fifty and one shades of high temperature superconductors · 2017. 3. 16. · m. s. grbić, n....
TRANSCRIPT
Classes of materials
EĞǀĞŶĂƌŝƓŝđInstitute of Solid State Physics, TU Wien, AustriaDepartment of Physics, Faculty of Science, University of Zagreb, Croatia
Fifty and One Shades of High Temperature Superconductors
The Janus-face of the localized carrier in cuprates: Generating the pseudogap and high temperature superconductivity
Superconductivity: How did it all started?
Nobel Prize 1913.
V = RI - Ohm's law
Temperature (K)
Re
sis
tiv
ity
Kamerlingh OnnesGilles Holst1911
Normal state
Superconducting“zero resistance”
state
TC
Big surprize!
Resistivity (or transport coefficients)
- first measured- last understood
Joule heat - dissipation
Corresponds to a weighted integration over the whole Fermi surface.
Resistivity R
ɐ even elastic scattering transforms the kinetic energy of center of mass to (internal) energy of the chaotic PRYHPHQWʙ5ʛFKDRV
ɐ 5ʽ independent of the type of the scattered particles: classical electrons, charged fermions, charged bosons
ɐ 5
Dilemma:
a) change in the state of the charge carriers -superconductivity
b) change in the state of the scattering centers - ideal conductivity
Joule heat - dissipation
Onnes, until his death in 1926, believed in b): scattering centers are vibrations of the crystal lattice, which freezes out at Tc
Few Words About the Superconductivity
ɐ Superconductivity is a particular state of the metalsɐ It is a physical phenomena of extreme conceptual importance:
From 115 Nobel prices in Physics 9 - superconductivity and superfluidity 2 -generalization of superconductivity to other problems
•1913. H. Kamerlingh Onnes•1962. L. D. Landau•1972. J. Bardeen, L. N. Cooper, J. R. Schrieffer•1973. L. Esaki, J. Giaever, B. D. Josephson•1978. P. Kapitsa, A. Penzias, R. W. Wilson (superfluidity)•1987. J. G. Bednorz, K. A. Müller•1991. P. –G. de Gennes (generalization)•1996. D. R. Lee, DD. Osheroff, R. C. Richardson(superfluidity)•1998. R. B. Laughlin, H. L. Störmer, D. C. Tsui (superfluidity)•2003. A. A. Abrikosov, V. L. Ginzburg, A. J. Leggett•2008. Y. Nambu, M. Kobayashi, T. Maskawa (generalization)
Huge technological importance… Great impact: need for higher TC
Understanding: BCS Theory
Discovery
+ +
+ +ͻe-
ͻe-
+ +
+ +ͻe-
ͻe-
+ +
+ +ͻe-
ͻe-
+ +
+ +ͻe-
ͻe-
Cooper pairs, Binding energy (gap): Δ
Sketch of the BCS theory
BCS Theory
Two electrons attract each other through a retarder interaction mediated by lattice vibrations.
Cooper pairs form a collective state.
To remove a Cooper pair from this state (gap) energy is required.
This causes infinite conductivity, or zero resistivity.
1986: Even Bigger Surprise!
Bednorz and Mueller
IBM Zuerich, 1986
Great impact: need for higher TC
Understanding: BCS Theory
Discovery
High temperature Unconventional
Low temperatureBCS
Zoo of 200+ cuprates
(La,Ba)2CuO
4YBa
2Cu
3O
7-ɷ Tl2Ba
2Ca
2Cu
3O
10Bi
2Sr
2CaCu
2O
8HgBa
2CuO
4+ɷ
H. Eisaki et al., Phys. Rev. B 69, 064512 (2004)
?
Cuprates: dramatically different?
