how one electron tells the story of gazillion electrons · how one electron tells the story of...
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Einstein’s Photoelectric Effect
How ONE electron tells the story of GAZILLION electrons
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 2
Overview
Photo-electric effect and Angle Resolved Photo-Electron Spectroscopy (ARPES)Emergent behaviorsHigh temperature superconductivity and ARPESUnconventional emergent behaviors and ARPES
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 3
“ Spark”UV light
History: The Photoelectric Effect
Hertz (1887)
Thompson & Lenard (1897-1902)Photo-electrons are involved
Einstein (1905, 1921 Nobel Prize)Quantum theory (Photon)
ehνEk = hν - Eb - Φ
ν
Ek, maxSlope = Material independent
Material DependentIntensity Independent
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 4
Einstein’s Theory – Controversial
Albert Einstein (1879 - 1955) published his theory of the photoelectric effect in 1905, the same year in which he published the Special Theory of Relativity and the paper on molecular dimensions which earned him his PhD from the University of Zurich. However, his reintroduction of the idea ofa corpuscular nature for light met with considerable scientific resistance. Even Planck rejected an idea which seemed to set science back one hundred years. As late as 1913, when Einstein was proposed for membership in the Prussian Academy of Science, the nominating committee felt it necessary to apologize for this "mistake" as a singular error ina series of successes. Then, in 1921 Einstein won the Nobel Prize for the theory of the photoelectric effect.
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 5
Einstein’s Theory – Controversial
In a recommendation for Einstein's membership in the Prussian Academy of Science, the sponsors wrote
“In sum, one can say that there is hardly one among the great problems in which modern physics is so rich to which Einstein has not made a remarkable contribution. That he may sometimes have missed the targeting his speculations, as, for example, in his hypothesis of light-quanta, cannot really be held too much against him, for it is not possible to introduce really new ideas even in the most exact sciences without sometimes taking a risk”
A. Pais, “Subtle is the Lord: The Science and the Life of Albert Einstein,” New York: Oxford University Press, 1982, p. 382
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 6
Current Understanding
Quantum Mechanics Governs Both Light (Photon) and Electron
• Light Wave energy is discrete (hν, 2hν, 3hν…) The quantum of energy (hν): Photon Particle Photon Particle is described by a Wave Function
• Electron Particle is described by a Wave Function
Particle Wave Duality
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 7
Current Understanding (Particle)
pp, Ep
px, Ex
pe, Ee
pe = pp + pxEe = Ep + Ex
Initial Final
Momentum ConservationEnergy Conservation
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 8
Current Understanding (Wave)
pp, Ep
px, Ex
pe, Ee
pe = pp + pxEe = Ep + Ex
Initial Final
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 9
Current Understanding (Wave)
kp, ωp
kx, ωx
ke, ωe
pe = pp + pxEe = Ep + Ex
Initial Final
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 10
What is measured and what is not
kp, ωp
kx, ωx
ke, ωe
pe = pp + pxEe = Ep + Ex
Initial Final
k = momentum p = h k / (2 π)ω = energy E = h ω / (2 π)
k = wave number = 2 π / λω = angular freq. = 2 π ν = 2 π / T
However, ω and k are not independent.DISPERSION RELATION
For instance, ω = ck for light (photon).Homework…
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 11
Photo-Electric Effect is Cool
• Photon Detectors
• Digital Camera, Camcorder, Solar Cells, …
• Angle Resolved Photoelectron Spectroscopy
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 12
Synchrotron
Advance Light SourceLawrence Berkeley National Laboratory
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 13
Electron StorageRing
Beam Line
Synchrotron = Electron Shaker
End Station
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 14
ARPES End Station
Sample transferCharacterization chamber
Electron Analyzer
7.6e2 Torr outside, 3e-11 Torr inside
Photon In
ARPESchamber
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 15
Electron Spectroscopy for Chemical Analysis (ESCAor XPS) (Siegbahn, 1951-, 1981 Nobel Prize)
X-ray sources, electron spectrometer, chemical shift
Photoelectron spectroscopy in UV (UPS) (Spicer, 1955-)
UV light sources and vacuum technology
ARPES (Smith, 1973-)
History of ARPES
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 16
Emergent Behaviors
R. P. Feynman : QED“I must clarify something: When I say that all the phenomena of the physical world can be explained by this theory, we don’t really know that. Most phenomena we are familiar with involve such tremendous numbers of electrons that it’s hard for our poor minds to follow that complexity.”
