2.0 k k [Å -1 ] - Direct view on electron-electron scattering - Correlation between band structure and t ee S. Mathias et al., Phys. Rev. B 81, (2010)

Electron dynamics at interfaces -0.8-0.4 0.0 0.

trapped at interface Quantum well states

28 Electron dynamics at interfaces E-E F [ev] The Pb/Cu interface New electronic states at hybrid interface Electron trapped at interface Quantum well states 2PPE-ARPES (3.12eV) d K [Å -1 ] Unoccupied valence band L. Grad et al., in preparation

E-E F [ev] Electron dynamics at interfaces 3.0 Lifetime Map τ [fs] Quantum well states @Pb/Cu interface 2.

29 E-E F [ev] Electron dynamics at interfaces 3.0 Lifetime Map τ [fs] Quantum well interface 2.5 k [Å -1 ] Larger lifetime at band bottom Intraband scattering Pure electron-electron scattering - Only exchange of energy and momentum - Lifetime depends on band dispersion - Only exchange of energy - Lifetime only depends on energy S. Mathias et al., Phys. Rev. B 81, (2010)

0 E-E F [ev] A=1 A=4 A=16 A=24 A=32 A=64 2PPE Data QWS of metal/metal interfaces: - Single particle excitation limit - Quasi

30 Time and Angle Resolved 2PPE Summary Bulk states of metals: - Lifetime determined by Fermi liquid theory (e-e scattering) - Lifetime depends on available phase space lifetime [fs] E-E F [ev] A=1 A=4 A=16 A=24 A=32 A=64 2PPE Data QWS of metal/metal interfaces: - Single particle excitation limit - Quasi particle lifetime of excited electron in unoccupied part of band structure - Lifetime depends on intraband scattering - Complex momentum dependent scattering phenomena

31 The Two Limits of Time-Resolved PES Single Excitation Limit Collective Excitation Limit Stanford Shen Lab - Low excitation density - Access to unoccupied states - Quasi-particle lifetime - High excitation density - Access to occupied/unoccupied states - Ensemble dynamics

32 Interactions in condensed matter In a condensed matter system: Separation into three sub-systems Periodic arrangement and chemical bonding lead to collective phenomena: Electrons - Valence electrons can delocalize - Collective vibrational modes Phonon modes - Collective spin-phenomena Magnetism, Rashba-effect Spins R(T) Lattice

33 temperature Interactions in condensed matter For simple metals/material: Electron wave functions without strong correlations with sub-systems Separation into three sub-systems Electrons Metal Spins Lattice Charge doping level in U/W R(T)

34 temperature Interactions in condensed matter For complex materials: Interactions and correlations result in formation of various phases of matter Separation into three sub-systems Insulator Electrons Metal SDW AFM Spins Lattice SC Charge doping level in U/W R(T) Fundamental question: Which interaction/mechanism is driving the formation of a particular phase

35 Collective excitation limit of tr-arpes Strong optical excitation driving condensed matter out of equilibrium R(T) Thermal equilibrium Optical excitation Non-equilibrium state Backrelaxation Dynamics of optical excitation and back relaxation can yield characteristic time scales of coupling mechanisms - Electron and Spin coupling: femtosecond time scales - Coupling to lattice system: high femtosecond to picosecond time scales

36 Time resolved pump-probe ARPES fs laser amplifier Higher Harmonic Generation 30 fs, 1.55eV 30 fs, 22 ev - sub 150 mev resolution! - typical integration time for spectra < 10s

37 High Harmonic Generation (HHG) x-ray beam Popmintchev et al., Nature Photonics 4, 822 (2010) Coherent x-rays are generated by focusing a femtosecond laser into a gas Broad range of harmonics generated simultaneously from UV kev Discovered in 1987, explained in 1993

