QCP for stripe order : An organizing principle of cuprates
Louis Taillefer
University of Sherbrooke
Canadian Institute for Advanced Research
Doiron-Leyraud & Taillefer, arXiv:1204.0490
Taillefer, Annual Review of CMP 1, 51 (2010)
arXiv:1003.2972
Collaborators
Measurements
Samples
Sherbrooke
N. Doiron-Leyraud
J. Chang, R. Daou, E. Hassinger, F. Tafti
O. Cyr-Choinière, S. Dufour-Beauséjour, G. Grissonnanche,
F. Laliberté, D. LeBoeuf, S. René de Cotret
Grenoble
K. Behnia, L. Malone, I. Sheikin
Toulouse
C. Proust, B. Vignolle
Tallahassee
L. Balicas, J. Y. Jo, J.-H. Park
YBCO
UBC
D. Bonn, W. Hardy, R. Liang, B. Ramshaw
Eu-LSCO Tokyo
S. Pyon, H. Takagi, T. Takayama, Y. Tanaka
Nd-LSCO Texas
J.-G. Cheng, J. B. Goodenough, J.-Q. Yan, J.-S. Zhou
Hg-1201 Minneapolis N. Barisic, M. Greven
Cuprate superconductors
Questions
•
Pairing ?
•
Tc dome ?
•
Linear-T resistivity ?
•
Quantum critical point ?
•
Pseudogap phase ?
Taillefer, Annual Review of CMP 1, 51 (2010) – arXiv:1003.2972
Organizing principle
Quantum critical point for SDW order
Features
• Quantum critical point (QCP)
• Spin-density-wave (SDW) order
• Fermi-surface reconstruction (FSR)
• Linear-T resistivity (A)
• Superconductivity – Tc dome
• A ~ Tc
Doiron-Leyraud & Taillefer, arXiv:1204.0490
The Archetype
(TMTSF)2PF6
Organic superconductor
Doiron-Leyraud et al., PRB 80, 214531 (2009)
Annu. Rev. Condens. Matter Phys. 2010.1:51-7
by UNIVERSITE DE SHERBROOK
Resistivity in cuprates, organics, and pnic
endsat thecritical pressurePc. (b) Temperature-dopingphasediagramof theiron-pnictidesupercondu
tor Ba(Fe1–xCox)2As2, as a function of nominal Co concentration x, showing a metallic SDW phas
below TSDW and superconductivity below a Tc that ends at the critical doping xc (33). In both panel
thevertical dashed line separates a regime in which the resistivity r (T) grows as
T2 (on
2
6 the right-han
2
side) fromaregimeinwhichit growsasT þ T (ontheleft-hand side). FigureadaptedfromReference31
The Archetype
(TMTSF) PF
Nd-LSCO
∆ρ(µΩ cm)
100
p = 0.20
11.8 kbar
T
p = 0.24
T2
p = 0.33
10
100
0.1
0.1
T (K)
Figure6
100
10
1
1
QCP for SDW order
8.4 kbar
10
10
1
Ba(Fe1 – xCox
(TMTSF)2PF6
Questions
x = 0.05
x= 0
T
1
T
T2
20.8 kbar
T2
1
10
0.1
10
T (K)
Answers
•
Temperature-dependent part of the in-plane normal-state resistivity of materials in three families of
Louis Taillefer, Annual Review of Condensed Matter Physics 1, 51 (2010)
(T) –r (QCP)
ter werechosen: below,
0 versusTonalog-logscale. Threevaluesof therelevant
Quantum criticalrpoint
• tuningparame
AF spin fluctuations
• Pairing ?
quantum critical points(QCPs). (Left panel) Data on hole-doped cupratesLa1.6–xNd0.4SrxCuO4 (NdSpin-density-wave
(SDW)
order
• aholedopingp
Phase competition
• 4 (LS
Tc CO)
dome
?
0.24
(21) andLa
at p¼0.33(17).
