The Superconductor-Insulator Transition in the LaAlO3-SrTiO3 Electron System Tunneling and Field Effect Investigations Lukas Kürten Max-Planck-Institut für Festkörperforschung Universität Stuttgart MAX-PLANCK-GESELLSCHAFT The Superconductor-Insulator Transition in the LaAlO3 { SrTiO3 Electron System Tunneling and Field Effect Investigations Von der Fakult¨atMathematik und Physik der Universit¨atStuttgart zur Erlangung der W¨urdeeines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Abhandlung vorgelegt von Lukas K¨urten aus Lindlar Hauptberichter: Prof. Dr. Jochen Mannhart Mitberichter: Prof. Dr. Martin Dressel Tag der m¨undlichen Pr¨ufung: 14.11.2017 Max-Planck-Institut f¨urFestk¨orperforschung Universit¨atStuttgart 2017 CONTENTS List of Figures viii Zusammenfassung 1 1 Introduction 7 1.1 Motivation . 7 1.2 Overview of this thesis . 8 1.3 The LaAlO3-SrTiO3 interface . 10 1.3.1 SrTiO3 .................................... 10 1.3.2 LaAlO3 .................................... 11 1.3.3 LaAlO3-SrTiO3 ................................ 11 2 Theory 15 2.1 Superconducting tunneling spectroscopy . 15 2.2 The Berezinski-Kosterlitz-Thouless transition . 18 2.2.1 Introduction to BKT . 18 2.2.2 The BKT transition in Josephson junction arrays . 21 2.2.3 Charge-vortex duality . 23 2.3 Transistor fundamentals . 23 2.3.1 LaAlO3-SrTiO3 transistors . 26 3 Methods 27 3.1 Sample preparation . 27 3.1.1 Substrate preparation . 27 3.1.2 Pulsed laser deposition . 29 3.1.3 RHEED . 29 3.1.4 Sample growth procedure . 30 3.1.5 Patterning of electrodes and electron system . 32 3.1.6 Sample growth overview . 33 3.2 Device designs . 35 3.2.1 Circular junctions . 35 3.2.2 Van der Pauw-geometry . 35 3.2.3 Superconducting transistor . 36 3.2.4 Patterned tunnel junctions . 36 3.2.5 Transistors . 38 3.2.6 Transistor-Hall bars . 39 v 3.3 Measurement of the phonon peaks in inelastic tunneling . 39 3.4 Measurements . 41 3.4.1 Low-temperature measurements . 41 3.4.2 High-pressure experiments . 41 4 LaAlO3 { SrTiO3 transistors under hydrostatic pressure 43 4.1 Standard transistors . 44 4.2 Transistor-Hall-bars . 47 4.3 Conclusion . 52 5 The critical magnetic field of the LaAlO3 { SrTiO3 2DES 55 5.1 Introduction . 55 5.2 Hc2 (T ) measurements . 56 5.3 Discussion . 59 6 The superconductor-insulator transition of the LaAlO3 { SrTiO3 2DES 63 6.1 Growth optimization . 63 6.1.1 The Lifshitz transition and its connection to superconductivity . 69 6.1.2 Alternative growth optimization: high electron mobility . 71 6.2 Measurement of the Berezinski-Kosterlitz-Thouless transition . 74 6.3 Resistance anomaly in the superconducting transition . 75 6.4 Superconducting transistor . 78 7 In-gap states in superconducting LaAlO3 - SrTiO3 { interfaces 83 7.1 Introduction . 83 7.2 In-gap states observed in tunneling spectroscopy . 84 7.3 Experiments . 88 7.4 Results . 91 7.5 Discussion . 92 7.6 Conclusions . 97 8 Conclusions and Outlook 99 8.1 Conclusions . 99 8.2 Outlook . 101 Appendices 103 A BCS theory 105 B Renormalization group theory 111 C Dilution refrigerator 115 D Multiband fitting 117 D.1 Fitting of the conductivities . 117 D.2 Fitting of the resistances . 118 vi D.3 Fitting of the Hall curve . 119 D.4 Discussion . 120 E List of samples 123 Bibliography 127 List of publications 143 Acknowledgements 145 vii LISTOFFIGURES 1.1 Band structure of the LaAlO3{SrTiO3 interface 2DES . 12 2.1 Schematic of superconducting tunneling . 17 2.2 Illustration of topological charge . 19 2.3 Illustration of a vortex pair . 21 2.4 Josephson junction array . 22 2.5 Idealized n-channel field-effect transistor . 24 2.6 Idealized source-drain characteristics . 25 2.7 Cross-sectional sketch of an LaAlO3{SrTiO3 transistor . 26 3.1 Fabrication steps of LaAlO3{SrTiO3 samples . 27 3.2 SrTiO3 substrate AFM images . 28 3.3 Sketch of a PLD system . 30 3.4 RHEED signal of LaAlO3 growth . 31 3.5 Steps of LaAlO3{SrTiO3 transistor growth . 34 3.6 Circular tunnel junction sample . 36 3.7 Van der Pauw - geometry sample . 37 3.8 Sketch of a superconducting transistor sample . 37 3.9 Patterned tunnel junction devices . 38 3.10 Transistors for high pressure studies . 39 3.11 Phonon peaks in inelastic tunneling . 40 3.12 Illustration of a free-standing transistor device . 42 4.1 Transfer characteristics of transistor sample 029 . 45 4.2 Analysis results from sample 029 . 46 4.3 Hysteretic behavior of the threshold voltage . 47 4.4 Optical micrograph of transistor-Hall bar sample 053 . 48 4.5 Transfer characteristics of transistor-Hall bar sample 053 . 48 4.6 Sheet carrier density of sample 053 . 49 4.7 Hall- and Magnetoresistance as a function of hydrostatic pressure . 50 4.8 Evolution of carrier density with pressure . 51 4.9 Anomalous transfer characteristics of sample 053 . 52 4.10 Simulations of multiband transistors . 53 5.1 R(H)-data of sample 011 . 56 5.2 Hc2(T ) of sample 011 . 57 viii 5.3 R(H) of sample T36 . 58 5.4 Hc2(T ) of sample T36 . 59 5.5 Hc2(T )-data compared to theoretical models . 61 6.1 Classification of LaAlO3{SrTiO3 samples . 64 6.2 Properties of sample 035 at 50 mK as a function of back-gate voltage . 68 6.3 Sheet resistance of van der Pauw samples . 69 6.4 Carrier density and mobility of van der Pauw samples . 70 6.5 Hall conductivity and magnetoconductivity of sample 070 . 71 6.6 Evolution of carrier density with back-gate voltage . 72 6.7 Superconducting parameters as function of backgate voltage . 72 6.8 Magnetoresistance of high-mobility sample P-ATK190 . 73 6.9 Shubnikov-de Haas oscillations . 74 6.10 I − V -characteristics of sample 035 . 76 6.11 Illustration of the current distribution in a circular junction device . 77 6.12 Resistance anomaly in the superconducting transition . 79 6.13 Superconducting parameters of sample 035 at the resistance anomaly . 80 6.14 Superconducting transistor characteristics . 81 7.1 Tunneling spectrum without in-gap features . 89 7.2 In-gap features in tunneling spectra . 90 7.3 Illustration of the quantitative analysis used to characterize the in-gap peaks. 92 7.4 Evolution of height and FWHM of the zero bias peak and of the side peaks . 93 A.1 BCS density of states . 109 C.1 Cross-sectional cut through a dilution refrigerator . 116 D.1 Multiband fitting of conductivities . ..