38 Normalized Intensity High Harmonic Generation (HHG) Photon spectrum 2ϖ spectrum 150 mev bandwidth 6 ev 6 ev Broad frequency range UV X-rays Energy [ev] Sn-filters Al-filters Eich et al., JESRP 195 (2014): hν max I laser λ laser 2

39 Time resolved pump-probe ARPES fs laser amplifier Higher Harmonic Generation 30 fs, 1.55eV 30 fs, 22 ev BBO Transient band structure Delay-line E -200 fs Se 4p Ti 3d 0 fs Folded Se 4p 100 fs Light source: - fs-laser amplifier system - secondary XUV source Detected Signal: - Transient occupied band structure k

40 Strong optical excitations in metals Optical non-equilibrium excitation Strong IR pulse R(T) Optical excitation

Strong optical excitations in metals Optical non-equilibrium excitation Strong IR pulse Optical excitation acts on electronic systems Non-thermal

41 Strong optical excitations in metals Optical non-equilibrium excitation Strong IR pulse Optical excitation acts on electronic systems Non-thermal distribution of excited electrons Thermalization of electrons by e-e scattering Hot electron distribution Adapted from M. Wolf et al. Fritz Haber Institute, Berlin

42 Strong optical excitations in metals Optical non-equilibrium excitation Strong IR pulse Thermalization of non-equilibrium electron distribution tr-arpes of Gd(0001) J. Phys. Cond. Matter 19, (2007)

Phonon system fs ps fs ps Spin system Optical

43 Energy dissipation of optical excitation Energy dissipation in coupled systems: Electron system Phonon system fs ps fs ps Spin system Optical excitation transfers energy into all sub systems

44 Optically induced phase transitions in condensed matter 2 examples of optically induced phase transitions in correlated systems: 1. Charge density wave Metal transition 2. Ferromagnetic Paramagnetic transition

45 Optically induced phase transitions in condensed matter 2 examples of optically induced phase transitions in correlated systems: 1. Charge density wave Metal transition 2. Ferromagnetic Paramagnetic transition

46 Charge Density Wave Transition Metal phase T>200K Charge density wave phase T<200K a 2a Charge density lattice TiSe 2

47 Charge Density Wave Transition Metal phase T>200K Charge density wave phase T<200K a 2a Charge density lattice Rohwer et al., Nature 471, 490 (2011) S. Mathias et al, Nature Commun. 7, (2016)

back-folding of the Se 4p bands to the M-point backfolded Se 4p Monney, C.

48 Static Charge Density Wave Transition Metal phase T>200K Charge density wave phase T<200K Se 4p Ti 3d Signature of the chargedensity wave state: back-folding of the Se 4p bands to the M-point backfolded Se 4p Monney, C. et al., New J. Phys. 12, (2010) Wiesenmayer et al., PRB 82, (2010)

49 E - E F (ev) Ultrafast CDW Transition Typical Tr-ARPES Data Set: Min. Max Ti 3d Se 4p Folded Se 4p M M M M -200 fs 0 fs 100 fs 3000 fs -1.0 Optically induced phase transition Delay [fs] Under investigation: - Transient changes of occupied band structure - Transient changes of unoccupied band structure very close the E F of thermal equilibrium Back-relaxation into ground state S. Mathias et al, Nature Commun. 7, (2016)

50 E - E F (ev) Ultrafast CDW Transition Typical Tr-ARPES Data Set: Min. Max M M M M -200 fs 0 fs 100 fs 3000 fs Ti 3d Se 4p Folded Se 4p -1.0 Optically induced phase transition Delay [fs] Under investigation: - Transient changes of occupied band structure - Transient changes of unoccupied band structure very close the E F of thermal equilibrium Back-relaxation into ground state CDW S. Mathias phase et al, transition Nature Commun. does not 7, occur (2016) instantaneously after optical excitation

51 Example: CDW System TiSe2 Intraband scattering Impact ionization Electrons drop down to bottom of Ti 3d band More carriers are generated via impact ionization E F

