Fermi surface models of high-temperature,

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Fermi surface models of high-temperature, unconven
tional, superconducting UPt3
Kathryn L. Krycka University of Massachusetts
Amherst University of Florida Summer 2000
REU Advisor Dr. P.J. Hirschfeld Presented
August 1, 2000
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(No Transcript)
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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
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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) gt Gap Function
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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?
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2. UPt3 -- Hexagonal Symmetry, etc.
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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)
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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
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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
gt T
C
Local theory Samples A and B, E1 g and E2
u T
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5. Experimental Results
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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

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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. gt ?
points
If statements Segment Complex s
Adaptive routines VMID
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6. TESTING ( Local )
?/?o vs. T
E1g, J l C
E1g, J ll C
?/?o vs. T
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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_at_aol.com
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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.