Springer Tracts in Modern Physics Volume 214 Managing Editor: G Höhler, Karlsruhe Editors: C Varma, California F Steiner, Ulm J Kühn, Karlsruhe J Trümper, Garching P Wölfle, Karlsruhe Th Müller, Karlsruhe Starting with Volume 165, Springer Tracts in Modern Physics is part of the [SpringerLink] service For all customers with standing orders for Springer Tracts in Modern Physics we offer the full text in electronic form via [SpringerLink] free of charge Please contact your librarian who can receive a password for free access to the full articles by registration at: springerlink.com If you not have a standing order you can nevertheless browse online through the table of contents of the volumes and the abstracts of each article and perform a full text search There you will also find more information about the series Springer Tracts in Modern Physics Springer Tracts in Modern Physics provides comprehensive and critical reviews of topics of current interest in physics The following fields 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Institut für Experimentelle Kernphysik Fakultät für Physik Universität Karlsruhe Postfach 69 80 76128 Karlsruhe, Germany Phone: +49 (7 21) 08 35 24 Fax: +49 (7 21) 07 26 21 Email: thomas.muller@physik.uni-karlsruhe.de www-ekp.physik.uni-karlsruhe.de Fundamental Astrophysics, Editor Joachim Trümper Max-Planck-Institut für Extraterrestrische Physik Postfach 13 12 85741 Garching, Germany Phone: +49 (89) 30 00 35 59 Fax: +49 (89) 30 00 33 15 Email: jtrumper@mpe.mpg.de www.mpe-garching.mpg.de/index.html Solid-State Physics, Editors Chandra M Varma Editor for The Americas Department of Physics University of California Riverside, CA 92521 Phone: +1 (951) 827-5331 Fax: +1 (951) 827-4529 Email: chandra.varma@ucr.edu www.physics.ucr.edu Peter Wölfle Institut für Theorie der Kondensierten Materie Universität Karlsruhe Postfach 69 80 76128 Karlsruhe, Germany Phone: +49 (7 21) 08 35 90 Fax: +49 (7 21) 69 81 50 Email: woelfle@tkm.physik.uni-karlsruhe.de www-tkm.physik.uni-karlsruhe.de Complex Systems, Editor Frank Steiner Abteilung Theoretische Physik Universität Ulm Albert-Einstein-Allee 11 89069 Ulm, Germany Phone: +49 (7 31) 02 29 10 Fax: +49 (7 31) 02 29 24 Email: frank.steiner@physik.uni-ulm.de www.physik.uni-ulm.de/theo/qc/group.html Gernot Goll Unconventional Superconductors Experimental Investigation of the Order-Parameter Symmetry With 67 Figures ABC Gernot Goll Universität Karlsruhe Physikalisches Institut Wolfgang-Gaede-Str 76128 Karlsruhe Germany E-mail: gernot.goll@phys.uni-karlsruhe.de Library of Congress Control Number: 2005933767 Physics and Astronomy Classification Scheme (PACS): 74.70.Tx, 74.70.Pq, 74.20.Rp, 74.50.+r, 74.25.Bt, 74.25.Nf ISSN print edition: 0081-3869 ISSN electronic edition: 1615-0430 ISBN-10 3-540-28985-2 Springer Berlin Heidelberg New York ISBN-13 978-3-540-28985-2 Springer Berlin Heidelberg New York This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights 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Heidelberg Printed on acid-free paper SPIN: 11010715 56/TechBooks 543210 O Lord, how manifold are your works! In wisdom have you made them all; the earth is full of your creatures (Psalm 104, 24) To Claudia, Anne and Julia S - a single word that still causes excitement, more than 90 years after its discovery S - an amazing phenomenon of lossfree transport and levitation in a magnetic field S - a challenging field of scientific activities between fundamental condensed-matter research and industrial applications S - fascinating both experimentalists and theorists S - sometimes