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

3. 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

4. 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

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

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

7. 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)

8. 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

9. 4. Example: Applying E1g to Sample 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 u T

10. 5. Experimental Results

11. 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

12. 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

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

14. 7. Importance of Results Future works 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 me at

15. 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.