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PAIRING SYMMETRY IN THE CUPRATES
One of the most controversial topics in the field of superconductivity
in the last decade has been the symmetry of the Cooper pairing in the
high critical temperature cuprate superconductors. Some of the possibilities
are shown here as polar plots.
J.R. Kirtley and C.C. Tsuei, "Probing High-Temperature Superconductivity",
Scientific American, August, 1996, p. 68
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We determined the symmetry of the pairing in a number of cuprate superconductors by epitaxially growing them as thin films on specially designed tricrystal substrates of SrTiO3 . In this geometry, any closed ring of superconducting material around the central point is "frustrated" for a d-wave superconductor, and spontaneously generates magnetic fields with half of the conventional total superconducting flux quantum at the center (tricrystal) point. This is the half-integer flux quantum effect.
C.C. Tsuei, J.R. Kirtley, C.C. Chi, Lock See Yu-Jahnes, A. Gupta,
T. Shaw, J.Z. Sun, and M.B. Ketchen, "Pairing Symmetry and Flux
Quantization in a Tricrystal Superconducting Ring of YBa2
Cu3O7-d",
Phys. Rev. Lett. 73,593(1994).
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The magnetic fields in these samples were imaged with a scanning Superconducting Quantum Interference Device (SQUID) microscope.
J.R. Kirtley, M.B. Ketchen, K.G. Stawiasz, J.Z. Sun, W.J. Gallagher,
S.H. Blanton, and S.J. Wind,"High-resolution integrated scanning SQUID
Microscope", Appl. Phys. Lett. 66 ,1138(1995).
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This microscope is very good for imaging superconducting vortices. In this
figure a sensor with 3 SQUIDs, to detect all 3 components of the magnetic
field, images a single vortex.
M.B. Ketchen, J.R. Kirtley, and M. Bhushan,
" Miniature Vector Magnetometer
for Scanning SQUID Microscopy", IEEE Trans. Appl. Supercond.7 ,
3139(1997).
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This is a scanning SQUID microscope image of a tricrystal sample of the high temperature superconductor YBCO. The central ring has exactly half of the superconducting flux quantum trapped in it; the outer three control rings have no flux. This is as expected for a d-wave superconductor in this geometry.
C.C. Tsuei, J.R. Kirtley, C.C. Chi, Lock See Yu-Jahnes, A. Gupta,
T. Shaw, J.Z. Sun, and M.B. Ketchen, "Pairing Symmetry and Flux
Quantization in a Tricrystal Superconducting Ring of YBa2
Cu3O7-d",
Phys. Rev. Lett. 73,593(1994).
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This is a 3-dimensional rendering of a scanning SQUID microscope image of
the tricrystal sample, cooled in nominally zero field.
J.R. Kirtley, C.C. Tsuei, J.Z. Sun, C.C. Chi, Lock See Yu-Jahnes,
A. Gupta, M. Rupp, and M.B. Ketchen, "Symmetry of the order parameter
in the high-Tc superconductor
YBa2Cu3O7-d",
Nature 373,225(1995).
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The spontaneous generatiion of flux at the tricrystal point occurs
independent of the how the high-Tc film is patterned. This is an image
of an unpatterned YBCO film on a tricrystal substrate. There are 7
conventional Abrikosov vortices in the grains, 4 conventional Josephson
vortices in the grain boundaries, and a half-quantum Josephson vortex
at the tricrystal point.
J.R. Kirtley, C.C. Tsuei, Martin Rupp, J.Z. Sun,
Lock See Yu-Jahnes, A.
Gupta, M.B. Ketchen, K.A. Moler, and M. Bhushan, "Direct imaging of integer
and half-integer Josephson vortices in high-Tc grain boundaries",
Phys. Rev. Lett. 76,1336(1996).
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The half-flux quantum effect occurs for all of the high-Tc superconductors
that have sufficiently high supercurrents across the grain boundaries.
This is an image of a BSCCO tricrystal sample. The central vortex has exactly
half as much flux in it as the others.
J.R. Kirtley, C.C. Tsuei, H. Raffy,
Z.Z. Li, A. Gupta, J.Z. Sun, and S. Megert,
"Half-integer flux quantum effect in tricrystal Bi2Sr2Ca
Cu2O8+d", Europhys. Lett. 36,707(1996).
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In a highly symmetric cuprate such as Tl2Ba2CuO6+d (Tl-2201) the pairing must be either s-wave or d-wave. We determined that Tl-2201 is pure d-wave by observing the half-flux quantum in this cuprate epitaxially grown on a special SrTiO3 "tetracrystal".
C.C. Tsuei, J.R. Kirtley, Z.F. Ren, J.H. Wang, H. Raffy, and Z.Z. Li, "Li., "Pure dx2- y2 order parameter symmetry in the tetragonal
superconductor Tl2Ba2CuO6 +d ", Nature 387,481 (1997).
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These are SQUID microscope images of the half-magnetic flux quantum in a tricrystal sample of YBCO at selected temperatures. Above Tc there is no magnetization in the sample. As the sample temperature is lowered through Tc, the half-vortex grows in amplitude and becomes narrower. It persists at all temperatures, with exactly half of the conventional superconducting quantum of flux, from 0.5K through Tc. This implies that d-wave superconductivity dominates, with very little (if any) imaginary component, at all temperatures.
J.R. Kirtley, C.C. Tsuei, and K.A. Moler, "Temperature Dependence of
The Half-Integer Magnetic Flux quantum ",
Science 285, 1373(1999).
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The cuprate superconductors are composed of planes of CuO2's separated by charge reservoirs. The planes can be either doped with holes or electrons. We have shown that both have predominantly d-wave pairing symmetry. This is an image of the half-magnetic flux quantum in a tricrystal sample of the electron-doped cuprate Nd2-xCexCuO4-y.
C.C. Tsuei and J.R. Kirtley "Phase-sensitive Evidence for d-wave Pairing Symmetry in Electron-doped Cuprate Superconductors", cond-mat/ 0002341.
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