Transcript Technology development of spectroscopic

Technology development
of spectroscopic
techniques
Topics
• ARPES
•
•
•
•
Throughput
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
Evolution of ARPES throughput
~2007 (time of flight detectors)
~1999
• 3D detection of electrons, E vs (kx,ky)
Red dots= pre 2D detectors
~2015: 3D detection
with hemispherical
analyzer
Resolution in ARPES experiment
Intensity in ARPES experiment:
I (k ,  )  I 0 (k , , A ) f ( ) A(k ,  )  R(k ,  )
“Matrix
elements”
FermiDirac
Function
Resolution
Ellipsoid
Convolution
 '' (k ,  )
A(k ,  )  
 [   k   ' (k ,  )]2  [ '' (k ,  )]2
1
“band structure + Interactions”
PRB 87, 075113 (2013)
Energy resolution
Origins of energy broadening
• Light source bandwidth
• Electrical noise
• Spectrometer
𝑒Δ𝑉
𝐸𝑝𝑎𝑠𝑠 = 𝑅1
𝑅2
−
𝑅2 𝑅1
= 0.5,1, 2,5,10eV, or more
𝑤 𝛼2
Δ𝐸𝑎 = 𝐸𝑝𝑎𝑠𝑠
+
𝑅0
4
𝑤 =width of entrance slit (as small as .05 mm)
𝑅0 =average radius of analyzer (~20 cm)
𝛼 =angular resolution (as small as .05°)
Momentum resolution
Ekin  h    | E B |
p ||  k || 
k || 
2mEkin  sin 
2mEkin  cos 


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
𝐸
𝑝 = (3% of Brillouin zone at 100 eV, 0.5% of Brilliouin zone at 20
𝑐
eV)
• Measure in 2nd or 3rd Brillouin zone to increase emission angle
Simulated effects of resolution
Evolving ARPES resolution: measurements
of cuprate superconducting gap
E=30meV
Laser ARPES
E=1-3meV
E=17meV
AN
AN
N
Shen et al. PRL 70 (1993)
N
Tc=87K
Vishik et al. PNAS
Ding et al. PRB 54
(1996)
6 hrs/k
1 hr/k
109 (2012)
5 min/k
Laser ARPES=nonlinear optics +
photoemission
Polarization in a medium due to applied electric field:
𝑃 𝑡 = 𝜒 1 𝐸 𝑡 + 𝜒 2 𝐸2 𝑡 + 𝜒 3 𝐸3 𝑡 + ⋯
Linear
Nonlinear optics
optics
Radiation with frequency 𝜔
𝐸 𝑡 = 𝐸𝑒 −𝑖𝜔𝑡 + 𝑐. 𝑐.
2
𝑃 2 𝑡 = 𝜒 (2) 𝐸𝑒 −𝑖𝜔𝑡 + 𝐸 ∗ 𝑒 𝑖𝜔𝑡
= 2𝜒 (2) 𝐸𝐸 ∗ + 𝜒 (2) [𝐸 2 𝑒 −2𝑖𝜔𝑡 + 𝑐. 𝑐. ] 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 = 𝐸1 𝑒 −𝑖𝜔1𝑡 + 𝐸2 𝑒 −𝑖𝜔2 𝑡 + 𝐸3 𝑒 −𝑖𝜔3𝑡 + ⋯ + 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/9780123694706)
Common energies for laser ARPES
Useful
frequency
Starting
frequency
Nonlinear
optical
(NLO)
medium
Comments
~6 eV
(200nm)
1.5 eV (800 BBO
nm),
Ti:Sapph
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
~10.5-10.8
eV (114118nm)
1064 or
1024 nm
BBO or
KDP, then
Xenon gas
Koralek et al. Rev. Sci.
Instrum. 78, 053905 (2007)
Capabilities of (high resolution) laser
ARPES
6 eV
7 eV
11 eV
PRB 87, 075113 (2013)
Liu et al. PRB 87, 075113 (2013)
He et al. Rev. Sci.
