1 Technology development of spectroscopic techniques

2 Topics ARPES Time-domain spectroscopies STM RXSThroughput Resolution Spin-resolved Micro/nano Time-domain spectroscopies Usability Attosecond ARPES STM Vibration isolation Low temperature Data analysis RXS Connect back to quantum materials in this course Announcements

3 Evolution of ARPES throughput~2007 (time of flight detectors) ~1999 3D detection of electrons, E vs (kx,ky) ~2015: 3D detection with hemispherical analyzer Red dots= pre 2D detectors

4 Resolution in ARPES experimentIntensity in ARPES experiment: Resolution Ellipsoid Fermi-Dirac Function “Matrix elements” Convolution “band structure + Interactions” PRB 87, (2013)

5 Energy resolution Origins of energy broadening Light source bandwidthElectrical noise Spectrometer 𝐸 𝑝𝑎𝑠𝑠 = 𝑒Δ𝑉 𝑅 1 𝑅 2 − 𝑅 2 𝑅 1 =0.5,1, 2,5,10eV, or more Δ 𝐸 𝑎 = 𝐸 𝑝𝑎𝑠𝑠 𝑤 𝑅 𝛼 2 4 𝑤=width of entrance slit (as small as .05 mm) 𝑅 0 =average radius of analyzer (~20 cm) 𝛼=angular resolution (as small as .05°)

6 Momentum resolution Related to angular resolution of spectrometer and beam spot size For a given spectrometer, how can one improve momentum resolution? Decrease photon energy in order to decrease kinetic energy for given binding energy Decrease photon energy to decrease momentum kick from photon 𝑝= 𝐸 𝑐 (3% of Brillouin zone at 100 eV, 0.5% of Brilliouin zone at 20 eV) Measure in 2nd or 3rd Brillouin zone to increase emission angle

7 Simulated effects of resolution

8 Evolving ARPES resolution: measurements of cuprate superconducting gapLaser ARPES DE=30meV DE=17meV DE=1-3meV AN AN N N Tc=87K Vishik et al. PNAS 109 (2012) Shen et al. PRL 70 (1993) Ding et al. PRB 54 (1996) 6 hrs/k 1 hr/k 5 min/k

9 Laser ARPES=nonlinear optics + photoemissionPolarization in a medium due to applied electric field: 𝑃 𝑡 = 𝜒 1 𝐸 𝑡 + 𝜒 2 𝐸 2 𝑡 + 𝜒 3 𝐸 3 𝑡 +… Linear optics Nonlinear optics 𝐸 𝑡 =𝐸 𝑒 −𝑖𝜔𝑡 +𝑐.𝑐. 𝑃 2 𝑡 = 𝜒 (2) 𝐸 𝑒 −𝑖𝜔𝑡 + 𝐸 ∗ 𝑒 𝑖𝜔𝑡 2 =2 𝜒 (2) 𝐸 𝐸 ∗ + 𝜒 (2) [ 𝐸 2 𝑒 −2𝑖𝜔𝑡 +𝑐.𝑐.] Radiation with frequency 𝜔 Radiation with frequency 2𝜔2nd harmonic generation (SHG) Same principle can be applied to systems with multiple frequencies to produce sum and difference frequencies 𝐸 𝑡 = 𝐸 1 𝑒 −𝑖 𝜔 1 𝑡 + 𝐸 2 𝑒 −𝑖 𝜔 2 𝑡 + 𝐸 3 𝑒 −𝑖 𝜔 3 𝑡 +…+𝑐.𝑐. Important details phase matching (all oscillators in medium need to add constructively in the forward direction Inversion symmetry breaking Resource: R. W. Boyd, Nonlinear Optics (2008) (http://www.sciencedirect.com/science/book/ )

10 Common energies for laser ARPESUseful frequency Starting frequency Nonlinear optical (NLO) medium Comments ~6 eV (200nm) 1.5 eV (800 nm), Ti:Sapph BBO Ultrafast or static experiments ~7 eV (170nm) 1.165 eV (1064 nm), Nd:YAG BBO or KDP; KBBF (3.5 eV7 eV) Heavily attenuated by air; requires inert environment ~ eV ( nm) 1064 or 1024 nm BBO or KDP, then Xenon gas Koralek et al. Rev. Sci. Instrum. 78, (2007)