TheQCPat
0.24markstheen
2–xSrxCuO
in Nd-LSCO (21,
28). Figure adapted from Reference36. (Middle
pane
l) Data on
the organic Bechg
Fermi-surface reconstruction
(FSR)
• SF
+ Pairing
correlations
• Linear-T resistivity ?
QCPat aBoston,
pressureP
kbar markstheend of thespin-density-wave(SDW) phase. Figureadapte
March 10
1, 2012
Linear-T resistivity
(A)
• aCo
SDW
order
• Quantum
?
pane
l) Dataon thepnictideBa(Fe
As2 (33).point
TheQCPat
conce
ntration x
0.10 marksth
1–xCox)2critical
•
Tc dome
•
•
•
•
A ~ Tc
•
Pseudogap phase ?
www.annualreviews.org
Scattering and Pairing in CuprateSuperconducto
QCP principle : examples
Organic superconductors
(TMTSF)2X
X = PF6 , ClO4
Electron-doped cuprates
PCCO & LCCO
Iron-based superconductors
Co-BaFe2As2 & P-BaFe2As2
Hole-doped cuprate
Nd-LSCO
Electron-doped cuprates
PCCO & LCCO
Hall
QCP for SDW order
•
Quantum critical point (QCP)
•
Spin-density-wave (SDW) order
•
Fermi-surface reconstruction (FSR)
•
Linear-T resistivity (A)
•
Tc dome
•
A ~ Tc
Dagan et al., PRL 2004
Jin et al., Nature 2011
pressurePc. (b) Temperature-dopingphasediagramof theiron-pnictidesuperconducAs2, as a function of nominal Co concentration x, showing a metallic SDW phase
uperconductivity below a Tc that ends at the critical doping xc (33). In both panels,
d line separates a regime in which theresistivity r (T) grows as T2 (on the right-hand
einwhichit growsasT þ T2 (ontheleft-handside). FigureadaptedfromReference31.
Iron-based superconductors
Nd-LSCO
Ba(Fe1 – xCox)2As2
(TMTSF)2PF6
p = 0.20
8.4 kbar
10
100
11.8 kbar
10
1
T
p = 0.24
T2
10
p = 0.33
100
0.1
0.1
T (K)
x = 0.05
T
x = 0.10
1
T
T2
20.8 kbar
T2
BaFe2As2
1
T (K)
10
0.1
x = 0.30
10
100
T (K)
QCP for SDW order
• part
Quantum
critical point
(QCP)
ndent
of the in-plane
normal-s
tate resistivity of materials in three families of superconductors, plotted as
ouis Taillefer, Annual Review of Condensed Matter Physics 1, 51 (2010)
onalog-logs
cale. Threevalue
sof there
levant tuningparameter werechosen: below, at, andabovetheir respective
• Spin-density-wave
(SDW)
order
oints(QCPs). (Left panel) Data on hole-doped cupratesLa1.6–xNd0.4SrxCuO4 (Nd-LSCO) at p ¼0.20 and p ¼
• Fermi-surface reconstruction (FSR)
0.24markstheendof thestripe-orderedphase
xSrxCuO4 (LSCO) at p¼0.33(17). TheQCPat aholedopingp
28).• Figure
adapte
d from Re
ference36. (Middle panel) Data on the organic Bechgaard salt (TMTSF)2PF6. The
Linear-T
resistivity
(A)
P • 10
kbar
March
1,
Tc2012
domemarkstheend of thespin-density-wave(SDW) phase. Figureadapted from Reference31. (Right
epnictideBa(Fe1–xCox)2As2 (33). TheQCPat aCo concentration x
0.10 markstheend of theSDW phase.