unconventional S S Preface In the past decades a growing number of metals exhibited evidence for exotic types of superconductivity The superconductivity is often called unconventional in order to classify superconductors with respect to the order-parameter symmetry Many intriguing experiments have been carried out to elucidate the order-parameter symmetry The characterization of the order parameter of superconducting materials needs information on (i) the pairing mechanism, (ii) the parity and spin state, (iii) the size and the nodal structure of the energy gap, and (iv) the macroscopic superconductive phase Each property can be accessed by different experiments For example, the nodal structure can be investigated by measurements of the temperature dependence of thermodynamic and transport properties, by angular-resolved thermalconductivity measurements, and by the directional dependence of current–voltage characteristics in point-contact and tunnelling measurements, though the latter experiments have been mainly applied for the determination of gap size and the density of states around EF On the other hand, the observation of a power law in the lowtemperature behaviour of one property, for example of the penetration depth, is not sufficient for the characterization of an unconventional superconductor and must be treated with some caution since there might be other, quite different and rather conventional explanations of the data Therefore, it is important to have corroborating evidence from a number of different experiments before a conclusive picture of the order-parameter symmetry is obtained As none of the experimental methods alone can definitely reveal the order-parameter symmetry, manifold experiments will be discussed, each of which accesses a certain aspect In particular, some emphasis will be put on the investigation of the energy gap of unconventional superconductors by point-contact spectroscopy The point-contact and tunnel spectra yield information on the size and the anisotropy of the superconductive energy gap, its temperature, and its field dependence This book is subdivided into three parts In part I, a brief overview on possible unconventional superconductors is followed by a short theoretical introduction of the main concepts of unconventional superconductivity combined with a general definition of often-used terms and notations Part II presents several experimental methods that allow a characterization of the order-parameter symmetry This include measurements of specific heat, thermal conductivity, penetration depth, and ultrasound attenuation for information on the nodal structure (Chap 3), nuclear X Preface magnetic resonance and muon spin rotation experiments for information on the parity and spin state (Chap 4), point-contact and tunnelling spectroscopy for information about the energy gap (Chap 5), and phase-sensitive probes, namely the Josephson effect (Chap 6) This part is concluded with an overview of experimental methods that probe the effects of an unconventional order parameter on single vortices and the symmetry of the flux-line lattice (Chap 7) Part III reviews three classes of unconventional superconductors, namely the Ce-based heavy-fermion superconductors (Chap 8), the U-based heavy-fermion superconductors (Chap 9), and the metal-oxide superconductors (Chap 10), especially Sr2 RuO4 This book is not intended to review the high-temperature superconductors There exist a vast number of excellent review articles and monographs that give a quite complete overview of the state-of-the-art research on these