Transcript Electron Crystal” in Underdoped Cuprates T. Hanaguri, C

QED3 Phase Diagram
Nernst Effect in HTS
Courtesy of N.P. Ong
Vortex fluctuations in the
pseudogap state !!
BiSrCaCuO
Z. A. Xu et al., Nature 406, 486 (2000)
HTS are Nodal d-wave Superconductors
(Phase sensitive exps., ARPES, FT-STS, etc.)
Tsuei &
Kirtley, 1997
FT-STS measured D
a
1.0
ky ( /a)
0.8
0.6
ARPES D(q), Mesot -PRL 83,840 (1999)
0.4
0.2
0.0
FT-STS from
0.0
0.2
Davis’ group,
Nature 422, 520 (2003).
0.4
0.6
kx ( /a)
0.8
1.0
Courtesy of J.C. Davis
“Electron Crystal” in Underdoped Cuprates
M. Vershinin et al., Science 303, 1995 (2004);
T. Hanaguri, C. Lupien et al., Nature 430, 1001 (2004)
Underdoped Ca2-xNaxCuO2Cl2
x=0.08 (I), 0.10 (SC), 0.12 (SC)
Courtesy of J.C. Davis
Courtesy of A. Yazdani
Pseudogap State
K-Space
100K
Modulation along
the Cu-O bond
direction
500Å x 200 Å
150 pS
Cu-O
35 pS
Vershinin et al. Science 303, 1995 (2004)
Hofstadter Butterfly and Cooper Pair Density Wave in HTS
“Electron Crystal” in HTS
(Vershinin, et al.,
Hanaguri, Lupien, et al.)
Hofstadter “Butterfly” Spectrum
Dual theory supplies the connection
between two phenomena. It leads to
Hofstadter “magic fractions” f = p/q
for Cooper pair CDW at special x:
f = p/q = (1-x)/2 !!