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Ultra-Low Temperature Measurements of London Penetration Depth in Iron Selenide Telluride Superconductors University of New Orleans ScholarWorks@UNO University of New Orleans Theses and Dissertations Dissertations and Theses Fall 12-20-2013 Ultra-low Temperature Measurements of London Penetration Depth in Iron Selenide Telluride Superconductors Andrei Diaconu University of New Orleans, [email protected] Follow this and additional works at: https://scholarworks.uno.edu/td Part of the Condensed Matter Physics Commons Recommended Citation Diaconu, Andrei, "Ultra-low Temperature Measurements of London Penetration Depth in Iron Selenide Telluride Superconductors" (2013). University of New Orleans Theses and Dissertations. 1731. https://scholarworks.uno.edu/td/1731 This Dissertation is protected by copyright and/or related rights. It has been brought to you by ScholarWorks@UNO with permission from the rights-holder(s). You are free to use this Dissertation in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/ or on the work itself. This Dissertation has been accepted for inclusion in University of New Orleans Theses and Dissertations by an authorized administrator of ScholarWorks@UNO. For more information, please contact [email protected]. Ultra-low Temperature Measurements of London Penetration Depth in Iron Selenide Telluride Superconductors A Dissertation Submitted to the Graduate Faculty of the University of New Orleans in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Engineering and Applied Science Physics by Andrei Diaconu B.S. “Alexandru Ioan Cuza” University, Iasi, Romania, 2006 M.S. “Alexandru Ioan Cuza” University, Iasi, Romania, 2008 M.S. University of New Orleans, New Orleans, USA, 2012 December, 2013 Dedication To my loving parents, Romeo and Maria. ii Acknowledgment I am deeply thankful to my advisor, Prof. Dr. Leonard Spinu, for his valuable guidance and constant support throughout my research here at University of New Orleans. Working under his supervision for the past years has been an amazing opportunity. I have learned a great deal about being a man of science from him and I am grateful for that. He has been an amazing teacher and a tremendous help in so many ways, professionally and personally. It has been an honor to be his student. I would like to thank our collaborators at Tulane University, Prof. Dr. Zhiqiang Mao and his students, Jin Hu and T.J. Liu for their extensive support, advice and assistance throughout the years. Their continuous help has made this work possible. To all my colleagues and friends at AMRI, whom I have had the pleasure of knowing and working with, I would like to extend my thanks for all their help and valued friendship. I would also like to thank my professors at UNO for their essential contribution to my scientific knowledge and laboratory skills. I am profoundly grateful to Dr. Vladimir Shvarts from Janis Research Company for his indispensable support and assistance in operating the dilution refrigerator and deeper understanding of the fascinating field of cryogenics. To my closest friends Kyle, Denny and Westly, I am extremely grateful for making my life in the United States a pleasurable and memorable experience. I want to express my deepest gratitude to Dr. Catalin Martin for his extensive support and essential contribution. This work would not have been possible without his invaluable assistance. iii Table of Contents List of Figures .............................................................................................................................................. v List of Tables .............................................................................................................................................. ix Abstract…………… .................................................................................................................................... x Introduction ................................................................................................................................................. 1 Chapter 1 Overview of Superconductivity .............................................................................................. 5 1.1. History of superconductivity ................................................................................................. 5 1.2. Theories and concepts in superconductivity ....................................................................... 11 1.3. Unconventional superconductivity...................................................................................... 23 Chapter 2 The London Penetration Depth in Superconductors ......................................................... 31 2.1. Magnetic fields in the Meissner state .................................................................................. 31 2.2. Magnetic penetration in rectangular slab shaped superconductors ..................................... 35 2.3. The structure of superconducting gap from λ(T) measurements ........................................ 40 Chapter 3 The Tunnel Diode Oscillator Technique ............................................................................. 50 3.1. Introduction ......................................................................................................................... 50 3.2. Timeline of tunnel diode oscillator based experimental methods ....................................... 52 3.3. Principle and theory of operation of a TDO circuit ............................................................ 54 3.4. The temperature dependence of TDO frequency ................................................................ 63 3.5. The TDO as a London penetration depth measurement technique ..................................... 66 3.6. Flat coils based TDO for measuring the in-plane penetration depth ................................... 74 3.7. Experimental TDO setup in a dilution refrigerator ............................................................. 80 Chapter 4 Iron Based Superconductors ................................................................................................ 87 4.1. Overview of iron based superconductors ............................................................................ 87 4.2. The iron chalcogenide Fe1+y(Te1-xSex) ................................................................................ 93 4.3. Fe1+y(Te1-xSex) single crystals growth and characterization ................................................ 99 4.4. Heat capacity and magnetic susceptibility investigations ................................................. 104 Chapter 5 London Penetration Depth in Fe1+y(Te1-xSex) Single Crystals ......................................... 114 5.1. Tunnel diode oscillator measurements .............................................................................. 114 5.2. Temperature dependence of the in-plane London penetration depth ................................ 119 5.3. Evidence for s± symmetry in the Fe1.02(Te1-xSex) system ................................................. 126 5.4. Evidence for nodal gap in the Fe1.02(Te1-xSex) system....................................................... 130 Conclusions .............................................................................................................................................. 137 Bibliography ............................................................................................................................................ 142 Vita………… ........................................................................................................................................... 155 iv List of Figures Figure 1.1 Magnetic flux expulsion from a superconductive sphere .......................................................... 12 Figure 1.2 Thermodynamic critical field diagram for Type I (left) and Type II (right) superconductors .. 19 Figure 1.3 Energy gap temperature dependence for conventional superconductors ................................... 22 Figure 1.4 Heat capacity temperature dependence in superconductors ...................................................... 23 Figure 1.5 Order parameter symmetry for s-wave (left) and d-wave (right) .............................................. 26 Figure 1.6 Left: Fermi surfaces topology in MgB2 [74]. Right: Anomalous temperature dependence of specific heat in MgB2 [75]. .......................................................................................................................... 27 Figure 1.7 A simplified representation of the Fermi surface topology and energy gap symmetry for multigap superconductors exhibiting: two gap s-wave pairing (a) and s± wave symmetry (b). ................. 28 Figure 1.8 Temperature dependence of superconductive gap for different pairing symmetries as evaluated from the gap equation (Eq. 1.29) (symbols) and the fit using the approximate expression in Eq. 1.47 (lines). Image taken from [17]. ................................................................................................................... 29 Figure 2.1 Magnetic field distribution in a superconductive semi-infinite domain under uniform applied field B0 ........................................................................................................................................................ 31 Figure 2.2 Meissner effect in a superconductive sphere. Calculated magnetic
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