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Microwave Frequency Vortex Dynamics of the Heavy Fermion

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Microwave Frequency Vortex Dynamics of the Heavy Fermion MICROWAVE FREQUENCY VORTEX DYNAMICS OF THE HEAVY FERMION SUPERCONDUCTOR CeCoIn5 by Natalie Murphy B.Sc., Trent University, 2010 THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN THE DEPARTMENT OF PHYSICS FACULTY OF SCIENCE c Natalie Murphy 2012 SIMON FRASER UNIVERSITY Fall 2012 All rights reserved. However, in accordance with the Copyright Act of Canada, this work may be reproduced, without authorization, under the conditions for “Fair Dealing." Therefore, limited reproduction of this work for the purposes of private study, research, criticism, review, and news reporting is likely to be in accordance with the law, particularly if cited appropriately. APPROVAL Name: Natalie Murphy Degree: Master of Science Title of Thesis: Microwave Frequency Vortex Dynamics of the Heavy Fermion Superconductor CeCoIn5 Examining Committee: Dr. Patricia Mooney, Professor (Chair) Dr. David M. Broun, Senior Supervisor Associate Professor Dr. J. Steven Dodge, Supervisor Associate Professor Dr. Erol Girt, Supervisor Associate Professor Dr. George Kirczenow, Internal Examiner Professor Date Approved: August 29th 2012 ii Partial Copyright Licence Abstract Magnetic fields penetrate superconductors as quantized tubes of magnetic flux, or vortices. A transport current passed through such a superconductor exerts a transverse force on the vortices. The dissipation resulting from vortex motion is characterized by a vortex viscos- ity, and microwave techniques provide a powerful means of accessing this in the presence of pinning. A novel microwave spectroscopy apparatus has been set up that allows sensitive mea- surements of the dynamical properties of vortices to be made at temperatures down to 80 mK, in magnetic fields up to 9 T, and at frequencies from 2.25 to 25 GHz. A com- prehensive study has been carried out at 2.5 GHz on the heavy fermion superconductor CeCoIn5. Surprising new behaviour is revealed in the vortex viscosity, which, at low fields, exhibits clear signatures of d-wave quasiparticle physics. This suggests that delocalized excitations outside the vortex cores are predominantly responsible for vortex dissipation in CeCoIn5. iii Acknowledgments I would like to give a big thanks to everyone who made this thesis a reality and most of all thank you all for your patience with my countless questions. David Broun is the most inspiring academic I have met and I consider myself lucky to have had the chance to work and learn in his lab. Wendell Huttema is a great baseball player and knows a thing or two about what goes on in the lab. Sonia Milbradt was a helpful friend to traverse the day-to-day Masters life with from the beginning and a coffee buddy who will be missed. Colin Truncik is the master of analysis and an intense workout buddy. Ricky is the best TA around and has a wisdom that only time can build. AJ Koenig is the bestest new seat friend and makes lots of pretty pictures on my demand. Eric Thewalt put lots of work into the design of the in-field apparatus. Ken Van Wieren, Vic Allen, Ken Myrtle, and Bryan Gormann are always willing to give a hand with machining and are always willing to grab the BBQ for me. Thank you. Lastly I would like to thank my mother for helping me believe that I can do anything that I set my mind to. iv Contents Approval ii Abstract iii Acknowledgments iv Contentsv List of Tables viii List of Figures ix 1 Introduction1 1.1 Superconductivity...............................1 1.1.1 Zero Electrical Resistivity......................2 1.1.2 Meissner Effect............................2 1.2 London Theory................................3 1.3 BCS Theory..................................6 1.4 Ginzburg–Laudau Theory and Vortices....................7 1.4.1 Vortices................................8 1.4.2 Type I vs. Type II Superconductors.................8 2 Meissner-State Electrodynamics 11 2.1 Generalized Two-Fluid Model........................ 11 2.1.1 Complex Conductivity........................ 11 2.2 Surface Impedance.............................. 13 v CONTENTS vi 2.2.1 Rs and Xs............................... 14 3 Vortex-state Electrodynamics 16 3.1 Bardeen–Stephen Model........................... 16 3.2 Introduction to Vortex Viscosity....................... 18 3.3 Pinning.................................... 20 3.4 Gittleman–Rosenblum Model......................... 21 3.5 Coffey–Clem Model............................. 22 3.6 The Waldram Model............................. 23 3.7 Interpretation of our Experiment....................... 23 4 Experimental Apparatus 27 4.1 Microwave Cavity Perturbation........................ 27 4.1.1 Cavity Perturbation Techniques................... 28 4.1.2 Surface Impedance.......................... 