•
A ~ Tc
www.annualreviews.org
Doiron-Leyraud et al., PRB 80, 214531 (2009)
Scattering and Pairing in CuprateSuperconductors 57
ndIron-based
spin fluctuations
superconductorsin P-Ba122
BaFe2As2
105, 107003 (2010)
P-doped BaFe2As2
PHY SI CA L REV I EW L ET TERS
3 SEPTEMBER 2010
week ending
Curie-Weiss law
a
a
1
b
(
s
)
1
a
(
s
K
)
on doping. Large changes in FS
sevia
charge-carrier
we
k ending
ERS
3
S
EP
TEMBER
2010
g thus necessarily involve dramatic modifica
tion in
ðEFÞand Fermi-surface nesting resulting in changes
n fluctuations. In a
ddition to possible cha
nges in Tc
2
0
0
.2
o the modification of spin excitation spectrum [6],
c changes in NðEFÞcan also affect severely Tc [25],
1
0may lead
hesuggested giant 0
m
agnetoelastic coupling
.1
her suppressions of Tc [26]. Therefore, thedecrease
ðEFÞas well as the suppression of spin fluctuations
0
.0
0
0
.2
0
.4
0
.6
d betaken into account
for theinte
rpre
tation
of posP
c
o
n
c
e
n
tr
a
tio
n
x
change
sinfor
Tc for
electron-dope
QCP
SDW
order d BaðFe1 yCoyÞ2As2.
ntrast, the nearly unperturbed Kspin by isovalent P
• mons
Quantum
critical
point
g de
trates tha
t BaFe
2ðAs1(QCP)
xPxÞ
2 is an ideal
sys
to test the relevance
of spin
fluctuations to
•tem
Spin-density-wave
(SDW)
order
conductivity.
• ntFermi-surface
nifica
low-energy AFreconstruction
fluctuations are(FSR)
probed near
1
1
maxim
Tc viaresistivity
T1 . ðT1TÞ
• um
Linear-T
(A) is described by the
vector averageof theimaginary part ofPthedynamiTc dome
00
usce•ptibility
ðq;! 0Þ, i.e., ðT1TÞ 1 / qjAðqÞj 2
•=! 0A whe
~ Tcre AðqÞrepresents the hyperfine cou! 0Þ
between 31Pnucle
ar spinsand thesurrounding elecine). The 31P nuclear spin-lattice relaxation
A
F
S
C
b
T
S
q
T
N
A
F
S
C
Nakai et al., PRB 2010
T
C
50
Iron-based superconductors
BaFe2As2
0
2
4
6
8
Tc
10
Cobalt doping x ( % )
0.8
TN
Pseudogap phase
•
Onset above TN
•
Nematic character
FSR
•
Upturn in Co-Ba122
•
Downturn in K-Ba122
QCP for SDW order
•
Quantum critical point (QCP)
•
Spin-density-wave (SDW) order
•
Fermi-surface reconstruction (FSR)
•
Linear-T resistivity (A)
•
Tc dome
•
A ~ Tc
r ( mW cm )
0.6
T*
rb
ra
0.4
0.2
0.0
x = 4.5 %
x = 8.5 %
rb
0
100
200
T(K)
Chu et al., Science 2010
300
Iron-based superconductors
Pseudogap phase
•
Onset above TN
•
Nematic character
FSR
•
Upturn in Co-Ba122
•
Downturn in K-Ba122
QCP for SDW order
•
Quantum critical point (QCP)
•
Spin-density-wave (SDW) order
•
Fermi-surface reconstruction (FSR)
•
Linear-T resistivity (A)
•
Tc dome
•
A ~ Tc
BaFe2As2
Iron-based superconductors
QCP principle
QCP for spin-stripe order
•
Quantum critical point
•
Stripe order
•
Fermi-surface reconstruction
•
Linear-T resistivity
•
Tc dome
•
A ~ Tc
+ Precursor nematic regime
T*
T(K)
