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
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
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
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
2. UPt3 -- Hexagonal Symmetry, etc.
3. Experimental Materials (4 x 0.5 x 0.5 mm3 )
C
B
1
B
2
1
J
J
SAMPLE A
2
C
SAMPLE B
Schuberth & Schottl (Phys. Review Lett, March 1999)
Orientation Effects on
Temperature-dependent 
J parallel to C
J perpendicular to C
Line
T3
Line
T
Pt. node
T4
Pt. node
T2
Quad node
T
Quad node
T3
4. Example: Applying E1g to Sample B
B
J
2
1
Face 1
Face 2
(JC)
( J  C )
Line, T
Line, T 3
Lin Pt, T 4
Lin Pt, T 2
T
T2
=> T
C
Local theory: Samples A and B, E1 g and E2 u
T
5. Experimental Results
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
6. The Computer Program
If   0 (non-local), then non-analytical solutions!!!


stuff 


2
  
w0
1
w/T
e
0  0
2p
sin( ) 2

 REAL{
}]
 1 2 
(2p   2  w2 ) w2  2p
(q2 + 1)
q=0
Floating point numbers
If statements
Singularities
Segment
Zeros in denominator
Complex #’s
Integrals go to + 
Adaptive routines
Adaptive Rtn. =>  points
VMID
6. TESTING ( Local )
/o vs.
T
E1g, J ll C
/o vs.
T
E1g, J l C
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
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.