11 Capabilities of (high resolution) laser ARPES6 eV 7 eV 11 eV He et al. Rev. Sci. Instrum. 87, (2016) PRB 87, (2013) Liu et al. PRB 87, (2013)

12 Spin-resolved ARPES How can we measure electron spin in photoemission experiments? A. Takayama, High-resolution spin-resolved photoemission spectrometer and the Rashba effect in Bismuth thin films (2015)

13 Mott Detectors Spin-orbit coupling (SOC): positively charged nucleus provides effective B-field in rest frame of electron: 𝑩=− 1 𝑐 𝒗×𝑬= − 1 𝑐 𝑍𝑒 𝑟 3 𝒗×𝒓= 𝑍𝑒 𝑚𝑐 𝑟 3 𝑳 Magnetic moment of electron: 𝜇 𝑒 =− 𝑔 𝑠 𝑒 2𝑚𝑐 𝑺 Interaction between electron and effective B field of nucleus: 𝑣 𝐿𝑆 =− 𝜇 𝑒 ∙𝑩= Ze 2 2 m 2 c 2 r 3 𝐋∙𝑺 Scattering cross section has angular asymmetry A. Takayama, High-resolution spin-resolved photoemission spectrometer and the Rashba effect in Bismuth thin films (2015)

14 Spin texture in 3D Tis via spin-resolved ARPES (Mott detector)Hsieh et al. Nature 460 (2009)

15 Problems with spin-resolved ARPESLow efficiency (related) Low resolution Single-channel detection

16 Solution 1: detectors based on exchange scatteringVLEED: “very low energy electron diffraction” Spin-dependent reflectivity of low energy (~10 eV) electrons from ferromagnetic surfaces Advantages Higher efficiency by factor of 100 Higher efficiency allows for improved resolution Do not need to accelerate/decelerate electrons very much Disadvantages Still single-channel detection Target has finite lifetime (up to several weeks) 𝟏𝟎 −𝟐 Okuda et al. Rev. Sci. Instrum. 79, (2008)

17 Solution 2: interface spin-resolved measurements with time-of-flight (TOF) spectrometerHigher resolution! Jozwiak et al. Rev. Sci. Instrum. 81, (2010)

18 Micro and nano ARPES “Standard” spot size ~200 𝜇𝑚“Small” spot size ~30-50 𝜇𝑚 “micro ARPES” spot size ~1-10 𝜇𝑚 “nano ARPES” spot size <1 𝜇𝑚 Micro ARPES Nano-ARPES Advantages Can avoid averaging over large-scale sample inhomogeneities Can study polycrystal Access to distinct physics from regular ARPES Disadvantages More difficult than regular ARPES and accesses same physics Requires hard x-rays: poorer resolution Laser ARPES AND tiny spot size PRB 87, (2013)

19 Topics ARPES Time-domain spectroscopies STM RXSThroughput Resolution Spin-resolved Micro/nano Time-domain spectroscopies Usability Attosecond ARPES STM Vibration isolation Low temperature Data analysis RXS Connect back to quantum materials in this course Announcements

20 Timescales in solids Electron-photon interactions (10-100 fs)Electron-electron interactions ( fs) Electron-phonon interactions ( fs) S. K. Sundaram & E. Mazur, Nat. Mater. (2002)

21 One class of experiment with ultrafast lasers: pump-probe experimentstime Intensity 100 fs 1 nJ ?

22 Pump-probe experimentsThe pump The probe Purpose (depends on specific experiment) Create specific excitation Whack the electronic system on a timescale faster than lattice response Cause destruction Frequency (depends on specific experiment) 1.5 eV (straight out of the Ti-Sapph laser) Mid-IR ( meV— relevant to excitations in solids) Ascertains system’s response as a function of time delay from pump Defines what experiment you are doing Optics (probe measures change in reflectivity or absorption) THz (measures changes in optical conductivity at low frequencies) ARPES (measures changes in band structure) Many others