materials Nevertheless, the high-temperature superconductors will be mentioned, as the huge amount of research on these compounds has pushed the whole field, both the theoretical and experimental activities, and has shed light on the understanding of many other topics related to unconventional superconductivity Finally, I thank all people who contributed to this work in many respects during the past years First of all, I am grateful to Prof H v Lăohneysen for continuous support, encouragement, and many stimulating discussions It is a pleasure to thank Prof I K Yanson for initiating the interest in the experimental technique of pointcontact spectroscopy, and Dr Y Naidyuk for helpful discussions and correspondence I thank Prof L Taillefer, Prof Y Maeno, Dr Z Q Mao, Dr F Lichtenberg, Dr V Zapf, and Dr E Bauer for providing the samples necessary for these studies and for useful discussions I would also like to acknowledge Prof M B Maple, Prof E Dormann, Prof C Bruder, Prof P Wăolfle, Prof J Wosnitza, Dr M Eschrig, Dr M Fogelstrăom, Dr R Werner, and Dr O Stockert for many fruitful and illuminating discussions I thank Dr C Obermair, Dr F Laube, T Brugger, S Kontermann, and M Marz for their contributions to the point-contact data reviewed here and all my colleagues for good collaboration I thank L Behrens for drawing, scanning, and editing many of the figures Last, but not least, I thank my wife Claudia and my daughters Anne and Julia for their patience and sympathy during my weekend writing of this manuscript This work was partly supported by the Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 195 “Lokalisierung von Elektronen in makroskopischen und mikroskopischen Systemen” and Graduiertenkolleg “Anwendungen der Supraleitung.” Karlsruhe, October 2005 Gernot Goll A Appendix 157 continued from previous page Compound Sample Technique Reference MacLaughlin et al [102, 103], Tien et al [104] Heffner et al [105] Heffner et al [106] Luke et al [107] Sonier et al [108] Dalmas de R´eotier et al [109] UBe13 pc sc sc Be NMR µSR -ZF,TFµSR -TFµSR -TFµSR -TFµSR -ZF,TF- URu2 Si2 pc mc, aligned 29 Si Ru NQR µSR -ZFµSR -TFµSR -TF- Kohori et al [110] Matsuda et al [111] Knetsch et al [112] Heffner et al [106] Luke et al [113] pc pc pc pc sc mc 27 Al NMR/NQR Al NQR 105 Pd NMR/NQR µSR -ZF,TFµSR -TFµSR -TF- Kyogaku et al [114] Tou et al [115] Matsuda et al [116] Amato et al [117] Amato et al [118] Feyerherm et al [119] pc sc pc 27 27 Al NMR/NQR Al NMR µSR -ZF- Kyogaku et al [114] Ishida et al [120] Amato et al [121] sc sc sc sc sc sc sc sc µSR -ZFµSR -ZF,TF17 O NMR 101 Ru NMR 101 Ru NQR 99 Ru NMR 17 O, 101 Ru NQR 101 Ru NQR Luke et al [122] Luke et al [74] Ishida et al [123] Ishida et al [124] Ishida et al [125] Ishida et al [126] Mukuda et al [127] Murakawa et al [128] 101 UPd2 Al3 27 UNi2 Al3 Sr2 RuO4 158 A Appendix Table A.3 A survey on experiments probing the energy gap of unconventional superconductors The experiments have been performed either on polycrystals (pc) or single crystals (sc) by classical point-contact technique (PC), mechanically controllable break-junctions (MCBJ), planar tunnel junctions (TJ) technique, and scanning tunneling spectroscopy (STS) Compound Sample Counterelectrode Technique Reference pc pc sc pc pc sc sc Nb Al Ag W, Cu, Ag Pb CeCu2 Si2 PtIr PC PC PC PC TJ MCBJ STS Han et al [129] Poppe [130] de Wilde et al [131] Gloos et al [132, 133, 134] Iguchi et al [135] Gloos et al [136] Goschke et al [137] sc sc sc Pt Au Pt-Ir PC PC PC Goll et al [138] Park et al [139] Rourke et al [140, 141, 142] sc pc sc pc pc sc pc sc Al, Nb, UPt3 Pt Pt