Dirac Fermions in Graphene and Graphite—a view from angle-resolved photoemission spectroscopy

84 Pages·2007·15.69 MB·English

by  Shuyun Zhou

Dirac Fermions in Graphene and Graphite
— a view from angle-resolved photoemission spectroscopy
by
Shuyun Zhou
M.A. (UC Berkeley) 2005
B.S. (Tsinghua University) 2002
A dissertation submitted in partial satisfaction
of the requirements for the degree of
Doctor of Philosophy
in
Physics
in the
GRADUATE DIVISION
of the
UNIVERSITY OF CALIFORNIA, BERKELEY
Committee in charge:
Professor Alessandra Lanzara, Chair
Professor Dung-Hai Lee
Professor Oscar Dubon
Fall 2007
The dissertation of Shuyun Zhou is approved.
Chair Date
Date
Date
University of California, Berkeley
Fall 2007
Dirac Fermions in Graphene and Graphite
— a view from angle-resolved photoemission spectroscopy
Copyright (cid:13)c 2007
by
Shuyun Zhou
Abstract
Dirac Fermions in Graphene and Graphite
— a view from angle-resolved photoemission spectroscopy
by
Shuyun Zhou
Doctor of Philosophy in Physics
University of California, Berkeley
Professor Alessandra Lanzara, Chair
Theresearchingraphenehasexplodedinthepastfewyears,duetoitsintriguingphysicsasanemerging
paradigm for relativistic condensed matter physics as well as its great promise for application in next gen-
eration electronics. Understanding the low energy electronic structure of graphene is fundamental as most
of the intriguing properties of graphene arise from its peculiar electronic dispersion, which resembles that
of relativistic Dirac Fermions. This thesis presents a detailed study of the low energy electronic structure
of graphene and its related three dimensional material - graphite - by using angle-resolved photoemission
spectroscopy (ARPES), a direct probe of the electronic structure. In particular, the evolution of the Dirac
Fermions in graphene and graphite as well as the effect of impurities is the focus of this thesis.
This thesis is organized as follows. The first chapter is an introduction of the electronic structure
of graphene and graphite, and the specialty of Dirac fermions compared to quasiparticles in conventional
condensedmattersystems. Chapter2isanintroductionofthetechniquesusedthroughoutthisthesis-angle
resolved photoemission spectroscopy (ARPES), X-ray photoemission spectroscopy (XPS) and low energy
electron microscopy (LEEM). Chapter 3 discusses the growth and characterization of epitaxial graphene on
SiC wafers.
Chapters 4 and 5 present the ARPES results on epitaxial graphene, the evolution of the low energy
electronic dynamics as a function of sample thickness and how to make graphene a finite band gap semi-
conductor. More specifically, chapter 4 discusses how a gap is induced between the valence and conduction
bandsbygraphene-substrateinteractionandchapter5showshowareversiblemetal-insulatortransitioncan
be possibly induced in epitaxial graphene by hole doping.
Chapter 6 and 7 show the ARPES results on three dimensional graphite samples. Chapters 6 shows
the coexistence of Dirac fermions with massive quasiparticles in different momentum space of single crys-
talline graphite and the effect of impurity. Chapter 7 shows the surprising results of obtaining the band
dispersions even in a partially polycrystalline graphite sample, the comparison with those obtained in sin-
gle crystalline graphite, as well as the implication for ARPES study of partially polycrystalline samples in
general.
