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Fermi surface models of high-temperature, unconventional, superconducting UPt 3

Fermi surface models of high-temperature, unconventional, superconducting UPt 3. Kathryn L. Krycka University of Massachusetts Amherst University of Florida Summer 2000 REU Advisor: Dr. P.J. Hirschfeld Presented: August 1, 2000. Outline. 1. Basics of Superconductors

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Fermi surface models of high-temperature, unconventional, superconducting UPt 3

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  1. Fermi surface models of high-temperature, unconventional, superconducting UPt3 Kathryn L. Krycka University of Massachusetts Amherst University of Florida Summer 2000 REU Advisor: Dr. P.J. Hirschfeld Presented: August 1, 2000

  2. Outline 1. Basics of Superconductors 2. Specifics of UPt3 3. Experimental Set-up 4. Local Theory predictions 5. Comparison of Experiment and Theory 6. Computer Programming 7. Significance of Findings and Future Work 8. Acknowledgments

  3. 1. Superconductors in a Nutshell • No resistance to current flow • Cooper pairing of electrons • Tc, the gap, and Fermi surfaces (FS) • Exclusion of magnetic fields -- Meissner Effect • Penetration Depth () and Coherence Length () • o =  o  o • Local vs. Non-local Effects Purpose : Study  (T, FS) => Gap Function

  4. Figure I. Fermi Surfaces(Gap functions plus sphere of radius 0.3) C E1 g 2Sin()Cos()  2 E2 u (27/4) Sin()2Cos()  2

  5. 2. UPt3 -- Hexagonal Symmetry, etc.

  6. 3. Experimental Materials (4 x 0.5 x 0.5 mm3 ) C B B 2 2 1 1 J J C SAMPLE A SAMPLE B Schuberth & Schottl (Phys. Review Lett, March 1999)

  7. Orientation Effects on Temperature-dependent  J parallel to C J perpendicular to C Line T Line T3 T4 Pt. node T2 Pt. node Quad node T T3 Quad node

  8. 4. Example: Applying E1g to Sample B B Face 1 ( J  C ) Face 2 ( J  C ) J Line, T Line, T 3 2 Lin Pt, T 4 Lin Pt, T 2 1 T T 2 => T C Local theory: Samples A and B, E1 g and E2 uT

  9. 5. Experimental Results

  10. 5.Possible Explanation: • Quadratic effects due to to impurity in SC? • RRR values of Samples A and B = 892, 970 • Another Possibility: Non-local Effects!!! • Need quantitative results • Non analytical solutions -- write computer program

  11. 6. The Computer Program If   0 (non-local), then non-analytical solutions!!!   (q2 + 1) q = 0 Floating point numbers Singularities Zeros in denominator Integrals go to +  Adaptive Rtn. =>  points If statements Segment Complex #’s Adaptive routines VMID

  12. 6. TESTING ( Local ) /o vs. T E1g, J l C E1g, J ll C /o vs. T

  13. 7. Importance of Results If non-local matches experiment: Should be able to distinguish between gap functions Show non-local effects are important Have program that will calculate the effects of non-locality Future works Hope to finish in August / September Co-author with Dr. Hirschfeld If interested please e-mail me at KKrycka@aol.com

  14. 8. Acknowledgments I would like to thank the following for their help: National Science Foundation University of Florida Advisor Dr.P.J. Hirschfeld Dr.K.Ingersent and Dr.B.Atkinson Dr.B.Coldwell for the use of VMID (a real life-saver!) Stephanie, Sasha, June, and Rob for accompanying me to the lab in the middle of the night when I was crazy enough to want to do another run! Thank you all.

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