Cooper pairs, d-wave superconductors, big binding energy (gap): Δ
Strong coupling regimeW ~ 1eV, U ~ 10 eV
Strong doping dependence:
complex phase diagram
A. P. Mackenzie et al., Phys. Rev. B 53, 5848 (1996)
General opinion in the community:Understanding of superconductivity requires understanding the normal state properties
Fermi-Liquid
Non-Fermi-Liquid
Pseudo gap
SCAF
SG
x
T
Ch
ara
cte
risti
c T
em
pe
ratu
re
p : charge/CuO2
Cuprates - Current paradigms
• Normal state is everything but
normal
Fermi-Liquid
Non-Fermi-Liquid
Pseudo gap
SCAF
SG
x
T
Ch
ara
cte
risti
c T
em
pe
ratu
re
p : charge/CuO2
• Fermi arcs lack quasiparticle properties to form a true Fermi surface
• Quasiparticles are not an appropriate concept to understand the “normal” state
T. J. Reber et al., Nat. Phys. 8, 606 (2012)H.-C. Jiang et al., Nature 493, 39 (2013)
M.A. Hossain et al., Nat. Phys. 4, 527 (2008)
YBCO
¾ Strong coupling theories (large Ud models, t-Jmodels)
¾ Resonance valence bond
¾ Quantum critical models
(marginal Fermi liquids)
¾ Spin-glass theories
¾ Stripe based models
…and many others
… often mutually exclusive, however they agree on one point, that normal state is…
…suggest different normal states…
… everything but Fermi liquid
Cuprates - Current paradigms
Fermi-Liquid
Non-Fermi-Liquid
Pseudo gap
SCAF
SG
x
T
Ch
ara
cte
risti
c T
em
pe
ratu
re
p : charge/CuO2
Main concepts
Cuprates - Current paradigms
• Quantum oscillations at high
fields and low temperatures
Fermi-Liquid
Non-Fermi-Liquid
Pseudo gap
SCAF
SG
x
T
Ch
ara
cte
risti
c T
em
pe
ratu
re
p : charge/CuO2
• Fermi surface well defined• Fermi liquid concept applicable
YBCO
M.A. Hossain et al., Nat. Phys. 4, 527 (2008)N. Doiron-Leyraud et al., Nature 447, 565 (2007)
YBCO has chains, planes and exhibits bilayer splitting, which can significantly affect experimental results and interpretation
Zoo of 200+ cuprates
(La,Ba)2CuO
4YBa
2Cu
3O
7-ɷ Tl2Ba
2Ca
2Cu
3O
10Bi
2Sr
2CaCu
2O
8HgBa
2CuO
4+ɷ
H. Eisaki et al., Phys. Rev. B 69, 064512 (2004)
Why is Hg1201 an exquisite material?
• Simple crystal structure (tetragonal)
• Disorder confined relatively far away from CuO2 layers
• Optimal superconducting transition temperature of nearly 100 K highest among single CuO2 layer compounds
HgBa2CuO4+δ
Drawback in 2006: Lack of sizeable, high-quality single crystals
Breakthrough in single crystal growth
• Gram-sized crystals
ab- plane ac- plane
1 g ~ 100 mm3
• Cleaved surfaces
X. Zhao et al., Adv. Mater. 18, 3243 (2006) N. Barišić et al., Phys. Rev. B 78, 054518(2008)
Sample uniformity as shown by resistivity
0 100 200 300 4000.0
0.2
0.4
0.6
0.8
Sample 1 Sample 2 Sample 3
ρ (mΩ
cm)
T (K)
Annealing conditions: 5200 C, AIR
0 100 200 300 4000.0
0.2
0.4
0.6
0.8
1.0
A
ρ/ρ(
T=40
0)
T (K)
V
c
1 2 3
N. Barišić et al., Phys. Rev. B 78, 054518 (2008)
High purity – Low Pinning
0 20 40 60 80
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
χ(ar
b.un
its)
T(K)
FC
ZFC
10 Oe abT
N. Barišić et al., Phys. Rev. B 78, 054518 (2008)
(La,Sr)2CuO4 ~ 50%
YBa2Cu3O6+δ ~ 40%–80%
prior work onHg1201 ~ 60%–70%
97%
T. Sasagawa et al., Phys. Rev. B 61, 1610 (2000)
R. Liang et al., Physica C 383, 1 (2002)
G. Le Bras et al., Physica C 271, 205 (1996)
SANS and ARPES Results
I.M. Vishik et al., PRB (2014)
First photoemission results, by Z.X. Shen’s group (Tc .7 .