Ag W Zn, Pb, NbTi UPt3 Pt PC PC PC PC PC PC MCBJ PC Poppe [130] Nowack et al [143] Goll et al [144, 145, 146, 147] de Wilde et al [131, 148] Gloos et al [133, 134] Naidyuk et al [149] Gloos et al [136] Obermair et al [150] pc pc pc pc pc pc pc Nb, Ta W UBe13 W Cu, Pt, Ir, Ta, UBe13 UBe13 Au PC PC PC PC PC MCBJ PC Han et al [129, 151] Nowack et al [143, 152] Moreland et al [153] Gloos et al [133, 154] Kvitnitskaya et al [155] Gloos et al [136] Wăalti et al [156, 157, 158] sc sc sc Ag Ag, URu2 Si2 Mo, W PC PC PC Naidyuk et al [159] Nowack et al [160] Hasselbach et al [161] continued on next page CeCu2 Si2 CeCoIn5 UPt3 UBe13 URu2 Si2 A Appendix continued from previous page Compound Sample Counterelectrode Technique Reference sc sc Ag Zn, NbTi PC PC pc pc sc sc sc sc Ag W Pt URu2 Si2 Pt, URu2 Si2 URu2 Si2 PC PC PC MCBJ PC MCBJ de Wilde et al [131] Nowack et al [162], Naidyuk et al [163] Samuely et al [164] Gloos et al [133, 134] Naidyuk et al [165] Naidyuk et al [166] Rodrigo et al [167] Gloos et al [136] pc sc sc sc film film Nb W UPd2 Al3 PtIr Au/Ag Pb PC PC MCBJ STS TJ TJ He et al [168] Gloos et al [133, 134] Gloos et al [136] Goschke et al [137] Jourdan et al [169] Jourdan et al [170] pc pc W UNi2 Al3 PC MCBJ Gloos et al [133, 134] Gloos et al [171, 136] sc sc sc sc Pt Pb In Pt/Ir PC TJ TJ STS Laube et al [172, 173, 174] Jin et al [175] Liu et al [176] Upward et al [177] UPd2 Al3 UNi2 Al3 Sr2 RuO4 159 160 A Appendix Table A.4 A survey on experiments probing the phase of unconventional superconductors by the Josephson effect Compound Junction Reference CeCu2.2 Si2 -Al (SS ) CeCu2.2 Si2 -Cu-Nb (SNS ) CeCu2.2 Si2 -Cu-Nb (SNS ) CeCu2 Si2 (MCBJ) Poppe et al [130] Sumiyama et al [178] Koyama et al [179] Gloos et al [180] CeIrIn5 -Cu-Nb (SNS ) Sumiyama et al [181] UPt3 -Al (SS ) UPt3 -Cu-Nb (SNS ) Poppe et al [130] Sumiyama et al [182, 178] UBe13 -Ta (SS ) UBe13 -Cu-Nb (SNS ) UBe13 -Nb (SS ) Han et al [151] Shibata et al [183] Shibata et al [183] URu2 Si2 -NbTi (SS ) URu2 Si2 -Nb (SS ) URu2 Si2 -Nb (SS ) URu2 Si2 -Cu-Nb (SNS ) Naidyuk et al [163, 162] Wasser et al [184] Tachibana et al [185] Tachibana et al [185] UPd2 Al3 -Cu-Nb (SNS ) UPd2 Al3 -Nb (SS ) Koyama et al [179] He et al [168] Pb-Sr2 RuO4 -Pb (SN S) Sr2 RuO4 -In (SS ) Sr2 RuO4 -Au0.5 In0.5 (SS ) Sr2 RuO4 -Sn (SS ) Sr2 RuO4 -Nb (SS ) Sr2 RuO4 -Au0.5 In0.5 (SQUID) Jin et al [175] Jin et al [186], Liu et al [176] Nelson et al [187] Sumiyama et al [188] Sumiyama et al [188] Nelson et al [189] CeCu2 Si2 CeIrIn5 UPt3 UBe13 URu2 Si2 UPd2 Al3 Sr2 RuO4 References 161 Table A.5 A survey on experiments probing the vortex lattice/structure of unconventional superconductors Compound Sample Technique Reference sc neutron diffraction Eskildsen et al [190] neutron diffraction neutron diffraction neutron diffraction Kleiman et al [191] Yaron et al [192] Huxley et al [193] µSR µSR neutron diffraction neutron diffraction µSQUID force microscope Aegerter et al [73] Luke et al [74] Kealey et al [194] Riseman et al [195] Dolocan et al [196] CeCoIn5 UPt3 Sr2 RuO4 sc, T c sc, T c sc, T c sc, T c sc, T c = 0.95 K = 1.45 K = 1.39 K = 1.28 K = 1.31 K References F Steglich, C.D Bredl, W Lieke, U 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104 UNi2 Al3 112 UPd2 Al3 112 UPt3 89 URu2 Si2 107 YBa2 Cu3 O7−δ 141 cuprates electron-phonon interaction excess current 51, 133 Fermi liquid theory ferromagnets itinerant superconducting flux quantum 62 half-integer 58 flux-line lattice 61 hexagonal squared transition in Hc2 measurements 27 CeCoIn5 77 CeCu2 Si2 69 CePt3 Si 82 He heat capacity heating model 42 heavy-fermion