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Quantum Critical Behavior in the Superfluid Density of High-Temperature Superconducting Thin Films

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Quantum Critical Behavior in the Superfluid Density of High-Temperature Superconducting Thin Films QUANTUM CRITICAL BEHAVIOR IN THE SUPERFLUID DENSITY OF HIGH-TEMPERATURE SUPERCONDUCTING THIN FILMS DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Iulian N. Hetel, Maitrise de Physique et Applications, M.S. Physics ***** The Ohio State University 2008 Dissertation Committee: Approved by Professor Thomas R. Lemberger, Adviser Professor Klaus Honscheid Adviser Professor R. Sooryakumar Physics Graduate Program Professor Nandini Trivedi ABSTRACT A central question in the physics of high-temperature superconductors is how su- perconductivity is lost at the extreme ends of the superconducting phase diagram, underdoping and overdoping. When mobile holes are removed from optimally doped cuprates, the transition temperature TC and superfluid density nS(0) decrease in a surprisingly correlated fashion. I succeeded in producing and measuring homoge- neous underdoped high-temperature superconducting films by partially substituting +2 +3 Ca for Y in Y Ba2Cu3O7−δ films with reduced oxygen concentrations in the CuO chains. I test the idea that the physics of underdoped cuprates is dominated by phase fluc- tuations by measuring the temperature dependence of superfluid density nS(T ) and by changing the dimensionality of the system from 3D thick samples to 2D ultrathin films. Thick Y1−xCaxBa2Cu3O7−δ films are in agreement with previous measure- ments of pure Y Ba2Cu3O7−δ samples and do not show any 2D or 3D-XY critical regimes in the temperature dependence of superfluid density. Moreover, the tran- sition temperature has a square-root dependence on absolute superfluid density at zero temperature, rather than showing the predicted linear dependence in the case of strong thermal phase fluctuations. When superfluid density is measured in under- doped 2D Y1−xCaxBa2Cu3O7−δ films as thin as only 2 unit cells for all doping levels, nS(T ) has a dramatic downturn consistent with a 2D vortex-antivortex pair unbind- ing transition and, at severe underdoping, TC is linearly proportional to nS(0). This ii dimensionality-dependent scaling relation is the result of quantum phase fluctuations that suppress superconductivity near a Quantum Critical Point at zero temperature. Further measurements in an additional family of high-temperature superconductors, La2−xSrxCuO4, are consistent with my results in underdoped Y1−xCaxBa2Cu3O7−δ. La2−xSrxCuO4 also provided the opportunity to study the other extreme end of the superconducting phase diagram. In the overdoped region, as carrier density in- creases, supefluid density and the transition temperature are both suppressed. While it still remains uncertain what produces this suppression, a plausible interpretation is that only a small fraction of the hole carriers contribute to the superfluid density and the pair breaking effects are so important that they destroy superconductivity. iii To my wife Laura iv ACKNOWLEDGMENTS Along the years I had the privilege to work with a number of people who taught me a lot about what it means to be a researcher. I want to thank my PhD adviser Tom Lemberger for welcoming me in his laboratory and providing me with an interesting and challenging research project. I have learned a lot from our interaction and I appreciated his guidance and patience along the difficult parts of this study. Nandini Trivedi, R. Sooryakumar, and Klaus Honscheid were kind enough to serve as reviewers of my project and gave insightful comments that I have incorporated in the final version of this dissertation. My discussions with Mohit Randeria and Zlatko Tesanovic helped me to get a better understanding of the direction and implications of my experimental results. Also, Rita Roknlin was very generous in offering technical support whenever I needed it. Before my coming to Ohio State University, several people introduced me to the fascinating field of superconductivity: Mircea Crisan and Utu Deac from Babes-Bolyai University, Cluj Napoca, Romania, Manuel Nunez-Regueiro from CRTBT-CNRS, Grenoble, France, and my advisers during my master’s degree in Sherbrooke, Patrick Fournier and Mario Poirier. I am grateful to all of them for the knowledge and passion for physics that they shared with me. v I was fortunate to share the Lemberger lab with two great colleagues, Mun Seog Kim and Yuri Zuev, who guided and welcomed me during my first months in the lab and supported me throughout the years. I am especially thankful to my (high- energy) colleagues from the high-energy group - Don Burdette, James Morris, Joe Regensburger and Evan Frodermann - who made lunchtime fun and included me in their clandestine Friday pizza meetings. My parents Felicia and Nicolae were always supportive and encouraged me to pursue my education even when it meant being far away from home. My younger brother Laurentiu shares my passion for science and managed to get to the PhD