Y. Li et al., PRB (2011)
Small-angle neutron scattering at the PSI, Switzerland: triangular vortex lattice(Tc = 94 K, T = 2 K)
Controlled doping by Annealing
TC=T
C,max[1-82.6(p-0.16)2]
0 20 40 60 80 100-1
0
T
UD 47K UD 67K UD 77K UD 81K UD 87K OPT 95K OD 81K OD 64K
χ (a
rb. u
nits
)
T (K)
H 5 Oe
0 0.08 0.16 0.24020406080
100
TC(K
)
hole concentration
Annealing conditions TC(K)
550 C 10-6 Torr 47
450 C 0.1 Torr 67
650 C air 77
500 C air 81
450 C air 87
350 C air 95
300 C ≈0.04 g/cm3 AgO 10-15 bar O2
81
300 C ≈0.1 g/cm3 AgO 20-30 bar O2
64
N. Barišić et al., Phys. Rev. B,78, 054518(2008)
But, is it good enough?
Fermi-Liquid
Non-Fermi-Liquid
Pseudo gap
SCAF
SG
x
T
Ch
ara
cte
risti
c T
em
pe
ratu
re
p : charge/CuO2
Quantum oscillations in underdoped cuprates
High quality crystals are
required!
Quantum oscillations – universal property of
underdoped cuprates
N. Barišić et al., Nat. Phys. 9, 761 (2013)
Fermi-Liquid
Non-Fermi-Liquid
Pseudo gap
SCAF
SG
x
T
Ch
ara
cte
risti
c T
em
pe
ratu
rep : charge/CuO2
Cyril Proust, Laboratoire National des
Champs Magnétiques Intenses of Toulouse
Normal state - Superconductivity
Fermi-Liquid
Non-Fermi-Liquid
Pseudo gap
SCAF
SG
x
T
Ch
ara
cte
risti
c T
em
pe
ratu
re
p : charge/CuO2
We are interested in the normal state properties!
We should first establish to which temperature superconductivity persists.
1st topic addressed:
superconducting fluctuations
f0
Fluctuation Regime
- Microwave Conductivity
∆f
resonant frequency f0Q-factor
B. Nebendahl et al., Rev. Sci. Instrum. 72
∆+∆
=∆
Qi
ff
21~
ωω
Measured quantity:
complex frequency shift
Intracavity arrangement:a) Sample in magnetic field maximum
f = 13.1 GHz
b) Sample in electric field maximum
f = 17.5 GHz
eTE112
eTE113
Measurement ConfigurationsAnalysis of the Q - factor
abQ ρ~21∆
M. S. Grbić, N. Barišić et al., Phys. Rev. B
HgBa2CuO4+þ
ab planeTc= 95 K
Analysis of the Q - factor
c- axisSkin depth:
ωµρδ0
2 cab = ċc=[ċab
M. S. Grbić, N. Barišić et al., Phys. Rev. B
73T8T
Results - Microwaves
¾ Three distinct characteristic temperatures are unambiguously determined :
Tc, T’, T*
¾ This was accomplished in a single measurement, from the raw data
¾ Narrow fluctuation regime
Tc
M. S. Grbić, N. Barišić et al., Phys. Rev. B
Magnetic Field – a Useful Tool
ɐ +Jɐ LSCOɐ BSCOɐ YBCO
Other dopings
0 20 40 60 80 100-1
0
T
UD 47K UD 67K UD 77K UD 81K UD 87K OPT 95K OD 81K OD 64K
χ (a
rb. u
nits
)
T (K)
H 5 Oe
Other HTSC‘s
R. Dauoet al., Nature 463, 519 )
0 10 20 300
