Time- and Angle-Resolved Photoemission Studies of Cuprate Superconductors

163 Pages·2014·10.14 MB·English

Time- and Angle-Resolved Photoemission Studies of Cuprate Superconductors
by
Christopher Lee Smallwood
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 Joseph W. Orenstein
´
Professor Tanja Cuk
Fall 2014
Time- and Angle-Resolved Photoemission Studies of Cuprate Superconductors
Copyright (cid:13)c 2014
by
Christopher Lee Smallwood
Abstract
Time- and Angle-Resolved Photoemission Studies of Cuprate Superconductors
by
Christopher Lee Smallwood
Doctor of Philosophy in Physics
University of California, Berkeley
Professor Alessandra Lanzara, Chair
The origin of high-temperature superconductivity in cuprate ceramics is one of the great
outstanding mysteries in physics. Discovered by Bednorz and Mu¨ller in 1986, the phe-
nomenon has continued to both fascinate and baffle scientists for almost 30 years. At
the heart of the cuprate problem lies the microscopic mechanism responsible for binding
together Cooper pairs, which are a superconductor’s lossless charge carriers. For most
low-temperature superconductors, phonons are responsible, but Cooper pairs in the high-
temperature superconductors may be bound together by magnetic interactions or even more
exotic phenomena.
Although this most fundamental question remains unresolved, important insights con-
tinue to be gained in the field of high-temperature superconductivity, and many of them have
originated from improved experimental methods and instrumentation. This thesis details
progress in understanding the cuprate problem through the development and implementa-
tion of a high-resolution apparatus for conducting time- and angle-resolved photoemission
spectroscopy (time-resolved ARPES). The technique works by using a near-infrared optical
pump pulse to drive an electronic system out of equilibrium, and using an ultraviolet probe
pulse to measure the subsequent dynamics of the nonequilibrium state using photoemission.
Sub-picosecond time resolution is obtained by varying the path length of the pump pulse,
and the net result is a movie of the relaxation dynamics of the band structure. Experimental
results on the bi-layered cuprate superconductor Bi Sr CaCu O (Bi2212) are presented
2 2 2 8+δ
and discussed in detail.
Content is organized into eight chapters. Chapter 1 gives an introduction and overview
of superconductivity research. Chapter 2 summarizes basic theoretical underpinnings of the
ARPES technique, and reviews analysis techniques that are relevant to ARPES and time-
resolved ARPES as well as simple models of quasiparticle recombination. Chapter 3 contains
a detailed overview of the time-resolved ARPES system constructed in the Lanzara research
group. Chapters 4, 5, 6, and 7 present scientific results obtained using time-resolved ARPES
to study Bi2212. Finally, conclusions and future directions are discussed in Chapter 8.
1
For Lindsey
i
Contents
Abstract 1
Contents v
List of Figures vi
List of Tables ix
Acknowledgments x
Curriculum vitae xiii
1 Introduction 1
1.1 Historical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 “The Gentleman of absolute zero” . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Early progress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.3 The triumph of BCS theory: 1957–1985 . . . . . . . . . . . . . . . . . 5
1.1.4 Discovery of the High-T cuprates . . . . . . . . . . . . . . . . . . . . 6
c
1.2 Quantitative models of superconductivity . . . . . . . . . . . . . . . . . . . . 8
1.2.1 London theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.2 The BCS theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.2.1 Hamiltonian and ground state wavefunction . . . . . . . . . 10
1.2.2.2 Solution by canonical transformation . . . . . . . . . . . . . 11
1.2.2.3 Coupling interaction . . . . . . . . . . . . . . . . . . . . . . 12
1.2.3 Physical predictions of the BCS theory . . . . . . . . . . . . . . . . . 13
1.2.3.1 Energy gap and critical temperature . . . . . . . . . . . . . 13
ii
1.2.3.2 Quasiparticle excitations . . . . . . . . . . . . . . . . . . . . 14
1.2.3.3 Meissner effect . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3 Beyond BCS: survey of cuprate phenomenology . . . . . . . . . . . . . . . . 16
1.3.1 BCS-like characteristics in the cuprates . . . . . . . . . . . . . . . . . 16
1.3.2 Exotic properties of the cuprates . . . . . . . . . . . . . . . . . . . . 17
1.4 Opportunities for time-resolved probes . . . . . . . . . . . . . . . . . . . . . 25
2 Analysis techniques 26
2.1 Theory of ARPES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.1.1 Theory of ARPES in the presence of interactions . . . . . . . . . . . 27
2.1.2 Experimental considerations . . . . . . . . . . . . . . . . . . . . . . . 29
2.1.3 Field theory techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.1.3.1 Green function approach to photoemission . . . . . . . . . . 31