finish line before me: I couldn’t be prouder of him. My wife Laura was a constant support and inspiration. Not only did she proofread my papers, but she also contributed to my experiments by changing the voltage in the drive coil (.002V). With one of us working on a PhD in physics and the other writing a PhD in the humanities at the same time, we never had a dull moment and we learned a lot from and about each other. This research project benefited from the support of several institutions. The Ohio State University Presidential Fellowship allowed to focus solely on my research during my last year of studies. The OSU Alumni Research Grant and the Sigma Xi Grant for Aid-in-Research provided funding for purchasing materials that were crucial for my project. Also, with the support of I2Cam and the Council of Graduate Students, I was able to share and test my research at scientific conferences. vi VITA July 18, 1976 . Born - Sibiu, Romania 1995-1999 . Engineering Physics, Babes-Bolyai University, Cluj-Napoca, Romania 1999-2000 . Agence Universitaire de la Franco- phonie Fellow, Universite Grenoble I, France 2001-2002 . Graduate Research Associate, Univer- site de Sherbrooke, Quebec, Canada 2002-2006 . Graduate Research Associate, The Ohio State University, USA 2007-2008 . Presidential Fellow, The Ohio State University, USA PUBLICATIONS Research Publications I. Hetel, T. R. Lemberger and M. Randeria. Quantum critical behaviour in the superfluid density of strongly underdoped ultrathin cuprate films Nature Physics, 3, 700 (2007. I. Hetel, T. R. Lemberger, A. Tsukada and M. Naito. Doping dependent superfluid density in La2−xSrxCuO4 thin films (in preparation). T. R. Lemberger, I. Hetel, A.J. Hauser, and F. Y. Yang. Superfluid density of superconductor-ferromagnet bilayers J. Appl. Phys. 103, 07C701 (2008). T. R. Lemberger, I. Hetel, J. W. Knepper, and F. Y. Yang. Penetration depth study of very thin superconducting Nb films Phys. Rev. B 76, 094515 (2007). vii Y. L. Zuev, I. Hetel, T. R. Lemberger. Search for Cooper-pair fluctuations in severely underdoped YBCO films Phys. Rev. B 74, 012502 (2006). R. Prozorov, D. D. Lawrie, I. Hetel, P. Fournier, and R. W. Giannetta. Field- dependent diamagnetic transition in magnetic superconductor Sm1.85Ce0.15CuO4−δ Phys. Rev. Lett. 93, 147001 (2004). P. Richard, G. Riou, I. Hetel, S. Jandl, M. Poirier and P. Fournier. Role of oxygen nonstoichiometry and the reduction process on the local structure of Nd2−xCexCuO4±δ Phys. Rev. B 70, 064513 (2004). P. Fournier, M.-E. Gosselin, S. Savard, I. Hetel, P. Richard and G. Riou. Fourfold oscillations and irreversibility of the magnetoresistance in the nonmetallic regime of electron-doped cuprates Phys. Rev. B 69, 220501(R) (2004). FIELDS OF STUDY Major Field: Physics Studies in: Experimental Condensed Matter Physics Low Temperature Physics Superconductivity viii TABLE OF CONTENTS Page Abstract . i Dedication . iii Vita......................................... vi List of Tables . xi List of Figures . xii Chapters: 1. INTRODUCTION . 1 2. BASIC CONCEPTS . 6 2.1 Superconductivity and superfluid density . 6 2.2 General properties of high-temperature superconductors . 9 2.3 Phase fluctuations in high-temperature superconductors . 11 3. EXPERIMENTAL METHODS . 15 ix 3.1 Preparation of atomically flat SrT iO3 substrates . 15 3.2 Thin film deposition . 23 3.3 Superfluid density measurements . 27 4. UNDERDOPING Y Ba2Cu3O7−δ ...................... 31 4.1 Chain disorder in underdoped Y Ba2Cu3O7−δ ............ 31 4.2 Y1−xCaxBa2Cu3O7−δ underdoping while adding holes . 33 4.2.1 Oxygen reduction in Y0.80Ca0.2Ba2Cu3O7−δ ......... 34 4.2.2 Doping dependence, homogeneity, and superfluid density . 36 5. UTRATHIN Y1−xCaxBa2Cu3O7−δ FILMS . 41 5.1 Challenges in the fabrication of films with reduced thickness . 41 5.2 Temperature dependence of superfluid density . 47 5.2.1 KTB transition in two-dimensional samples . 49 5.2.2 Frequency dependence of KTB transition . 54 5.2.3 TC vs nS(0). Scaling next to a Quantum Critical Point . 57 5.2.4 Temperature dependence of 1/λ2: 2D vs. 3D . 63 6. SUPERFLUID DENSITY MEASUREMENTS IN La2−xSrxCuO4 FILMS 67 6.1 Evolution of transition temperature and superfluid density with doping 69 6.2 2D fluctuations in ultrathin La1.85Sr0.15CuO4 ............ 78 6.3 Frequency and current dependence of the 2D transition in ultrathin La1.85Sr0.15CuO4 ............................ 82 x 7. CONCLUSIONS . 84 Appendices: A. Appendix: Y1−xCaxBa2Cu3O7−δ films summary . 86 B. Appendix: Atomic Force Microscopy . 89 Bibliography . 91 xi LIST OF TABLES Table Page 5.1 The upper limit on the transition temperatures for several 2 unit cell Y1−xCaxBa2Cu3O7−δ films when thermal phase fluctuations effects are suppressed by quantum fluctuations. 65 6.1 Properties of La2−xSrxCuO4−δ films as a function of doping. x is the nominal Sr doping, TC (ρ = 0) sets the upper limit on the transition temperature, ρab(50K) is the ab-plane resistivity just above the onset −2 of transition, and ρab(50K)×λ (0)/µ0 is related to the scattering rate τ −1....................................
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