Cover Page
The handle http://hdl.handle.net/1887/63332 holds various files of this Leiden University dissertation.
Author: Sulangi, M.A.
Title: Disorder and interactions in high-temperature superconductors
Issue Date: 2018-07-05
Disorder and Interactions in High-Temperature
Superconductors
Proefschrift
ter verkrijging van
de graad van Doctor aan de Universiteit Leiden, op gezag van Rector Magnificus prof. mr. C. J. J. M. Stolker,
volgens besluit van het College voor Promoties te verdedigen op donderdag 5 juli 2018
klokke 15.00 uur
door
Miguel Antonio Sulangi
geboren te Manilla, de Filipijnen in 1989
Promotor: Prof. dr. J. Zaanen
Promotiecommissie: Prof. dr. P. J. Hirschfeld (University of Florida) Prof. dr. ir. H. T. C. Stoof (Universiteit Utrecht) Prof. dr. J. Aarts
Dr. M. P. Allan
Prof. dr. ir. T. H. Oosterkamp Prof. dr. K. E. Schalm
Casimir PhD series, Delft-Leiden 2018-19 ISBN 978-90-8593-348-9
An electronic version of this thesis can be found at https://openaccess.leidenuniv.nl.
The research described in this thesis is supported by the Netherlands Organisation for Scientific Research (NWO/OCW) as part of the Fron- tiers of Nanoscience (NanoFront) program.
The cover is a photograph, taken by the author, of the mouth of the Puerto Princesa Underground River from inside the cave.
To Elmer, Rhodora, and Thea Sulangi.
C O N T E N T S
1 i n t r o d u c t i o n 3
2 p h e n o m e n o l o g y o f t h e c u p r at e s 15
2.1 Angle-Resolved Photoemission Spectroscopy 17 2.2 Scanning Tunneling Spectroscopy 20
2.3 Superconductor 21 2.4 Pseudogap 29 2.5 Strange Metal 33
3 r e v i s i t i n g q ua s i pa r t i c l e s c at t e r i n g i n t e r f e r e n c e i n h i g h-temperature superconductors: the prob- l e m o f na r r o w p e a k s 43
3.1 Introduction 43
3.2 Model and Methods 50
3.2.1 Green’s Functions and the Local Density of States 52 3.2.2 Modeling the Measurement Process 55
3.3 Pointlike Scatterers 57
3.3.1 Single Weak Pointlike Impurity 59 3.3.2 Multiple Weak Pointlike Impurities 61 3.3.3 Multiple Unitary Pointlike Impurities 66 3.3.4 Dependence of the Power Spectrum on the Im-
purity Strength 68 3.4 Smooth Disorder 70
3.4.1 Single Smooth Scatterer 73 3.4.2 Multiple Smooth Scatterers 75
3.4.3 Quantifying the Range of the Potential 78 3.5 Spatially Random On-Site Energies 81
3.6 Spatially Random Superconducting Gap 85 3.7 Discussion and Conclusion 89
3.A Appendix: Single Unitary Pointlike Scatterer 93
iii
Contents
4 q ua s i pa r t i c l e d e n s i t y o f s tat e s, localization, and d i s t r i b u t e d d i s o r d e r i n t h e c u p r at e s u p e r c o n d u c- t o r s 97
4.1 Introduction 97 4.2 Methods 102
4.2.1 Quasiparticle Density of States 103 4.2.2 Specific Heat 108
4.2.3 Localization Length 109 4.3 Models of Disorder 111
4.3.1 Random-Potential Disorder 111 4.3.2 Multiple Unitary Scatterers 112 4.3.3 Smooth Disorder 114
4.4 Quasiparticle Density of States: An Overview 118 4.5 Correlation Between the LDOS and the Disorder Poten-
tial 137
4.6 Properties of the Density of States near E=0 141 4.7 Low-Temperature Specific Heat 148
4.8 Quasiparticle Localization 150 4.9 Discussion and Conclusion 160
5 s e l f-energies and quasiparticle scattering inter- f e r e n c e 169
5.1 Introduction 169
5.2 Self-Energies and Broadening 174 5.3 Methods 178
5.4 Self-Energies in the Superconducting State 181 5.5 Self-Energies in the Normal State 199
5.6 Discussion and Conclusion 216 6 c o n c l u s i o n s a n d o u t l o o k 221
6.1 The Unreasonable Effectiveness of QPI 221 6.2 Disorder: Old Dog, New Tricks 224
6.3 Stretching QPI to Its Breaking Point 227 Bibliography 233
Samenvatting 261 Acknowledgements 265
iv
c o n t e n t s
List of Publications 269 Curriculum Vitae 271
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