New Insights into High-Tc Superconductivity from Angle-Resolved Photoemission at Low Photon ...

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University of Colorado, Boulder
CU Scholar
Physics Graduate Theses & Dissertations Physics
Spring 1-1-2011
New Insights into High-Tc Superconductivity from
Angle-Resolved Photoemission at Low Photon
Energies
Nicholas Clark Plumb
University of Colorado at Boulder, [email protected]
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Recommended Citation
Plumb, Nicholas Clark, "New Insights into High-Tc Superconductivity from Angle-Resolved Photoemission at Low Photon Energies"
(2011).Physics Graduate Theses & Dissertations. 32.
https://scholar.colorado.edu/phys_gradetds/32
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New Insights into High-T Superconductivity from
c
Angle-Resolved Photoemission at Low Photon Energies
by
Nicholas Clark Plumb
B.A., Colorado College, 2002
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
Department of Physics
2011
This thesis entitled:
New Insights into High-T Superconductivity from Angle-Resolved Photoemission at Low Photon
c
Energies
written by Nicholas Clark Plumb
has been approved for the Department of Physics
Daniel S. Dessau
Asst. Prof. Kyle McElroy
Date
The final copy of this thesis has been examined by the signatories, and we find that both the
content and the form meet acceptable presentation standards of scholarly work in the above
mentioned discipline.
iii
Plumb, Nicholas Clark (Ph.D., Physics)
New Insights into High-T Superconductivity from Angle-Resolved Photoemission at Low Photon
c
Energies
Thesis directed by Prof. Daniel S. Dessau
Angle-resolved photoemission spectroscopy (ARPES) is one of the most direct and powerful
probes for studying the physics of solids. ARPES takes a “snapshot” of electrons in momentum
space (k-space) to reveal details of the dispersion relation E(k), as well as information about the
lifetimes of interacting quasiparticles. From this we learn not only where the electrons live, but
also, if we are crafty, what they are doing. Beginning with work by our group in 2006 using a 6-eV
laser, ARPES experiments have begun to make use of a new, low photon energy regime (roughly
hν = 6–9 eV). These low photon energies give drastic improvements in momentum resolution,
photoelectron escape depths, and overall spectral sharpness. This has led to several important new
findings in the intensively-studied problem of high-temperature superconductivity.
This thesis will focus on two of the latest results from our group using low-energy ARPES
(LE-ARPES) to study the cuprate high-T superconductor Bi Sr CaCu O (Bi2212). The first
c 2 2 2 8+δ
of these is an investigation into the nature of many-body interactions at a well-known energy
scale (∼ 60–70 meV) where the dispersion shows a large bend, or “kink”. Using LE-ARPES
measurements, the k-dependence of this kink is investigated in unprecedented detail. An attempt
is then made to map the feature’s k evolution into the scattering q-space of boson dispersions. In
our analysis, the q-dispersion of the kink bears more resemblance to dispersive spin excitations
than phonons — a surprising finding in light of previous evidence that the the kink originates from
interactions with phonons. However, phonons cannot be ruled out, and the results may hint that
both types of interactions contribute to the main nodal kink.
A second result is the discovery of a new ultralow (< 10 meV) energy scale for electron
interactions, corresponding to a distinct, smaller kink in the electron dispersion. The temperature
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and doping dependence of this feature show not only that it turns on near T — signalling a
c
possible relation to the mechanism of high-T superconductivity — but also that it leads to a
c
subtle breakdown of the so-called “universal” Fermi velocity v along nodes of the anisotropic
F
superconducting gap. Moreover, v is found to depend quite strongly on temperature, which may
F
be an important factor in the physics of cuprates.
Dedication
To Bridget, who has true grace
Acknowledgements
The thesis of a previous student from our group begins with a quote from the sci-fi sage
Yoda: “Do, or do not. There is no try” [Gromko, 2001]. I recall a profound sinking feeling when I
first read this, because I entered graduate school with nearly the opposite mindset, which can be
summedupas: “Goaheadandtry, butjustrememberthere’snoshameifyoucometofindoutthat
you can’t hack it as a physicist.” To me grad school amounted to a commitment to a multi-year
experiment in probing the outer limits of my intellect and determination. I viewed failure as a an
undesirable but quite possible outcome. In hindsight, it is quite clear to me that no one should
be able to survive the challenges of earning a Ph.D. while maintaining such an attitude. Thus, I
am here despite myself, and it is largely due to the assistance, advice, encouragement, and love of
many people. They believed in me even when my self-confidence wavered.
My advisor, Dan Dessau, is one of these people. In all likelihood, I never would have gone
to grad school in physics (and certainly would not have gotten into such a prestigious program)
were it not for Dan. He has always shown utter confidence in my talents and potential, and this
has fostered a deep mutual trust and respect. He is a mentor in the most profound sense of the
word: someone who gives great advice to his students, who keeps them on track, who supports
them when they need it, and who guides by example. Dan has rewired the synapses of my brain.
He has shown me what it truly means to have “physical intuition” and to think like a physicist.
He has made me better in Science and in Life.