Professor Alessandra Lanzara
Dissertation Committee Chair
1
Contents
Abstract 1
Contents i
Acknowledgements iii
vitae vi
1 Introduction 1
1.1 Graphene - an emerging paradigm for relativistic condensed matter physics . . . . . . . . . . 1
1.2 Electronic structure of graphene in the tight binding model . . . . . . . . . . . . . . . . . . . 3
1.3 Massless Dirac fermions and massive quasiparticles . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Electronic structure of infinite layer graphite . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Experimental techniques 10
2.1 Angle resolved photoemission spectroscopy (ARPES) . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.1 ARPES and the photoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2 Three step model and sudden approximation . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.3 Single particle spectral function description of ARPES . . . . . . . . . . . . . . . . . . 15
2.1.4 Energy distribution curves (EDCs) and momentum distribution curves (MDCs) . . . . 16
2.1.5 Electron mean free path and the probing depth of ARPES. . . . . . . . . . . . . . . . 18
2.1.6 State of the art ARPES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 X-ray photoelectron spectroscopy (XPS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Low energy electron microscopy (LEEM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3 Growth and characterization of epitaxial graphene 24
3.1 Growth of epitaxial graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Characterization of epitaxial graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.1 Scanning electron microscopy (SEM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.2 X-ray photoemission spectroscopy (XPS) . . . . . . . . . . . . . . . . . . . . . . . . . 27
i
3.2.3 Angle-resolved photoemission spectroscopy - ARPES . . . . . . . . . . . . . . . . . . . 29
3.2.4 Low energy electron microscopy (LEEM) . . . . . . . . . . . . . . . . . . . . . . . . . 30
4 Gap opening in epitaxial graphene 33
4.1 Dirac fermions in epitaxial graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 Departure from conical dispersion in single layer epitaxial graphene . . . . . . . . . . . . . . . 35
4.3 Gap interpretation vs many body interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.4 Thickness dependence of the gap and Dirac point energy . . . . . . . . . . . . . . . . . . . . . 40
4.5 Possible mechanisms of the gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.5.1 Inter-Dirac-point scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.5.2 Quantum confinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.5.3 Breaking of the sublattice symmetry due to graphene-substrate interaction . . . . . . 46
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5 Metal-insulator transition in epitaxial graphene by molecular doping 50
5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.2 Valence band of graphene with adsorption of nitrogen dioxide . . . . . . . . . . . . . . . . . . 51
5.3 Gas adsorption and metal-insulator transition in bilayer graphene . . . . . . . . . . . . . . . . 53
5.4 Metal-insulator transition in single layer graphene . . . . . . . . . . . . . . . . . . . . . . . . 55
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6 Dirac fermions and effect of impurities in single crystalline graphite 59
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.2 Electronic structure of single crystal graphite . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.2.1 Dispersions at H - massless Dirac fermions. . . . . . . . . . . . . . . . . . . . . . . . . 61
6.2.2 Dispersions at K - massive quasiparticles . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.3 Effect of defect states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7 ARPES study of partially polycrystalline graphite: HOPG 71
7.1 Electronic structure of polycrystalline materials measured by ARPES . . . . . . . . . . . . . 71
7.2 ARPES study of the electronic structure of polycrystalline graphite. . . . . . . . . . . . . . . 73
7.3 Explanation of the paradoxical coexistence based on a density of states argument . . . . . . . 75
7.4 Dispersions along the surface normal direction. . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7.5 Comparison of data taken from HOPG and single crystalline graphite . . . . . . . . . . . . . 79
7.5.1 Interlayer coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
7.5.2 Low energy dispersions and Dirac fermions . . . . . . . . . . . . . . . . . . . . . . . . 80
7.5.3 Defect states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
ii
7.6 Conclusions and implication of this study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Bibliography 87
List of Figures 96
iii
Acknowledgements
I am very lucky to work with a group of talented and kind people in my Ph.D., from whom I have
benefited greatly. All the work presented here would not have been possible without them.
First of all, my deepest thanks go to my advisor, Alessandra Lanzara. I am very lucky to have such
an inspiring, creative and considerate advisor, who has made my Ph.D. fruitful and enjoyable. Besides the
training, encouragement and support that she gave me in science, I also appreciate her willingness to care
about students’ life beyond work. The past few years of working with her has been a fortune for me. Her
endless enthusiasm for science, her open-mindedness and her wisdom to balance work and life, have set her
as a role model for me.
I could not ask for better colleagues than the people in Lanzara group. Dr. Gey-Hong Gweon taught
me numerous things in my first three years, ranging from experimental skills to different physics topics. I
appreciate his mentoring and the efforts that he has put in to make me a good experimentalist. Dr. Kyle
McElroy taught me the importance of understanding the physics problems in different perspectives. Jeff
Graf, Chris Jozwiak and I joined the group as the first generation graduate students and we shared the
longest memories of our Ph.D. lives. Besides intelligent, they are the best colleagues who are always willing
to share their knowledge and skills and provide immediate help whenever needed. Daniel Garcia’s talks are
the most wonderful sound of the group and I appreciate his help to improve my speech skills, though I have
toadmitthatIamnotafastlearnerinthisaspect. DavidSiegelremindedmeoftheearlyyearsofmyPh.D.
It is a pleasure to see that he has become very good at communications and experiments. The interaction
with visitors Dr. Marco Portalupi and Dr. Andreas Bill, as well as undergrads Elizabeth Rollings, Annie
Endozo and Max Watson, has also been very pleasant.