23 General developments in ultrafast experimentsInside of Ti:sapphire laser Making pulsed lasers user-friendly Commercial Ti:Sapph lasers Commercial optical parametic oscillators/amplifiers (OPO/OPA) to perform difference-frequency generation and produce other wavelengths of pulsed light Making shorter pulses Several hundred femtosecondsseveral femtoseconds Image source: https://en.wikipedia.org/wiki/Ti-sapphire_laser

24 Recent development: attosecond ARPES

25 Review: 3 step model in ARPESImage: https://en.wikipedia.org/wiki/Photoelectric_effect Optical excitation of electron in the bulk Travel of excited electron to the surface Escape of photoelectrons into vacuum Photoemission intensity is given by product of these three processes (and some other stuff)

26 1. Optical excitation of electron in bulkStart: electron in occupied state of N-electron wavefunction, Ψ 𝑖 𝑁 End (of this step): electron in unoccupied state of N electron wavefunction, Ψ 𝑓 𝑁 Sudden Approximation: no interaction between photoelectron and electron system left behind Probability of transition related to Fermi’s golden rule: 𝑤 𝑓𝑖 = 2𝜋 ℏ < Ψ 𝑓 𝑁 − 𝑒 𝑚𝑐 𝑨∙𝒑| Ψ 𝑖 𝑁 > ​ 2 𝛿( 𝐸 𝑓 𝑁 − 𝐸 𝑖 𝑁 −ℎ𝜈) p=electron momentum A=vector potential of photon Hufner. Photoelectron Spectroscopy (2003) Express as product of 1-electron state and N-1 electron state e.g.: Ψ 𝑓 𝑁 =𝒜 𝜙 𝑓 𝒌 Ψ 𝑓 𝑁−1 Relevant to this discussion: final state lifetime contributes to broadness of observed ARPES spectra

27 Attosecond ARPES Produce short pulses with high photon energy via high-harmonic generation (HHG) in noble gas Sample = Ni (111) Observe photoemission time delay at certain photon energy because of enhanced final-state lifetime Δ𝐸~300 𝑚𝑒𝑉 Z. Tao et al., Science /science.aaf6793 (2016)

28 Topics ARPES Time-domain spectroscopies STM RXSThroughput Resolution Spin-resolved Micro/nano Time-domain spectroscopies Usability Attosecond ARPES STM Vibration isolation Low temperature Data analysis RXS Connect back to quantum materials in this course Announcements

29 General developments in STM techniqueVibration isolation Low temperature Data analysis Cuprate QPI comparison Hoffman et al Science (2002) Zhou et al Nat. Phys 2013. Kohsaka et al Nature (2008)

30 Novel data analysis techniquesUsing machine learning to discern recurring features in STM spectra Attempt to overcome limitations of FT-STS Phase problem Materials with different types of disorder Rosenthal et al, Nat. Phys. 10 (2014)

31 Topics ARPES Time-domain spectroscopies STM R(I)XSThroughput Resolution Spin-resolved Micro/nano Time-domain spectroscopies Usability Attosecond ARPES STM Vibration isolation Low temperature Data analysis R(I)XS Connect back to quantum materials in this course Announcements

32 R(I)XS: development Improving resolutionImage source: https://www.psi.ch/sls/adress/HomeEN/ADRESS_Oct2010.pdf Improving resolution 5m arm Ghiringhelli et al. Rev. Sci. Instrum. 77,

33 Class discussion What are some unanswered questions in quantum materials and how can recent developments address them? Charge density wave systems Unconventional superconductors Cuprates Iron-based Heavy fermion Topological and dirac materials 3D Tis Graphene Dirac and Weyl semimetals

34 Topics ARPES Time-domain spectroscopies STM R(I)XSThroughput Resolution Spin-resolved Micro/nano Time-domain spectroscopies Usability Attosecond ARPES STM Vibration isolation Low temperature Data analysis R(I)XS Connect back to quantum materials in this course Announcements

35 Announcements Colloquium speaker today: Joel Moore (Berkeley)Quantum materials winter school at UMD: https://www.nanocenter.umd.edu/events/fqm Last HW due wednesday in-class Next class: applications of quantum materials Course evaluations online: https://eval.ucdavis.edu/student