Mywife, Bridget, towhomthisthesisisdedicated, isanothersuchbeliever. Imethershortly
beforestartinggradschool. Astherelationshipprogressed, Irecallwarningherthathertimingwas
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really bad — not for me, but for her. The first two years of classes are notoriously time-consuming,
but she insisted on hanging around anyway. I’m glad she did. My life is richer for having Bridget in
it. She is the truest and most steadfast companion I have (will) ever had (have). She is a wellspring
ofjoy, comfort, contentment, andbeauty. AndIpromise, dear, therewillbeahoneymoonsomeday.
Iofcourseoweahugedebtofthankstomyfamily—especiallymyparents,PrestonandJudy,
and my siblings, “Cinco,” Kristen, and Nathan. My family did everything in its power to foster
my early interest in science. Mom and Dad bankrolled the R&D of my childhood: microscopes,
chemistry sets, encyclopedias, model rockets (actually, Cinco bought me the first one), erector
sets, LEGOs, electronics kits, pinewood derby cars, subscriptions to Popular Science, summertime
“College for Kids,” the list goes on. At every juncture my parents went above and beyond the call
of duty. Here’s just one example: In sixth grade I wanted to do the Mendel experiment for the
science fair. Bear in mind this is the experiment that involves cross-breeding fruit flies to test the
inheritance of dominant and recessive genes. Mom made contact with a lab at San Diego State,
somehow convinced them to loan us equipment (including a very nice Bausch & Lomb binocular
microscope), and then helped her son raise a couple generations of fruit flies in his bedroom over
the next several weeks. The point is there are perfectly wholesome, loving parents who would never
go to such lengths for their kids. The fact that mine did really speaks to their love and devotion
to their children.
I must thank my coworkers in the Dessau lab. Jake Koralek (now at UC Berkeley) built the
first laser-based ARPES system, ushering in a new era in photoemission and thereby setting the
stage for all the work presented in this thesis. Fraser Douglas (now at Intel) performed the isotope
experiments that are foundational to my own work with isotope samples. Ted Reber has been
focusing on cuprate analysis concurrent with my own studies. It was actually Ted who collected
the data that is the foundation of Chapter 4. As our studies have progressed alongside each other,
my work has benefitted immensely from the insights acquired by Ted. I only hope he can say the
same about me. Zhe “Joe” Sun was a student and later a postdoc in our group, who just left for
a position at the University of Science and Technology of China. Joe is a close approximation to
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a living, breathing encyclopedia of ARPES on correlated electron systems. Qiang “Quinn” Wang
is an enormously talented physicist, and it has been a pleasure to progress through grad school
alongside him. Justin Griffith is our in-house mechanical designer and all-around lab jock. He is
utterly indispensable and a great guy to boot. More recent members of our group — Yue “Scott”
Cao, Steve Parham, Sunita Kannan, and Justin Waugh — are all outstanding, and it has been fun
to work with them.
I have benefited from some excellent outside collaborations and assistance. In addition to
the laser-based system in Colorado, ARPES data in this thesis comes from beamline 5-4 at Stan-
ford Synchrotron Radiation Lightsource (SSRL) and beamline 9A of the HiSOR synchrotron of
the Hiroshima Synchrotron Radiation Center (HSRC). Samples used in my work have come from
Yoshihiro Aiura, Hiroshi Eisaki, and Yoshiyuki Yoshida at the National Institute of Advanced In-
dustrial Science and Technology (AIST) in Tsukuba, Japan. Genda Gu at Brookhaven National
Laboratory has also prepared very high-quality samples for us. On my visits to the HiSOR, I have
had the wonderful opportunity to work closely with Aiura, Hideaki Iwasawa, Koji Sato (now at
Hitachi), Kenya Shimada, and Masashi Arita. I am especially indebted to Aiura and Iwasawa, who
are not only great scientific collaborators but also very kind and generous hosts. They have always
made me feel welcome and comfortable in Japan. Arigatou gozaimasu.
Outside of formal collaborations, I have also enjoyed many helpful and informative conver-
sations with other researchers in the field of high-T superconductivity. I am especially grateful
c
to Tom Devereaux, Steve Johnston, Sasha Balatsky, and two of my Ph.D. committee members,
Dmitry Reznik and Kyle McElroy.
Lastly, I would like to thank my dear friend Jason Underwood, who used to work across
the hall from our lab but currently is down the street as a NRC postdoctoral fellow at NIST. He
introduced me (via his wife, Margie) to many other good friends, and he is one of the forces that
helped keep me (relatively) sane these past few years. To paraphrase my brother, What are the
odds of finding two physicists who both enjoy the band Faraquet? Indeed.
To everyone, thanks.
Contents
Chapter
1 Introduction 1
2 The Technique of Angle-Resolved Photoemission Spectroscopy 4
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Energetics of the photoemission process . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Angle-resolved photoemission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Modern ARPES spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.1 Hemispherical analyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.2 Electron lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.3 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.4 Light source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.5 Vacuum chamber, surface preparation, and cryostat manipulator . . . . . . . 19
2.5 Theory of the spectral function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6 Interpretation and analysis of ARPES data . . . . . . . . . . . . . . . . . . . . . . . 23
2.6.1 Momentum and energy distribution curves. . . . . . . . . . . . . . . . . . . . 23
2.6.2 Many-body self-energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.6.3 Matrix elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.7 ARPES in the low photon energy regime . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.7.1 Momentum and energy resolution. . . . . . . . . . . . . . . . . . . . . . . . . 32