200
Hole-doped cuprate
TN
Nd-LSCO
100
TCO
0.1
Eu
/Nd -LSCO
YBCO
200
TN
0.20
T*
Tc
0
0.0
300
300
Nd-LSCO
200
200
TCO
100
0.24
T*
TH
TT((KK))
r ( mW cm )
NQR
X-rays
T*
Pseudogap
Pseudogap
Nernst
Nernst
Resistivity
Resistivity
CDW order
CDW order
NQR
NMR
X-rays
TCO
TSDW
T
CO
0
0
50
100
150
0
0
0.0
0.0
300
Eu /Nd -LSCO
0.2
0.0
Quantum critical point
•
Stripe order
•
Fermi-surface reconstruction
•
Linear-T resistivity
•
Tc dome
•
A ~ Tc
-0.2
200
0.16
T(K)
•
Pseudogap phase
•-0.4 Onset above0.20
TCO
0.24
0
50
100
150
0.2
0.2
0.3
0.3
Resistivity
CDW order
NMR
TH
SDW order
Neutrons
mSR
100
Tn
-0.6
Tc
Tc
Hole doping, pPseudogap
Nernst
T*
TN
2
n / T ( nV / K T )
QCP for stripe order
0.1
0.1
YBCO
0.125
0.3
SDW order
Neutrons
mSR
TN
100
100
0.2
TSDW T
CO
Tc
200
T(K)
0
0.0
0.1
0.2
Hole doping, p
Daou et al., Nature Physics 2009
0.3
mperature-pressure phase diagram of (TMTSF)2PF6, showing a spin-density-wave (SDW) phase
TSDW (orange dots) and superconductivity (SC) below Tc (blue dots) (24, 31). The latter phase
thecritical pressurePc. (b) Temperature-dopingphasediagramof theiron-pnictidesuperconducFe1–xCox)2As2, as a function of nominal Co concentration x, showing a metallic SDW phase
TSDW and superconductivity below a Tc that ends at the critical doping xc (33). In both panels,
ical dashed line separates a regime in which theresistivity r (T) grows as T2 (on the right-hand
omaregimeinwhichit growsasT þ T2 (ontheleft-handside). FigureadaptedfromReference31.
Resistivity
in
cuprates,
organics,
and
pnictides
QCP principle
CUPRATE
ORGANIC
Nd-LSCO
∆ρ(µΩ cm)
100
p = 0.20
8.4 kbar
10
100
11.8 kbar
10
1
T
1
Ba(Fe1 – xCox)2As2
(TMTSF)2PF6
10
1
PNICTIDE
p = 0.24
T2
10
T (K)
p = 0.33
100
0.1
0.1
x = 0.05
T
x = 0.10
1
T
T2
20.8 kbar
T2
1
T (K)
10
0.1
x = 0.30
10
100
T (K)
6
ature-dependent part of the in-plane normal-state resistivity of materials in three families of superconductors, plotte
Louis Taillefer, Annual Review of Condensed Matter Physics 1, 51 (2010)
0 versusTonalog-logscale. Threevaluesof therelevant tuningparameter werechosen: below, at, andabovetheir respec
m critical points(QCPs). (Left panel) Data on hole-doped cupratesLa1.6–xNd0.4SrxCuO4 (Nd-LSCO) at p ¼0.20 and
1) andLa2–xSrxCuO4 (LSCO) at p¼0.33(17). TheQCPat aholedopingp 0.24markstheendof thestripe-orderedph
LSCO (21, 28). Figure adapted from Reference36. (Middle panel) Data on the organic Bechgaard salt (TMTSF)2PF6.
Taillefer,nd
Annual
Review
of ns
CMP
1, 51 (2010)
–phas
arXiv:1003.2972
aBoston,
pressureP
10
kbar
marksthee
of
thes
pin-de
ity-wave(S
DW)
e. Figureadapted from Reference31. (R
March 1, 2012
Dataon thepnictideBa(Fe1–xCox)2As2 (33). TheQCPat aCo concentration x
0.10 markstheend of theSDW phase.