ElectronPhoton
Interaction
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 17
Tyranny of Power
Computer memory of one particle wavefunction : XNumber of particles: NTotal memory: XN
Say, X = 2 (minimum).210 = 1024, 230 = 1.07e9, 2100 = 1.3e30 N = 1023 → XN ~ 103e22
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 18
Emergent Behaviors
More is different (Anderson) – Symmetry Breaking
Patterns, Life, Brain, Colony, …Phases, Temperature, Heat, Friction, …Laws, Particles …
Physics, Chemistry, Biology, Psychology, Social Sciences …
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 19
Renormalization Group
Start with the full Hamiltonian
Integrate out the high energy dynamics
Obtain effective low energy Hamiltonian
ccmp1.phys.metro-u.ac.jp/ccmp/simulation/xy.gif
E.g., “block spin” transformation
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 20
High Temperature Superconductivity
No problem in physics in our time hasreceived more attention, and with less in the way of concretesuccess, than that of the behavior of the cuprate superconductors,whose superconductivity was discovered serendipitously,and whose properties, especially in the underdoped region,continue to surprise. As the high-Tc community haslearned to its sorrow, deduction from microscopics has notexplained, and probably cannot explain as a matter of principle,the wealth of crossover behavior discovered in the normal stateof the underdoped systems, much less the remarkably highsuperconducting transition temperatures measured at optimaldoping. Paradoxically high-Tc continues to be the most importantproblem in solid-state physics, and perhaps physics generally,because this very richness of behavior strongly suggests thepresence of a fundamentally new and unprecedented kind ofquantum emergence.
Laughlin and Pines, “The Theory of Everything,” PNAS vol. 97, 28 (1999)
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 21
Magnetic Levitation Devices—Trains (Superconducting Coil)Magnetic Resonance Imaging (MRI)Power LinesParticle AcceleratorsMotorsSQUIDs
Applications of Superconductivity
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 22
RESISTANCELESS CONDUCTION
Temperature
Resi
stiv
ity
0
Metal
Superconductors
Tc
1911 K. Onnes Superconductivity in Hg
MEISSNER EFFECT: Perfect diamagnetism
1933 Meissner effect
What is Superconductivity?
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 23
http://www.fys.uio.no/super/levitation/
Meissner Effect
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 24
Meissner Effect
http://www.fys.uio.no/super/levitation/
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 25
High Temperature Superconductivity
1900 1920 1940 1960 1980 20000
20
40
60
80
100
120
140
160
180
Nb3Ge
Nb3Sn
NbNNbPbHg
Conventional SC
Year of Discovery
Tran
sitio
n Te
mpe
ratu
re (K
)
BCS TheoryBCS Theory
C60 MgB2
HTSC
Hg-Ba-Ca-Cu-O
Tl-Ba-Ca-Cu-O
Bi-Sr-Ca-Cu-O
Y-Ba-Cu-O
La-Ba-Cu-O
Hg-Ba-Ca-Cu-O (pressure)
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 26
High Tc is Complicated - Work in Progress
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 27
X
Y
Zhve-
φ
θ
Electron detector
Crystal
TiTe2
V∼ )k
kω∂
∂ (∼m*
1Slope = Velocity
What can ARPES do?
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 28
EF
kF
E
k
E
k
EF
kF
Low Energy State High Energy State
Statistics, High and Low Energy
Electrons are Fermions
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 29
ARPES, High and Low Energy(Bi2212)
Momentum
V∼ )k
kE∂
∂ (∼m*
1
Why does the velocity change suddenly??
“Kink”
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 30
Qualitative Understanding
“Kink”
• Peak is sharp – Stable• Area Under Curve << 1
(Many body state)
• Peak is broad – Unstable• Area under curve ~ 1
(Electron like state)
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 31
Qualitative Understanding
Bare ElectronFree ElectronNon-interacting Horse
Real ElectronHeavy ElectronBare Electron + All Others
+ + …
Electron
Feynman Diagram
Real Excitation = Electron + Other Stuff
Landau ’56Mattuck ‘67
Renormalization : Emergence of Heavy Electron
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 32
Qualitative Understanding
• Peak is sharp – Stable• Area Under Curve << 1
(Many body state)
• Peak is broad – Unstable• Area under curve ~ 1
(Electron like state)
ARPES measures bare electron, i.e. bare horse, one at a time.
Eigenstates of High E Hamiltonian
Eigenstates of Low E Effecitve Hamiltonian
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 33
Why care about Kink?
Two Kinks
Low E Kink = Lattice(~ 70 meV)
GHG et al.,Nature 430, 187 (04)GHG et al.,PRL 97, 227001 (06)
High E Kink = Spin(~ 600 meV)
Graf, GHG et al.,cond-mat/0607319
Kink = InteractionInteraction mediates SC
Renormalization, Emergence
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 34
SC is dance of electron pairs
Phys. Today, March ‘04
All to the same tune!Phase coherent SC condensate
Signature of this emergence?