52 Optically induced phase transitions in condensed matter 2 examples of optically induced phase transitions in correlated systems: 1. Charge density wave Metal transition 2. Ferromagnetic Paramagnetic transition

53 Band structure view on Ferromagnetic Paramagnetic transition The way to ultrafast data storage? HDD: hard disk drive Magnetic material

Ultrafast Demagnetization HDD: hard disk drive 0 1 0 0

54 Band structure view on Ferromagnetic Paramagnetic transition The way to ultrafast data storage? Ultrafast Demagnetization HDD: hard disk drive Magnetic material Beaurepaire et al. Phys. Rev. Lett (1996)

55 Band structure view on Ferromagnetic Paramagnetic transition The way to ultrafast data storage? Collective interactions in ferromagnets Exchange Coupling J Stroner (Band structure) Model: Opt. exciation reduces Δ Ex? Magnetic material J leads to Δ Ex

56 Band structure view on ultrafast demagnetization Occupied band structure of ferromagnetic Cobalt SR-XUV photoelectron spectroscopy Co Au

57 Band structure view on ultrafast demagnetization Occupied band structure of ferromagnetic Cobalt SR-XUV photoelectron spectroscopy SP = N N N + N Co Au

58 Band structure view on ultrafast demagnetization PES Yield [arb. U.] Occupied band structure of ferromagnetic Cobalt SR-XUV photoelectron spectroscopy SP = N N N + N 0.2 Spin polarization SP = N N N + N E-E F [ev] Haag et al., New J. Phys.18 (2016) Co Au

Band structure view on ultrafast demagnetization Occupied band structure of ferromagnetic Cobalt SR-XUV photoelectron spectroscopy PES Yield [arb. U.

59 Band structure view on ultrafast demagnetization Occupied band structure of ferromagnetic Cobalt SR-XUV photoelectron spectroscopy PES Yield [arb. U.] fs pump pulse (30fs, 1.55eV) 0.2 Spin polarization SP = N N N + N E-E F [ev] Haag et al., New J. Phys.18 (2016) fs XUV pulse (22eV) Co Cu

60 Band structure view on ultrafast demagnetization Occupied band structure of ferromagnetic Cobalt Demagnetization trace of Co PES Yield [arb. U.] 0.2 Spin polarization SP = N N N + N E-E F [ev] Haag et al., New J. Phys.18 (2016) Eich et al. Sci. Adv. (2017), 3, e

Partial Intensity [10 4 counts] Spin polarization Band structure view

61 Partial Intensity [10 4 counts] Spin polarization Band structure view on ultrafast demagnetization fs Majority -50 fs electrons 6 0 fs 50 fs 100 fs fs Minority electrons -100 fs -50 fs 0 fs 50 fs 100 fs 150 fs SP = N N N + N 100 fs 50 fs 150 fs 0 fs -50 fs -100 fs Binding energy [ev] Binding energy [ev] Eich et al. Sci. Adv. (2017), 3, e

62 Ultrafast band renormalization E-E F Partial Intensity Majority I majo (Δt) Minority I mino (Δt) Transient band structure renormalization Binding energy [ev] Spin mixing of band structure

63 Ultrafast band renormalization E-E F Partial Intensity Majority I majo (Δt) Minority I mino (Δt) Transient band structure renormalization Binding energy [ev] Spin mixing of band structure

64 Ultrafast band renormalization Partial Intensity Opt. exciation reduces Δ Ex? J leads to Δ Ex E-E F Majority I majo (Δt) Minority I mino (Δt) Collapse of exchange splitting Transient band structure renormalization Binding energy [ev] Spin mixing of band structure

65 Ultrafast band renormalization E-E F Partial Intensity Intensity [Arb. Units] 8 Majority Spin Minority Spin 6 Total Carriers Delay [fs] Majority I majo (Δt) Minority I mino (Δt) Hot electron dynamics - Different dynamics for minority and majority electrons - Dynamics of hot electrons different compared to dynamics of band structure renormalization Transient band structure renormalization Binding energy [ev] Spin mixing of band structure

after strong optical excitation - Quasi particle dynamics of occupied and unoccupied part of band