2.1.3.2 Non-interacting Fermi gas (T = 0) . . . . . . . . . . . . . . 32
2.1.3.3 Green functions for an interacting system (T = 0) . . . . . . 32
2.1.3.4 Finite temperature . . . . . . . . . . . . . . . . . . . . . . . 34
2.1.3.5 Self-energy, and concrete electron interaction models . . . . 34
2.2 ARPES and time-resolved ARPES analysis . . . . . . . . . . . . . . . . . . . 37
2.2.1 EDCs, MDCs, and delay curves . . . . . . . . . . . . . . . . . . . . . 38
2.2.2 Superconducting gap characterization . . . . . . . . . . . . . . . . . . 39
2.2.2.1 EDC symmetrization . . . . . . . . . . . . . . . . . . . . . . 39
2.2.2.2 Division by the Fermi-Dirac distribution function . . . . . . 40
2.2.2.3 Gap fitting model . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2.2.4 Other gap fitting characterization methods . . . . . . . . . . 41
2.3 Quasiparticle relaxation models . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3.1 Rothwarf-Taylor model . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3.1.1 Limiting cases . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3.1.2 Probe penetration depth considerations . . . . . . . . . . . 47
2.3.1.3 Momentum-dependent recombination . . . . . . . . . . . . . 48
2.3.2 Alternatives to the Rothwarf-Taylor model . . . . . . . . . . . . . . . 49
2.3.2.1 Two-temperature model . . . . . . . . . . . . . . . . . . . . 49
2.3.2.2 Keldysh contour approach . . . . . . . . . . . . . . . . . . . 50
iii
3 Time-resolved ARPES 51
3.1 The time-resolved ARPES technique . . . . . . . . . . . . . . . . . . . . . . 51
3.2 Classes of time-resolved ARPES systems . . . . . . . . . . . . . . . . . . . . 52
3.3 Ti:sapphire lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.1 Principles of operation . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.2 Figures of merit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4 Lanzara group experimental scheme . . . . . . . . . . . . . . . . . . . . . . . 56
3.4.1 Light source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4.2 Sample orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4.3 Photoelectron detection . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.5 Fluence considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.5.1 Overall characterization . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.5.2 Impact of spot size and alignment on fluence . . . . . . . . . . . . . . 60
3.5.3 Impact of geometry on fluence . . . . . . . . . . . . . . . . . . . . . . 62
3.5.4 Impact of reflectance on fluence . . . . . . . . . . . . . . . . . . . . . 62
3.6 Time and energy resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.6.1 Overall characterization . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.6.2 Impact of second- and fourth-harmonic generation . . . . . . . . . . . 65
3.6.3 Impact of the analyzer on energy resolution . . . . . . . . . . . . . . 67
3.6.4 Impact of space charge on energy resolution . . . . . . . . . . . . . . 68
3.7 Detector nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.8 Contact potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.8.1 Modeling contact potential effects . . . . . . . . . . . . . . . . . . . . 72
3.8.2 Correcting contact potential effects . . . . . . . . . . . . . . . . . . . 75
3.9 Sample heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4 Quasiparticle dynamics in Bi Sr CaCu O at low fluence 79
2 2 2 8+δ
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2 Dispersion effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3 Superconducting gap response . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.4 Quasiparticle dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.5 Recombination model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
iv
5 Time- and momentum-resolved gap dynamics in Bi Sr CaCu O 87
2 2 2 8+δ
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2 Experimental details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3 Fermiology: Fermi-division analysis . . . . . . . . . . . . . . . . . . . . . . . 89
5.4 Fermiology: Symmetrized EDC analysis . . . . . . . . . . . . . . . . . . . . 93
5.5 Quantitative dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.5.1 Near-nodal gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.5.2 Momentum dependent gap . . . . . . . . . . . . . . . . . . . . . . . . 97
5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6 Quasiparticle dynamics in Bi Sr CaCu O at high fluence 101
2 2 2 8+δ
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2 Correlations between quasiparticles and the superconducting gap . . . . . . . 102
6.3 Momentum- and energy-dependent trends . . . . . . . . . . . . . . . . . . . 104
6.4 Doping dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7 Nonequilibrium cuprate phase diagram 110