The collaboration with many theorists has been quite beneficial and pleasant. Dung-Hai Lee is the
longest theoretical collaborator. His deep physics insights and his enthusiasm for finding the most beautiful
solutions are very inspiring. The collaboration with A.N. Castro Neto, F. Guinea S.G. Louie and C.D.
Spataru has been a great pleasure.
Alexei Fedorov has collaborated in most of the research work presented here. His assistance in the
experiments and his support for trying new experiments is highly appreciated. I am grateful to Andreas
Schmid and Farid El Gably for providing extensive help with the LEEM measurements at the most critical
time. JohnPepperis verytalentedinmachiningandIthank him formakingmodifications to accommodate
the needs of some challenging experiments. I thank Prof. P. N. First and Prof. W. A. de Heer for providing
the graphene samples at the beginning of this project. I thank Prof. Oscar Dubon and Prof. Michael F.
Crommie for serving as my committee members for the qualifying exam. J. T. Robinson and J. W. Beeman
havebeenverynicetohelpmewithsubstratetreatment. IthankthefriendlyandhelpfulpeopleontheALS
floor: X. J. Zhou, W. L. Yang, N. Manella, K. Tanaka, S.-K. Mo, Y.-D. Chuang, J. H. Guo, B. K. Freelon,
B. S. Mun. The LBL security people have been very kind to escort me to work and to home in many late
nights.
My personal interaction with other physicists also helps me greatly. I thank Z. Hussain, Z.-X. Shen,
Y.-R. Shen and B.-F. Zhu for being patient to listen to me and give me advice. The encouragement from
M. A. H. Vozmediano and N. Berrah is also appreciated.
Finally,specialthankstomyhusbandPuforhisencouragementandsupportthroughoutalltheseyears.
Thanks to my parents for letting me travel a long way from home and visiting me for the last three months
of my Ph.D. Thanks to my brother and sister-in-law for having taken good care of my parents, my little
nephew for adding a lot of fun to the family.
iv
Curriculum Vitæ
Shuyun Zhou
Education
2007 University of California, Berkeley, CA, USA
Ph.D., Physics
2005 University of California, Berkeley, CA, USA
M.A., Physics
2002 Tsinghua University, Beijing, China
B.S., Physics
Honors and Awards
2007 ALS Doctoral fellowship, Lawrence Berkeley National Laboratory
2007 Chinese Government Award for Outstanding Self-financed Students Abroad
2006 ALS Doctoral fellowship, Lawrence Berkeley National Laboratory
2006 UC Berkeley Graduate Division Conference Travel Grant
2005 Scholarship from International School of Physics ‘Enrico Fermi’, Italy
Publications
Graphene and Graphite:
1 Metal to insulator transition in epitaxial graphene induced by molecular doping.
S. Y. Zhou, D. A. Siegel, A. V. Fedorov and A. Lanzara.
In preparation.
2 Departure from the conical dispersion in epitaxial graphene.
S. Y. Zhou, D. A. Siegel, A. V. Fedorov and A. Lanzara.
Physica E, in press (2007).
3 Substrate induced band gap opening in epitaxial graphene.
S. Y. Zhou,G.-H.Gweon,A.V.Fedorov,P.N.First,W.A.deHeer,D.-H.Lee,F.Guinea,
A. H. Castro Neto and A. Lanzara.
Nature Mat. 6, 770 (2007).
4 First direct observation of Dirac fermions in graphite.
S.Y. Zhou,G.-H.Gweon,J.Graf,A.V.Fedorov,C.D.Spataru,R.D.Diehl,Y.Kopelevich,
D.-H. Lee, S.G. Louie, A. Lanzara.
Nature Phys. 2, 595 (2006).
5 Low energy excitations in graphite: the role of dimensionality and lattice defects.
S.Y. Zhou, G.-H. Gweon, and A. Lanzara.
Ann. Phys. 321, 1730 (2006).
6 Synthesis and characterization of atomically-thin graphite films on a silicon carbide sub-
strate.
E. Rollings, G.-H. Gweon, S.Y. Zhou, B.S. Mun, J.L. McChesney, B.S. Hussain, A.V.
Fedorov, and A. Lanzara.