66 Summary Time resolved pump-probe ARPES Optical excitation Non equilibrium state Stanford Shen Lab Timescale of back relaxation yields information about dominant interactions - Collective response after strong optical excitation - Quasi particle dynamics of occupied and unoccupied part of band structure -200 fs Se 4p Charge density wave transition 100 fs Ti 3d Folded Se 4p Magnetic transition

67 Outline Introduction: Ultrafast phenomena in atoms and solids Band structure of solids and angle resolved photoemission Time and Angle Resolved 2 Photon Photoemission: Lifetime of electrons in condensed matter Time and Angle Resolved Photoemission: Optically excited phase transitions in Outlook: Challenges and Perspectives of time resolved ARPES

68 Outlook: Challenges and Perspectives of time resolved ARPES Angle resolved photoelectron spectroscopy hν E Solid k ±15 E kin = ħ2 2 m e k² hν

69 Outlook: Challenges and Perspectives of time resolved ARPES Angle resolved photoelectron spectroscopy hν E Solid k ±15 E kin = ħ2 2 m e k² hν

70 Perspective: Momentum microscopy y x Time-of-flight energy analyzer Photoemission electron microscope optics

71 Perspective: Momentum microscopy k y k x Time-of-flight energy analyzer Photoemission electron microscope optics

72 Perspective: Momentum microscopy Constant energy maps k y k y k x E-E F Time-of-flight energy analyzer Photoemission electron microscope optics

73 Perspective: Momentum microscopy Constant energy maps k y k x Δt Time-of-flight energy analyzer Photoemission electron microscope optics

74 Perspective: Momentum microscopy Constant energy maps Momentum space dynamics of hot carriers k y k x Δt Time-of-flight energy analyzer Photoemission electron microscope optics

75 Perspective: Momentum microscopy Constant energy maps Momentum space dynamics of hot carriers Momentum space view on optically induced phase transitions in condensed matter k y k x Δt Time-of-flight energy analyzer Photoemission electron microscope optics

76 Perspective: Momentum microscopy Constant energy maps Momentum space dynamics of hot carriers Momentum space view on optically induced phase transitions in condensed matter k y k x Δt Time-of-flight energy analyzer Ideal tool to trace Photoemission ultrafast electron electron dynamics microscope through optics momentum, space and time on nm-length and (sub-) fs timescales

77 The ELI facilities Extreme Light Infrastructure - Attosecond Light Pulse Source: ELI-ALPS

78 The ELI facilities Extreme Light Infrastructure - Attosecond Light Pulse Source: ELI-ALPS

79 The ELI facilities Extreme Light Infrastructure - Attosecond Light Pulse Source: ELI-ALPS Vacuum space charge in ARPES: Example: Surface State of Cu(111) surface 80 MHz oscillator 1 KHz amplifier Journ. Appl. Phys. 100, (2006)

80 AG Aeschlimann Ultrafast phenomena at surfaces Acknowledgment Peter Grünberg Institut C. M. Schneider M. Plötzing University of Dortmund M. Cinchetti University of Göttingen S. Mathias University of Kiel K. Rossnagel M. Bauer MPI Halle J. Kirschner C. Tusche JILA, University of Colorado M.M. Murnane H.C. Kapteyn

Sfb 658 Colloquium 11 May Part II. Introduction to Two-Photon-Photoemission (2PPE) Spectroscopy. Martin Wolf

Sfb 658 Colloquium 11 May Part II. Introduction to Two-Photon-Photoemission (2PPE) Spectroscopy. Martin Wolf Sfb 658 Colloquium 11 May 2006 Part II Introduction to Two-Photon-Photoemission (2PPE) Spectroscopy Martin Wolf Motivation: Electron transfer across interfaces key step for interfacial and surface dynamics