Hole-doped cuprates
Pnictides
QCP principle
QCP for spin-stripe order
•
Quantum critical point
•
Spin-stripe order
•
Fermi-surface reconstruction
•
Precursor nematic regime
•
Linear-T resistivity
•
A ~ Tc
•
Tc dome
Hole-doped cuprates
QCP principle
QCP for stripe order
•
Quantum critical point
•
Stripe order
•
Fermi-surface reconstruction
•
Precursor nematic regime
•
Linear-T resistivity
•
A ~ Tc
•
Tc dome
Hole-doped cuprates
Quantum oscillations
QCP & FSR
Hall & Seebeck coefficients
Toulouse
Toulouse
Tallahassee
Grenoble
Doiron-Leyraud et al., Nature 2007
•
UD: small electron pocket
LeBoeuf et al., Nature 2007
Laliberté et al., Nature Comm. 2011
Hole-doped cuprates
QCP & FSR
Hall & Seebeck coefficients
Toulouse
Tallahassee
•
UD: small electron pocket
•
OD: large hole pocket
•
QCP in between
LeBoeuf et al., Nature 2007
Grenoble
Laliberté et al., Nature Comm. 2011
Hole-doped cuprates
QCP principle
QCP for stripe order
•
Quantum critical point
•
Stripe order
•
Fermi-surface reconstruction
•
Precursor nematic regime
•
Linear-T resistivity
•
A ~ Tc
•
Tc dome
Hole-doped cuprates
Stripe order
YBCO
Seebeck coefficient
Eu-LSCO
YBCO
p = 0.125
TCO
0.4
-0.5
-2
S / T ( mV K )
-2
0.8
0.0
p = 0.12
TCO
0.2
0.0
0.0
-0.3
-0.2
0.0
-1.0
Eu-LSCO
-0.6
p = 0.11
1.2
0.4
-0.5
0.3
-2
-2
TCO
p = 0.11
TCO
0.2
0.0
0.1
-0.5
NMR splitting
X-ray intensity
0.8
0.0
0.5
S / T ( mV K )
0.5
S / T ( mV K )
NMR asymmetry
X-ray intensity
S / T ( mV K )
0.3
1.2
0.5
0.0
0.0
-1.0
0
50
100
150
T(K)
-1.0
0
50
100
150
T(K)
X-ray: Fink et al., PRB 2011
NMR: Wu et al., Nature 2011
Stripe order is universal in hole-doped cuprates
Doiron-Leyraud & Taillefer, arXiv:1204.0490
Laliberté et al., Nature Comm. 2, 432 (2011)
Hole-doped cuprates
QCP principle
QCP for stripe order
•
Quantum critical point
•
Stripe order
•
Fermi-surface reconstruction
•
Precursor nematic regime
•
Linear-T resistivity
•
A ~ Tc
•
Tc dome
Hole-doped cuprates
Pseudogap phase
T* from resistivity
300
Pseudogap
Nernst
Resistivity
Eu /Nd -LSCO
CDW order
NQR
X-rays
T*
T(K)
200
TN
100
TCO
Tc
0
0.0
0.1
0.2
0.3
300
YBCO
T*
TN
T(K)
200
Pseudogap
Nernst
Resistivity
CDW order
NMR
TH
SDW order
Neutrons
mSR
100
0
0.0
TSDW T
CO
0.1
Tc
0.2
0.3
Hole doping, p
Doiron-Leyraud & Taillefer, arXiv:1204.0490
T(K
Hole-doped cuprates
TN
Pseudogap phase
100
TCO
Tc
0
0.0
Nernst coefficient
0.1
0.2
0.3
300
YBCO
0.1
(n a - n b) / T ( nV / K T )
2
TH
3
RH ( mm / C )
T*
0
0.0
200
-4
-0.1
0
50
100
150
200
250
T(K)
CDW order
NMR
TH
SDW order
Neutrons
mSR
100
2
-2
T*
TN
T(K)
4 YBCO p = 0.12
Pseudogap
Nernst
Resistivity
0
0.0
TSDW T
CO
0.1
Tc
0.2
0.3
Hole doping, p
