Pairing symmetry in the cuprate superconductors is an important and controversial topic. The recent development of phase-sensitive tests, combined with the refinement of several other symmetry-sensitive techniques, has for the most part settled this controversy in favor of predominantly d-wave symmetry for a number of optimally hole-and electron-doped cuprates. This paper begins by reviewing the concepts of the order parameter, symmetry breaking, and symmetry classification in the context of the cuprates. After a brief survey of some of the key non-phase-sensitive tests of pairing symmetry, the authors extensively review the phase-sensitive methods, which use the half-integer flux-quantum effect as an unambiguous signature for d-wave pairing symmetry. A number of related symmetry-sensitive experiments are described. The paper concludes with a brief discussion of the implications, both fundamental and applied, of the predominantly d-wave pairing symmetry in the cuprates. CONTENTS I. Introduction 969 A. Evidence for Cooper pairing in cuprates 969 B. Order parameter in superconductors 970 C. Broken symmetry and symmetry classification of the superconducting state 971 1. Tetragonal crystal lattice 972 2. Orthorhombic crystal lattice 973 3. Cu-O square/rectangular lattice 973 II. Non-Phase-Sensitive Techniques 974 A. Penetration depth 974 B. Specific heat 975 C. Thermal conductivity 975 D. Angle-resolved photoemission 976 III. Half-Integer Flux-Quantum Effect 977 A. Josephson tunneling 977 B. Flux quantization in a superconducting ring 980 C. Paramagnetic Meissner effect 981 IV. Phase-Sensitive Tests of Pairing Symmetry 982 A. SQUID interferometry 982 B. Single-Josephson-junction modulation 984 C. Tricrystal and tetracrystal magnetometry 985 1. Design and characterization of controlledorientation multicrystals 985 2. Magnetic-flux imaging 986 3. Nature of the observed half-integer flux quantization 988 4. Integer and half-integer Josephson vortices 989 5. Evidence for pure d-wave pairing symmetry 993 a. Tetragonal Tl 2 Ba 2 CuO 6ϩ␦ 994 b. Orthorhombic Bi 2 Sr 2 CaCu 2 O 8ϩ␦ 995 D. Thin-film SQUID magnetometry 997 E. Universality of d-wave superconductivity 997 1. Hole-doped cuprates 998 2. Electron-doped cuprates 998 3. Temperature dependence of the ⌽ 0 /2 effect 1000 V. Related Symmetry-Sensitive Experiments 1000 A. Biepitaxial grain-boundary experiments 1000 B. c-axis pair tunneling 1001 1. Tunneling into conventional superconductors 1001 2. c-axis twist junctions 1004 VI. Implications of d x 2 Ϫy 2 Pairing Symmetry 1004 A. Pairing interaction 1004 B. Quasiparticles in d-wave superconductors 1006 C. Surfaces and interfaces 1006 1. Zero-bias conductance peaks 1006 2. Time-reversal symmetry breaking 1007 3. Josephson junctions in d-wave superconductors 1007 D. Vortex state 1007 VII. Conclusions 1008 Acknowledgments 1009 References 1009

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The recent discovery of iron-based superconductors 1-3 challenges the existing paradigm of high-temperature superconductivity. Owing to their unusual multi-orbital band structure 4-5 , magnetism 6 , and electron correlation 7 , theories propose a unique signreversed s-wave pairing state, with the order parameter changing sign between the electron and hole Fermi pockets 8-14 . However, because of the complex Fermi surface topology and material related issues, the predicted sign reversal remains unconfirmed. Here we report a novel phase-sensitive technique for probing unconventional pairing symmetry in the polycrystalline iron-pnictides. Through the observation of both integer and half-integer flux-quantum transitions in composite niobium/iron-pnictide loops, we provide the first phase-sensitive evidence of the sign change of the order parameter in NdFeAsO 0.88 F 0.12 , lending strong support for microscopic models predicting unconventional s-wave pairing symmetry 9-14 . These findings have important implications on the mechanism of pnictide superconductivity, and lay the groundwork for future studies of new physics arising from the exotic order in the FeAs-based superconductors.