30 4.1.3 Vortex Dynamics and Cavity Perturbation.............. 31 4.2 In-Field Microwave Cavity Perturbation Apparatus............. 32 4.2.1 The Sample Stage.......................... 35 4.3 Dilution Refrigeration............................. 38 5 CeCoIn5 42 5.1 CeIn3 — Parent Compound of CeCoIn5 ................... 42 5.2 Structure and Fermi Surface of CeCoIn5 ................... 44 5.3 Superconducting Properties of CeCoIn5 ................... 44 5.3.1 Evidence For d-Wave Superconductivity............... 46 5.4 Quasiparticle Dynamics........................... 50 6 Results on CeCoIn5 51 6.1 Vortex Viscosity in Ortho-II YBCO..................... 51 6.2 Zero-Field Microwave Conductivity of CeCoIn5 ............... 53 6.3 Vortex Dynamics of CeCoIn5 ......................... 55 6.3.1 Surface Impedance.......................... 55 6.3.2 Pinning................................ 57 CONTENTS vii 6.3.3 Vortex Viscosity........................... 59 6.3.4 Flux-Flow Resistivity......................... 61 7 Conclusions 64 Bibliography 66 List of Tables 3.1 Vortex unit cell — magnetic field and frequency limits........... 25 3.2 Summary of model parameters........................ 26 viii List of Figures 1.1 London penetration depth...........................5 1.2 Ginzburg–Laudau vortex profile.......................8 1.3 B–T phase diagram of type I and type II superconductors.......... 10 3.1 Vortex free body diagram........................... 17 3.2 Induced vortex electric fields......................... 18 3.3 Pinning potential............................... 20 3.4 Free-flow and the pinning limit........................ 24 4.1 Base mode magnetic field profile....................... 28 4.2 Cavity perturbation - ∆f0 and ∆fB ...................... 30 4.3 Illustration of in-field experiment....................... 33 4.4 In-field microwave cavity apparatus..................... 34 4.5 Sample stage illustration........................... 36 4.6 Photos of experimental set-up........................ 37 4.7 3He cycle in the dilution refrigerator..................... 40 4.8 Thermal profile of the in-field apparatus................... 41 5.1 Crystal structure of CeIn3 and CeCoIn5 ................... 43 5.2 Pressure–temperature phase diagram of CeIn3 ................ 43 5.3 Bc2(T ) of CeCoIn5 .............................. 45 5.4 Alloy series phase diagram of CeXIn5 .................... 45 5.5 Heat capacity of CeCoIn5 ........................... 47 5.6 Superfluid density of CeCoIn5 ........................ 47 5.7 Penetration depth and superfluid density of CeCoIn5 ............. 48 ix LIST OF FIGURES x 5.8 Frequency dependence superfluid density of CeCoIn5 ............ 49 5.9 Quasiparticle conductivity of CeCoIn5 and YBCO.............. 50 6.1 Vortex viscosity of Ortho-II YBCO...................... 52 6.2 Flux-flow resistivity of Ortho-II YBCO................... 53 6.3 Zero-field complex conductivity of CeCoIn5 ................. 54 6.4 Surface resistance of CeCoIn5 ........................ 56 6.5 Surface resistance on a log scale....................... 56 6.6 Surface reactance of CeCoIn5 ......................... 57 6.7 Depinning frequency............................. 58 6.8 Pinning constant................................ 58 6.9 Vortex viscosity................................ 60 6.10 Vortex viscosity at low magnetic fields.................... 60 6.11 Vortex viscosity plotted against pB ..................... 61 6.12 Flux-flow resistivity of CeCoIn5 ....................... 62 6.13 Flux-flow resistivity divided by magnetic field of CeCoIn5 ......... 62 Chapter 1 Introduction This thesis describes a set of experiments that use microwave techniques to reveal the dy- namical properties of vortices in the heavy fermion superconductor CeCoIn5. I will intro- duce superconductivity, zero-field and vortex state electrodynamics, then present specifics of the experiment and particular sample properties, ending with the presentation of new data on the vortex dynamics of CeCoIn5. In this chapter, I will introduce superconductivity and some of the theories that describe its properties, with a particular focus on showing how vortices emerge from flux quantiza- tion. 1.1 Superconductivity Superconductivity is a macroscopic quantum mechanical phenomenon discovered in 1911 by Heike Kemerlingh Onnes [1], in Leiden, Netherlands. His lab had recently discovered how to liquify helium, making experiments at low-temperatures possible. At the time there were two competing theories on the behaviour of metals at low- temperatures. Some scientists believed conduction would completely stop at absolute zero, corresponding to an infinite resistivity. On the other hand, some thought the electrical resis- tivity would slowly decrease until it reached zero. Onnes was astonished to find that when measuring a sample of mercury the
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