J. Phys. Chem. Solids 67, 2172 (2006).
7 Coexistence of sharp quasiparticle dispersions and disorder features in graphite.
S.Y. Zhou,G.-H.Gweon,C.D.Spataru,J.Graf,D.-H.Lee,StevenG.Louie,A.Lanzara.
Phys. Rev. B 71, 161403(R) (2005).
High T superconductors:
c
v
1 A universal high energy anomaly in angle resolved photoemission spectra of high temper-
ature superconductors - possible evidence of spinon and holon branches.
J. Graf, G.-H. Gweon, K. McElroy, S.Y. Zhou, C. Jozwiak, E. Rotenberg, A. Bill, T.
Sasagawa, H. Eisaki, S. Uchida, H. Takagi, D.-H. Lee and A. Lanzara.
Phys. Rev. Lett. 98, 067004 (2007).
2 Strong and complex electron-lattice correlation in optimally doped Bi Sr CaCu O .
2 2 2 8+δ
G.-H. Gweon, S.Y. Zhou, M.C. Watson, T. Sasagawa, H. Takagi and A. Lanzara.
Phys. Rev. Lett. 97, 227001 (2006).
3 ElasticscatteringsusceptibilityofthehightemperaturesuperconductorBi Sr CaCu O :
2 2 2 8+δ
a comparison between real and momentum space photoemission spectroscopies.
K. McElroy, G.-H. Gweon, S.Y. Zhou, J. Graf, S. I. Uchida, H. Eisaki, H. Takagi, T.
Sasagawa, D. -H. Lee, A. Lanzara.
Phys. Rev. Lett. 96, 067005 (2006).
4 Oxygen isotope effect on electron dynamics in Bi Sr CaCu O : angle-resolved photoe-
2 2 2 8+δ
mission spectroscopy.
T. Sasagawa, A. Lanzara, G.-H. Gweon, S. Zhou, J. Graf, Suryadijaya, H. Takagi.
Physica C-superconductivity and its applications 426, 436 (2005).
5 AnomalousisotopeeffectontheelectrondynamicsofBi Sr CaCu O hightemperature
2 2 2 8+δ
superconductor.
G.-H. Gweon, T. Sasagawa, S.Y. Zhou, J. Graf, H. Takagi, D. H. Lee and A. Lanzara.
Nature 430, 187 (2004).
6 Strong influence of phonons on the electron dynamics of Bi Sr CaCu O .
2 2 2 8+δ
G. -H. Gweon, S.Y. Zhou, A. Lanzara.
J. Phys. Chem. Solids 65, 1397 (2004).
7 Lattice dynamics and paired electrons in high temperature superconductors.
A. Lanzara, G.-H. Gweon, S.Y. Zhou.
Kluwers Academic Publishers B.V., Vol. NATO Science Series II - Mathematics, Physics
and Chemistry (2004).
Charge density wave:
1 Probing the band structure of LaTe using Angle Resolved Photoemission Spectroscopy.
2
D.R. Garcia, S.Y. Zhou, G.-H. Gweon, M.H. Jung, Y.S. Kwon, A. Lanzara
J. Elec. Spec. Relat. Phenom. 156-158, 58 (2007).
2 Revealing charge density wave formation in the LaTe system by Angle Resolved Photoe-
2
mission Spectroscopy.
D.R. Garcia, G.-H. Gweon, S.Y. Zhou, J. Graf, C.M. Jozwiak, M.H. Jung, Y.S. Kwon, A.
Lanzara.
Phys. Rev. Lett. 98, 166403 (2007).
Science Highlights
1 S.Y. Zhou et al, Substrate induced band gap opening in epitaxial graphene, Nature Mat. 6, 770
(2007)
• “Graphene: Mind the gap” by Kostya Novoselov, News and Views - Nature Mat. Vol. 6, 720
(2007)
2 S.Y. Zhou et al, First direct observation of Dirac fermions in graphite, Nature Phys. 2, 595 (2006)
• “First direct evidence of Dirac fermions in graphite”, ALS News Vol. 277, June 27, 2007
• SelectedasScienceHighlightfortheAdvancedLightSource(ALS)annualactivityreport2006
3 G.-H. Gweon et al, Anomalous isotope effect on the electron dynamics of Bi Sr CaCu O high
2 2 2 8+δ
temperature superconductor, Nature 430, 187 (2004)
• “Giant Effects of Lattice-Vibrations on Electron Dynamics in a High-Temperature Supercon-
ductor”, Japan Science and Technology Agency, Nov. 2005
vi