Pseudogap phase = Nematic regime
Daou et al., Nature 463, 519 (2010)
LeBoeuf et al., PRB 83, 054056 (2011)
Doiron-Leyraud & Taillefer, arXiv:1204.0490
Hole-doped cuprates
QCP principle
QCP for stripe order
•
Quantum critical point
•
Stripe order
•
Fermi-surface reconstruction
•
Precursor nematic regime
•
Linear-T resistivity
•
A ~ Tc
•
Tc dome
Hole-doped cuprates
Universality
of
linear-T
resistiv
Linear-T resistivity
a quantum critical point
Resistivity per CuO2 plane:
Resistivity
8/ NPHYS1109
5.0
50
SCO
p = 0.20
Nd-LSCO p = 0.24
p
H = 33 T
r ( kW )
r ( mW cm )
5.0
25
H=0
H = 15 T
Nd-LSCO
Tl-2201
2.5
2.5
LSCO
0.3
0
0
20
T(K)
, et Nd-LS
al., Nature
mof
CO Phys. 5, 31 (2009)
cles) andthe
(blue
–513 (1999)
observed
38
(2000)
(black
espectively
zero, (2) the
at high
o-field muon
y diffraction
otheeye.
ation. T⇤ is
40
0.0
0
100
200
T(K)
et al., arXiv:0905.0964v1
Linear-T resistivity is universalNDL
in hole-doped
cuprates
Boston, March 1, 2012
N. Doiron-Leyraud et al., arXiv:0905.0964
300
0.0
0
Hole-doped cuprates
QCP principle
QCP for stripe order
•
Quantum critical point
•
Stripe order
•
Fermi-surface reconstruction
•
Precursor nematic regime
•
Linear-T resistivity
•
A ~ Tc
•
Tc dome
30 K (14, 15). At slightly lower doping, r (T) becomes purely linear, with r (T) ¼r 0
msto
below 80 K or so, as found in La1.6–xNd0.4SrxCuO4 (Nd-LSCO) at p ¼ 0.24 (21
rmi-liquid
signatures LSCO at p ¼0.23 (22), both measured down to T 1 K in a magnetic field largeen
acoherent
to suppress superconductivity (see Figure 2). At still lower doping, the linearity of
ation
between
linear-T
resistivity
and, up
Tc to 300 K and above. To describe the broad evol
mi
surface
,
extends
to highe
r temperature
ann-Franz
of r (T) with doping, availableLSCO data (in zero field) (23) wererecently fit to the
2
deResistivity
penR. A. Cooper et al., Science
2
r
(T)
¼r
þ
AT
þ
BT
,
ove
r ate
mperatureinterval from200 to 400 K (24). Theresul
323,
603 (2009)
0
resistivity
Hole-doped cuprates
Linear-T resistivity
shown in Figure 3, where the
100 parameter A is plotted versus p; A is seen to extrapola
LS
C
O
xSrxCuO4
A ro at p ¼0.27 ¼p
ze
0 at thesamedoping asTc ! 0. Recent
Nd-LS
CO other words, A !
c. In
YBCO
field measurementson
overdoped LSCO show that thesamefit performed over an int
Tl-2201
SrxCuO4
from 1 to 200 K providesa good description of thelow-temperaturedata and leadst
12
samecorrelation between A and Tc (22). Data on Tl-2201 asp ! pc (16) yield A T
Tc
Figure
4). This remarkable
correlation between linear resistivity and Tc strongly sug
pc
that anomalous (non-Fermi-liquid) scattering and pairing have a common origin.