Instrum. 87, 011301
(2016)
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)
Mott Detectors
• Spin-orbit coupling (SOC): positively charged nucleus
provides effective B-field in rest frame of electron:
1
1 𝑍𝑒
𝑍𝑒
𝑩 = − 𝑐 𝒗 × 𝑬= − 𝑐 𝑟 3 𝒗 × 𝒓 = 𝑚𝑐𝑟 3 𝑳
• Magnetic moment of electron:
𝑔𝑠 𝑒
𝜇𝑒 = −
𝑺
2𝑚𝑐
• Interaction between electron and effective B field of
nucleus:
Ze2
𝑣𝐿𝑆 = −𝜇𝑒 ∙ 𝑩 =
𝐋∙𝑺
2m2 c 2 r 3
• Scattering cross section has angular asymmetry
A. Takayama, Highresolution spin-resolved
photoemission spectrometer
and the Rashba effect in
Bismuth thin films (2015)
Spin texture in 3D Tis via spin-resolved
ARPES (Mott detector)
Hsieh et al. Nature 460 (2009)
Problems with spin-resolved ARPES
• Low efficiency
• (related) Low resolution
• Single-channel detection
Solution 1: detectors based on
exchange scattering
VLEED:
• “very low energy electron
diffraction”
• Spin-dependent reflectivity of
low energy (~10 eV) electrons
from ferromagnetic surfaces
𝟏𝟎−𝟐
Okuda et al. Rev. Sci. Instrum. 79,
123117 (2008)
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)
Solution 2: interface spin-resolved
measurements with time-of-flight (TOF)
spectrometer
Higher resolution!
Jozwiak et al. Rev. Sci.
Instrum. 81, 053904 (2010)
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
Laser ARPES
AND tiny
spot size
PRB 87, 075113 (2013)
Micro ARPES
Advantages
Nano-ARPES
• Can avoid
• Access to
averaging
distinct
over largephysics from
scale sample
regular
inhomogenei
ARPES
ties
• Can study
polycrystal
Disadvantages More difficult
than regular
ARPES and
accesses same
physics
Requires hard
x-rays: poorer
resolution
Topics
• ARPES
•
•
•
•
Throughput
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
Timescales in solids
Electron-photon interactions (10-100 fs)
Electron-electron interactions (10-100 fs)
Electron-phonon interactions
(50-5000 fs)
S. K. Sundaram & E. Mazur, Nat. Mater. (2002)
Intensity
One class of experiment with ultrafast
lasers: pump-probe experiments
1 nJ
100 fs
time
Pump-probe experiments
The pump
The probe
• Purpose (depends on
specific experiment)
• Ascertains system’s
response as a function of
time delay from pump
• Defines what experiment
you are doing
• 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 (70-500 meV—
relevant to excitations in
solids)
• 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
General developments in ultrafast
experiments
Inside of Ti:sapphire laser
Image source:
https://en.wikipedia.org/wiki/Tisapphire_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
Recent development: attosecond
ARPES
Review: 3 step model in ARPES
Ekin  h    | EB |
p ||  k ||
2mEkin  sin 
Image:
https://en.wikipedia.org/wiki/P
hotoelectric_effect
1. Optical excitation of electron in the bulk
2. Travel of excited electron to the surface
3. Escape of photoelectrons into vacuum
Photoemission intensity is given by product of
these three processes (and some other stuff)
1. Optical excitation of electron in bulk
Start: electron in occupied state of N-electron
wavefunction, Ψ𝑖𝑁
End (of this step): electron in unoccupied state
of N electron wavefunction, Ψ𝑓𝑁
Sudden Approximation: no interaction between
photoelectron and electron system left behind
Probability of transition related to Fermi’s golden rule:
2
2𝜋
𝑒
𝑁
𝑁
𝑤𝑓𝑖 =
< Ψ𝑓 −
𝑨 ∙ 𝒑|Ψ𝑖 > 𝛿(𝐸𝑓𝑁 − 𝐸𝑖𝑁 − ℎ𝜈)
ℏ
𝑚𝑐
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.: Ψ𝑓𝑁 = 𝒜𝜙𝑓𝒌 Ψ𝑓𝑁−1
Relevant to this discussion: final state lifetime contributes to broadness of
observed ARPES spectra
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 finalstate lifetime
• Δ𝐸~300 𝑚𝑒𝑉
Z. Tao et al., Science 10.1126/science.aaf6793 (2016)
Topics
• ARPES
•
•
•
•
Throughput
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
General developments in STM
technique
• Vibration isolation
• Low temperature
• Data analysis
Cuprate QPI comparison
Kohsaka et al Nature (2008)
Hoffman et al
Science (2002)
Zhou et al Nat. Phys 2013.
Novel data analysis techniques
• Using 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)
Topics
• ARPES
•
•
•
•
Throughput
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
R(I)XS: development
• Improving resolution
5m arm
Ghiringhelli et al. Rev. Sci. Instrum. 77, 113108 2006
Image source:
https://www.psi.ch/sls/adress/Ho
meEN/ADRESS_Oct2010.pdf
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
Topics
• ARPES
•
•
•
•
Throughput
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
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