Bound Pairby Interaction
Binding energy= SC gap
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 35
Signature of SC Condensate
Fedorov et al.PRL ‘99
Pair Binding EnergySC Gap
Intensity~ SC Condensate Size
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 36
High Tc is Complicated - Work in Progress
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 37
Signature of SC Condensate
Fedorov et al.PRL ‘99
Pair Binding EnergySC Gap
Intensity~ SC Condensate Size
The real mystery is normal state!
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 38
Another Emergent Behavior
Electron Fractionalization
High TcLow-Dimensional Metals
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 39
Quasi-electron ≈ Electron
Fermi LiquidOpposite of Fractionalization
Fractionalization?
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 40
Fractionalization?
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 41
Fractionalization?
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 42
Dead Horse
NOT FractionalizationDead Horse cannot move. (Electron cannot be cut.)
Fractionalization?
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 43
Whangbo ('88)Onoda ('87)
c
a
LiO
Mo
QuasiQuasi--1D Metal1D Metal
Low-D Metal Example – Li Purple Bronze
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 44
Dimensionality MattersNew State of Matter beyond Landau Fermi Liquid
No individual particle motion, but only collective density wave motion
Quantum world →Charge and Spin wave
Charge and Spin propagate separately due to different charge-charge and spin-spin interaction
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K0.3MoO3 (K Blue Bronze)
TiTe2
SmTe3
Li0.9Mo6O17(Li Purple Bronze)
AMo6O17 (A=Na,K) (Purple Bronze)
Dimensionality of EF Electronic Structure1 2
“Stra
ngen
ess”
HTSC cupratesΓ
Χ
Y
1 11
M
30K
Low Dimensional Metals
Fermi Surface
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Signature of Electron Fractionalization
E
k
EF
kF E
Num
ber o
f Ele
ctro
ns p
er Δ
E
EF
ΔE
Density of States (DOS)Non-Interacting Electrons Momentum-Integrated PES
Momentum Integration
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 47
Signature of Electron Fractionalization
E
k
EF
kF E
Num
ber o
f Sta
tes p
er Δ
E
EF
ΔE
Density of States (DOS)Fermi Liquid
Area Under Curve << 1(Many body state)
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 48
Signature of Electron Fractionalization
E
Num
ber o
f Ele
ctro
ns p
er Δ
E
EF
E
k
EF
kF
ΔE
Density of States (DOS)FractionalizationMomentum-Integrated PES
“Pseudo-Gap”
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Signature of Electron Fractionalization
E – EF (eV)
Au
Li Purple
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Nov 28, 2006 G.-H. Gweon, Physics 10, UCSC 50
Signature of Electron Fractionalization
Sato et al, Physica C (‘00)
Pseudo-Gap
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Fence
No Individual Horse Motion (No Quasi-Electron) !
“Horse Mass” Wave(=Charge Wave)
“Roll” or Spin Wave(quantum horse)
Horse Mass + RollFractionalization!
Single Horse Moves in the form of Many Collective WavesNo Quasi-Horse Motion
Electron Fractionalization
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Charge Wave (“Holon”) and Spin Wave (“Spinon”)
E-EF (eV)
Holonpeak
B
A
kF
kF
Spinonedge
1D Li Purple Bronze (Li0.9Mo6O17) – Luttinger LiquidJ. D. Denlinger, GHG et al, PRL 99GHG et al., PRB 03; F. Wang et al., PRL 06
A
E-EF (eV)
Spin Charge Separation – suggestive but not definite
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Almost an emergence?SrCuO2
Kim et al., Nature Physics, 2, 397 (2006)
Also, see TTF-TCNQClaessen et al., 88, 096402 (2002)
Two dispersing things but at high energy!
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Spin Charge Separation in Cuprates
Graf, GHG, et al., PRL in review
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Conclusions
Complex physics in condensed matter systems (High Tc, Low-D conductors, etc)
Signatures of various types of emergence –New era of condensed matter physics beyond simple Landau Fermi Liquid paradigm
One electron carries the message of emergence of gazillion electrons through wave function overlaps
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Further Reading
R. Feynman, “QED: The Strange Theory of Light and Matter,”
Princeton University Press (1988)
R. D. Mattuck, “A Guide to Feynman Diagrams in the Many-Body
Problem,” Dover (1976)
P. W. Anderson, “More is different,” Science vol. 177, 393 (1972)
R. B. Laughlin and D. Pines, “The Theory of Everything,” Proceedings of
the National Academy of Science, vol. 97, 28 (2000)
R. B. Laughlin, “A Different Universe – Reinventing physics from bottom
down,” Basic Books (2006)
P. W. Anderson, “When electron falls apart,” Physics Today 50 (10): 42-
47 OCT 1997