0
0
0.15 correlation is supporte
0.30
d
by
angle-dependent magneto-resistance studies of overd
p
Tl-2201 that yield an anisotropic linear-T scattering rate that peaks in the same dire
NDL et al., arXiv:0905.0964v1
Doiron-Leyraud
et al.,
arXiv:0905.0964
Cooper et al., Science 2009
Louis Taillefer,N.
Annual
Review
of Condensed
Matter
Physics
1, 51 (2010)
asthed-wavegap
(25)
and also scaleswith Tc (26).
near resistivity of cupratesper CuO2 plane, A□ ¼A / d, asa function of doping
p,
Note that the linear resistivity is a universal property of hole-doped cuprates
hLS
1,CO)
2012 (red dots; 23, 27), La1.6–xNd0.4SrxCuO4 (Nd-LSCO) (blue dots; 21, 28),
O) (purpletriangle
; 23),re
and
(Tl-2201)
(greenve
square
16, 29).
The(A coefficient) at a given doping,
2Ba2CuO
6þ de
diffe
ntTlmate
rials
xhibit the
ry ss;ame
slope
2
romfits(24) of theformr 0 þ AT þ BT to published data. Thered dashed lineisa
measure
d per CuOspondingT
ee24). In other words, theanomalous scattering isuniv
2 plane(s
O datapoints. Thegray
dotsarethecorre
c for LSCO (23). Thegray line
resistivity
and Tc The answer to our i
¼Tcmax [1 – 82.6and
(p – 0.16)
],Correlation
with Tscmax
K. Notethat
thecoe
fficie
nt of
therconductivity.
it s2witche
on¼37
at between
the
same linear-T
doping
as
supe
Tc in LSCO (K)
A (Ω /K)
24
zero at thepoint at which superconductivity vanishes, i.e., A ! 0 asTc ! 0, at pc ¼
d from Reference24.
L. Taillefer, Annual Review of CMP 1, 51 (2010) – arXiv:1003.2972
Nd-LSCO
Hole-doped cuprates
QCP principle
QCP for stripe order
•
Quantum critical point
•
Stripe order
•
Fermi-surface reconstruction
•
Precursor nematic regime
•
Linear-T resistivity
•
A ~ Tc
•
Tc dome
Hole-doped cuprates
Tc suppression
20
120
Eu-LSCO
80
10
40
A
0
Hc2* ( T ) in Eu-LSCO
Hc2 ( T ) in YBCO
YBCO
0
YBCO
SC fluctuations
Hc2 ( T )
160
Tc ( K )
via Nernst signal above Tc
80
Tc
40
0
0.04
80
B
0.12
Hole doping, p
•
Hc2 decreases with underdoping
•
Decrease is non-monotonic : Stripe order
J. Chang et al., unpublished
0
0.20
Hole-doped cuprates
QCP principle
QCP for stripe order
•
Quantum critical point
•
Stripe order
•
Fermi-surface reconstruction
•
Precursor nematic regime
•
Linear-T resistivity
•
A ~ Tc
•
Tc dome
T
TN
100
T
Hole-doped
cuprates
Summary
CO
Tc
0
0.0
0.1
0.2
0.3
300
YBCO
T*
TN
T(K)
200
Pseudogap
Nernst
Resistivity
CDW order
NMR
TH
SDW order
Neutrons
mSR
100
0
0.0
TSDW T
CO
0.1
Tc
0.2
QCP for stripe order
•
Quantum critical point
•
Stripe order
•
Fermi-surface reconstruction
•
Precursor nematic regime
•
Linear-T resistivity
•
A ~ Tc
•
Tc dome
0.3
Hole doping, p
Doiron-Leyraud & Taillefer, arXiv:1204.0490
h-DOPED CUPRATE
e-DOPE CUPRATE
PNICTIDE
ORGANIC
The QCP principle – a universal scenario ?
Thank you.
Doiron-Leyraud & Taillefer, arXiv:1204.0490
Taillefer, Annual Review of CMP 1, 51 (2010)
arXiv:1003.2972