QED3 Phase DiagramQED3 Phase Diagram

Nernst Effect in HTSNernst Effect in HTS

BiSrCaCuO

Courtesy of N.P. Ong

Vortex fluctuations in the pseudogap state !!

Z. A. Xu et al., Nature 406, 486 (2000)

HTS are Nodal d-wave Superconductors (Phase sensitive exps., ARPES, FT-STS, etc.)

FT-STS measured

ARPES Mesot -PRL 83,840 (1999)

Courtesy of J.C. Davis

Tsuei &Kirtley, 1997

0.0 0.2 0.4 0.6 0.8 1.0 0.0

0.2

0.4

0.6

0.8

1.0

F ig . 4

a

k ax ( / )

ka

y (

/)

FT-STS from Davis’ group, Nature 422, 520 (2003).

““Electron Crystal” in Underdoped Cuprates Electron Crystal” in Underdoped Cuprates M. Vershinin et al., Science M. Vershinin et al., Science 303303, 1995 (2004); , 1995 (2004);

T. Hanaguri, C. Lupien et al., Nature T. Hanaguri, C. Lupien et al., Nature 430430, 1001 (2004), 1001 (2004)

Courtesy of J.C. Davis

Underdoped Ca2-xNaxCuO2Cl2

x=0.08 (I), 0.10 (SC), 0.12 (SC)

Vershinin et al. Science 303, 1995 (2004)

35 pS

150 pS500Å x 200 Å

Cu-O

0

0.05

0.1

0.15

0.2

0.25

0.3

-120 -80 -40 0 40 80 120

Voltage [meV]

100K

Pseudogap State

Modulation along the Cu-O bond direction

K-Space

Courtesy of A. Yazdani

Hofstadter Butterfly and Cooper Pair Density Wave in Hofstadter Butterfly and Cooper Pair Density Wave in HTS HTS

Hofstadter “Butterfly” Spectrum

“Electron Crystal” in HTS(Vershinin, et al., Hanaguri, Lupien, et al.)

Dual theory supplies the connectionbetween two phenomena. It leads to Hofstadter “magic fractions” f = p/qfor Cooper pair CDW at special x:

f = p/q = (1-x)/2f = p/q = (1-x)/2 !!