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Probing Superconductors using Point Contact Andreev Reflection Pratap Raychaudhuri Tata Institute of Fundamental Research Mumbai Collaborators: Gap anisotropy in YNi 2 B 2 C G. Sheet, S. Mukhopadhyay, D. Jaiswal, S. Ramakrishnan, H. Takeya (Japan) Phys. Rev. Lett. 93, 156802 (2004). Nanostructured Nb S. Bose, P. Vasa, P. Ayyub, R. Bannerjee (Ohio)

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Free path: the electron accelerates V Scattering Centre (elementary excitation, defects): the electron loses energy K.E imparted to the electron= Mean free path Sample size eV Lattice a<

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Spectroscopy using Point Contact Electron phonon interaction (Au foil/ Au tip) Superconducting energy gap Superconductor Normal Metal

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Normal Reflection Andreev reflection Fitting parameters: superconducting gap Z-barrier height parameter -broadening parameter N(E) E(meV) BCS density of states

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Superconducting Energy Gap Angle resolved probe capable of probing different k directions on the Fermi surface Fitting parameters: superconducting gap Z-barrier height parameter -broadening parameter

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Superconducting gap anisotropy in YNi 2 B 2 C Discovered in TIFR in 1994 T c ~14.6K Type II Supserconductor: BCS Superconductor with conventional electron phonon coupling Unusual Vortex Symmetries evolving with temperature Thermal Conductivity Izawa et al., PRL 89, 137006 (2002) Specific Heat Park et al., PRL 92, 237002 (2004) Angular variation in magnetic field

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Unusual gap function symmetry s+g (mixed angular momentum symmetry) K Maki, P Thalmeier and others Purely Geometrical with no microscopic origin

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k of YNi 2 B 2 C S-wave superconductivity s+g symmetry of the order parameter Multiband superconductivty???

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Crystal used for this study Very low defect density

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Gap anisotropy I||c / I||a ~ 7 at 1.75 K

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Temperature dependence

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Two Band Superconductor Suhl et al, PRL 3, 552 (1959) No Interband scattering Weak Interband Scattering TcTc Temperature dependent s+g Yuan and Thalmeier PRB 68, 174501 (2003)

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Magnetic field dependence

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Zero bias density of States

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Comparison with theoretical predictions for a two band superconductor Zero bias density of states Superconducting energy gap Koshelev & Golubov, PRL 90,177002 (2003)

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Two band superconductivity in MgB 2 Gonnelli et al., PRL 89, 247004 (2002).

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Band Structure of YNi 2 B 2 C 3 bands crossing the FS produce 5 FS sheets Cylindrical FS Square FS Ellipsoidal FS I||a I||c Mostly fast electrons:responsible for small gap Mostly slow electrons: responsible for large gap Encloses only 0.3% of the Fermi surface volume. Not important in PC expt.

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Epilogue What is special about MgB 2 (or YNi 2 B 2 C)? The clear demonstration of multiband superconductivity in MgB 2 calls for a closer look at all the known superconductors. Under what limiting condition will a multiband superconductor behave like a single band superconductor? Interband scattering

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Size effect in nanoscale superconductors Complete destruction of superconductivity Open Questions How does the superconducting properties evolve at small sizes? In Al, Sn, T c gets enhanced by a factor of 2 before destruction of superconductivity In Pb, Nb T c decreases monotonically Softening of the (surface) Phonon modes vs. quantum size effect? Softening of Phonon Modes increased electron phonon coupling Quantum size effect N(0) will decrease 2 /k B T c

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Evolution of Superconducting properties in nanostructured Nb Mechanism of destruction of T c Magnetization Resistivity

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Nature of the grain boundary Weakly coupled Josephson Junction

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Evolution of Energy Gap with Particle size 45nm 15nm 10nm 8nm Remains in the weak coupling limit down to the lowest size

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Temperature variation of

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Summary In Nb, T c decreases monotonically with decreasing particle size. 2 /k B T c remains constant down to the Anderson limit. The suppression of T c in nanocrystalline Nb is possibly governed by quantum size effects rather than phonon softening.

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YNi 2 B 2 C: Superconducting properties Critical fields T c ~14.6K Type II Supserconductor: Coherence length: BCS Superconductor with conventional electron phonon coupling Tuson Park et al. PRL92, 237002(2004) Specific heat C H 1/2 Thermal Conductivity Izawa et al., PRL 89, 137006 (2002) Specific Heat Park et al., PRL 92, 237002 (2004) Angular variation in magnetic field Unusual Vortex Symmetries evolving with temperature

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