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
7.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7.3 Quasiparticle dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
7.4 Fluence and temperature dependence . . . . . . . . . . . . . . . . . . . . . . 113
7.5 Phase diagram and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 118
8 Conclusions and future directions 121
Bibliography 126
v
List of Figures
1.1 Heike Kamerlingh Onnes and the discovery of superconductivity . . . . . . . 3
1.2 Schematic illustration of the Meissner effect . . . . . . . . . . . . . . . . . . 4
1.3 Handwritten notes from Cooper in 1956 . . . . . . . . . . . . . . . . . . . . 5
1.4 Maximum known superconducting critical temperature as a function of time 7
1.5 BCS energy gap versus temperature . . . . . . . . . . . . . . . . . . . . . . . 14
1.6 A (k,ω) for a linear bare band . . . . . . . . . . . . . . . . . . . . . . . . 15
BCS
1.7 Flux quantization measurement in YB Cu O . . . . . . . . . . . . . . . . 16
2 3 7−δ
1.8 ARPES verification of particle-hole mixing in Bi2212 . . . . . . . . . . . . . 17
1.9 Visualization of a d-wave superconducting order parameter . . . . . . . . . . 18
1.10 Early ARPES measurements of gap anisotropy in Bi2212 . . . . . . . . . . . 19
1.11 Phenomenology of the pseudogap . . . . . . . . . . . . . . . . . . . . . . . . 20
1.12 Nernst effect measurements of phase fluctuations in Bi2212 . . . . . . . . . . 21
1.13 Charge density wave Bragg peak in YBCO as measured by x-ray diffraction 22
1.14 Phase diagrams of unconventional superconductors . . . . . . . . . . . . . . 23
1.15 Evidence for electron-phonon coupling in cuprates . . . . . . . . . . . . . . . 24
2.1 Schematic cartoon of the ARPES technique . . . . . . . . . . . . . . . . . . 27
2.2 Typical measured ARPES dispersion spectra for Bi2212 . . . . . . . . . . . . 29
2.3 Simulated ARPES spectral functions . . . . . . . . . . . . . . . . . . . . . . 35
2.4 Simulated real and imaginary parts of electronic self-energy . . . . . . . . . . 37
2.5 Energy distribution curve (EDC) and momentum distribution curve (MDC)
definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.6 Fermi-function-divided equilibrium ARPES dispersions . . . . . . . . . . . . 40
2.7 Graph of a minimally broadened BCS spectral function. . . . . . . . . . . . . 42
vi
2.8 Comparison between leading-edge gap measurements and symmetrized EDC
fitting methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.9 Rothwarf-Taylor simulated quasiparticle population recovery in the decoupled
regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.10 Rothwarf-Taylorsimulatedquasiparticlepopulationrecoveryinthebottleneck
regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.1 Illustration of the time-resolved ARPES technique . . . . . . . . . . . . . . . 52
3.2 Energy level diagrams for a 4-level laser . . . . . . . . . . . . . . . . . . . . . 54
3.3 Kerr-lens modelocking in a Ti:sapphire laser . . . . . . . . . . . . . . . . . . 55
3.4 Experimental apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.5 Pump and probe beam transverse spatial profiles . . . . . . . . . . . . . . . 61
3.6 Reflectance of single-crystal Bi2212 . . . . . . . . . . . . . . . . . . . . . . . 63
3.7 Time and energy resolution calibration methodology . . . . . . . . . . . . . . 64
3.8 Second-harmonic pulse duration versus BBO crystal length . . . . . . . . . . 66
3.9 Schematic illustration of energy resolution in a hemispherical analyzer . . . . 67
3.10 Space charge effects on Bi2212 . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.11 Sample photocurrent versus incident probe power . . . . . . . . . . . . . . . 69
3.12 Detector nonlinearity calibration measurements . . . . . . . . . . . . . . . . 70
3.13 Effect of correcting detector nonlinearity on cuprate data . . . . . . . . . . . 71
3.14 Sample of Bi2212 mounted on a 1-inch copper puck . . . . . . . . . . . . . . 72
3.15 Electric potential plots resulting from work function differences between a
sample and puck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.16 Simulations of contact potential effects on photoelectron trajectory . . . . . 74
3.17 Comparison between contact potential simulations and ARPES data . . . . . 75
3.18 Momentum-space maps of equilibrium ARPES intensity . . . . . . . . . . . . 76
3.19 Equilibrium low-temperature gap in Bi2212 . . . . . . . . . . . . . . . . . . 77
3.20 Dependence of spectral decay on laser repetition rate . . . . . . . . . . . . . 78
3.21 Pump-induced heating in Bi2212 . . . . . . . . . . . . . . . . . . . . . . . . 78
4.1 ARPES dispersions before and after pumping for nodal and gapped regions
of k-space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.2 Evolution of the superconducting gap following pump excitation . . . . . . . 83
4.3 Quasiparticle recombination dynamics vs. pump fluence and crystal momentum 84
vii