compounds heavy-fermion superconductors high-temperature superconductor 5, 140 impurity scattering 22, 50 170 Index inelastic broadening 50 Josephson effect 55 CeCu2 Si2 71 CeIrIn5 80 dc Josephson effect 55 Sr2 RuO4 135 UBe13 107 UPd2 Al3 115 UPt3 102 URu2 Si2 110 Josephson junction 55 critical current 55 Knight shift µ+ Knight shift 31 nuclear magnetic resonance Kohlrausch relation 42 28 Landauer formula 41 London penetration depth UBe13 105 UPd2 Al3 113 UPt3 93 URu2 Si2 109 magnetic penetration depth 23 Maxwell resistance 42 Meissner screening 17 metal-oxide superconductor 121 Sr2 RuO4 122 muon spin rotation 30 µ+ Knight shift 31 CeCoIn5 78 CeCu2 Si2 70 CeIrIn5 78 CePt3 Si 81 Sr2 RuO4 127, 137 study of vortices 63 UBe13 105 UNi2 Al3 114 UPd2 Al3 113 UPt3 96 URu2 Si2 109 NMR/NQR measurements CeCoIn5 77 CeCu2 Si2 70 CeIrIn5 77 CePt3 Si 83 Sr2 RuO4 128 UBe13 105 UNi2 Al3 113 UPd2 Al3 113 UPt3 96 URu2 Si2 108 nodal structure CeCoIn5 74 CeCu2 Si2 69 CeIrIn5 74 CePt3 Si 83 Sr2 RuO4 123 UBe13 104 UPd2 Al3 112 UPt3 92 URu2 Si2 108 non-Fermi-liquid 4, CeCoIn5 74 nuclear magnetic resonance UPd2 Al3 113 order parameter 13 nodes 15 organic superconductor 28 pair amplitude 12 pairing nonunitary 17 singlet 3, 6, 12 triplet 6, 12 pairing symmetry d-wave p-wave 3, 132 s-wave 3, paramagnetic limit 27 Pauli matrices 12 Pauli principle 12 Pauli susceptibility penetration depth Sr2 RuO4 125 phase diagram UPt3 90 phase-sensitive experiments point-contact spectroscopy 39 break junction 40 CeCoIn5 78 CeCu2 Si2 70 edge-to-edge contact 40 Index N-N contact 40 N-S contact 44 nanolithographic contact 40 needle-anvil contact 40 regimes of ballistic 41 diffusive 43 thermal 42 Sr2 RuO4 129 UBe13 106 UNi2 Al3 114 UPd2 Al3 114 UPt3 97 URu2 Si2 109 PuCoGa5 74 PuRhGa5 74 Quantum criticality quantum-critical point CeCoIn5 74 CeCu2 Si2 68 ruthenates scanning tunnelling spectroscopy 37 study of vortices 62 Sharvin resistance 41 small-angle neutron scattering 62 CeCoIn5 81 Sr2 RuO4 137 UPt3 102 specific heat 21 CeCu2 Si2 69 Sr2 RuO4 123 UBe13 104 UPd2 Al3 112 UPt3 92 URu2 Si2 108 spin fluctuation spin-lattice relaxation 28 spin-orbit coupling 17 Sr2 RuO4 122 superconductor borocarbide conventional cuprate ferromagnetic heavy-fermion high-temperature 5, 140 organic ruthenate unconventional supercurrents, spontaneous 17 Tersoff-Hamann model 37 thermal conductivity 21 Bi2 Sr2 CaCu2 O8 142 influence of impurities 22 Sr2 RuO4 125 UBe13 105 UPd2 Al3 113 UPt3 92 URu2 Si2 108 YBa2 Cu3 O6.9 142 time-reversal symmetry 17 breaking of 17 tricrystal SQUID experiment YBa2 Cu3 O7−δ 146 tunnelling spectroscopy 35, 40 Sr2 RuO4 129 UPd2 Al3 114 UPt3 97 YBa2 Cu3 O7−δ 143 UBe13 103 ultrasound attenuation 24 Sr2 RuO4 126 UPt3 94 unconventional superconductor UNi2 Al3 111 UPd2 Al3 111 UPt3 89 URu2 Si2 107 3, 14 vacuum tunnelling 37 vacuum-tunnelling spectroscopy UPd2 Al3 114 vortex lattice 6, 61 vortices 61, 102 Wexler formula 43 zero-bias anomaly 59 zero-bias conductance peak 36, 59 171 ... elucidate the order- parameter symmetry The characterization of the order parameter of superconducting materials needs information on (i) the pairing mechanism, (ii) the parity and spin state, (iii) the. .. picture of the order- parameter symmetry is obtained As none of the experimental methods alone can definitely reveal the order- parameter symmetry, manifold experiments will be discussed, each of which... www.physik.uni-ulm.de/theo/qc/group.html Gernot Goll Unconventional Superconductors Experimental Investigation of the Order- Parameter Symmetry With 67 Figures ABC Gernot Goll Universität Karlsruhe