20
40
60
80
100
120
140
T (K
)
Hole doping (%)
Tc - Wang PRB 2006
Tc - Liang PRB 2006
LSCOYBCOHg1201Tc - Yamamoto PRB 2000
+J YBCO LSCO
Phase Diagram
L. S Bilbro et al., Nat. Phys. 11)M. Grbić03RØHN$'XOčić, Y. Li, X. Zhao, G. Yu, M. Greven, N. Barišić, manuscript in preparation
LSCO - Thin Films
Microwave Conductivity - Summary
¾ Three distinct characteristic temperatures are unambiguously determined :
Tc, T’ , T*
¾ This was accomplished in a single measurement, from the raw data
¾ Narrow fluctuation regime: T’ from microwaves is universally (Hg1201, YBCO, LSCO) only 10 - 20K above Tc
0,0 0,1 0,2 0,30
20
40
60
80
100
120
140
T (K
)
Hole doping p
LSCOYBCOHg1201
M. Grbić03RØHN$'XOčić, Y. Li, X. Zhao, G. Yu, M. Greven, N. Barišić, manuscript in preparation
2nd topic addressed:
Electrical resistivity in the normal state
Nature of the state between T´ and T*
ρ ~ T2
ρ ~ T
~
~
Tc
T´
SC
AF
Hole doping (%)
T (K
)
T*
0 10 20 300
100
200
300
N. E. Hussey, J. Phys.: Condens. Matter 20, 123201 (2008)
T*T
ρ ~ T
ρ ~ T2
ρ ~ T
~
~
Tc
T´
SC
AF
Hole doping (%)
T (K
)
T*
0 10 20 300
100
200
300 Hg1201
2 4 60
0.25
0.50
T´ ~ 91 K
T** ~ 170 K
~
~
ρ (m
Ωcm
)
T2 (104 K2)
0
0.2
0.4
0.6
0.8
1.0100 200 300 400
Tc ~ 80 K
T* ~ 290 K~
~
ρ/ρ(
400K
)
T (K)
Tc=80 Kp ~ 0.11~
2 4
~
T**~170 K
T´~91 K
dρ/d
T2
T2 (104 K2)
~
N. Barišić et al., PNAS 110, 12235 (2013)
Nature of the state between T´ and T*
ρ ~ T2
ρ ~ T2~
ρ ~ T
~
~
Tc
T´
SC
AF
Hole doping (%)
T (K
)
T*T**
0 10 20 300
100
200
300
Characteristic temperatures Tc, T´, T** and T*
Hg1201
0 100 200 300 4000.0
0.2
0.4
0.6
0.8
1.0
Tc ~ 80 K
T* ~ 290 K~
~
ρ/ρ(
400K
)
T (K)
0
0.2
0.4
0.6
0.80 2 4 6
190 K
Tc= 47 Kp ~ 0.055ρ(
mΩ
cm)
Hg1201100 K
0
0.2
0.4
0.6 218 K
84 K
Tc= 67 Kp ~ 0.075ρ(
mΩ
cm)
0 2 4 60
0.2
0.4~
T2 (104 K2)
ρ(mΩ
cm)
T** ~ 170 K
T ' ~ 85 K
Tc= 80 Kp ~ 0.11
~
N. Barišić et al., PNAS 110, 12235 (2013)
..
. .
0
0,2
0,4
0,6
0,80 2 4 6
190 K
Tc= 47 Kp ~ 0.055ρ(
mΩc
m)
Hg1201100 K
0
0,2
0,4
0,6 218 K
84 K
Tc= 67 Kp ~ 0.075ρ(
mΩc
m)
0 2 4 60
0,2
0,4
T2 (104 K2)
ρ(mΩc
m)
170 K
85 KTc= 80 Kp ~ 0.11
ρ ~ T2
ρ ~ T2~
ρ ~ T
~
~
Tc
T´
SC
AF
Hole doping (%)T
(K)
T*T**
0 10 20 300
100
200
300
Nature of the state between T´ and T**
Hg1201
[
.
YBCO
LSCO
0 2 4 6 8
16
18
20
LSCO 1%
ρ (mΩc
m-1)
T2 (104K2)
Y. Ando et al., Phys. Rev. Lett. 92,197001 (2004)
..
. .
0
0,2
0,4
0,6
0,80 2 4 6
190 K
Tc= 47 Kp ~ 0.055ρ(
mΩc
m)
Hg1201100 K
0
0,2
0,4
0,6 218 K
84 K
Tc= 67 Kp ~ 0.075ρ(
mΩc
m)
0 2 4 60
0,2
0,4
T2 (104 K2)
ρ(mΩc
m)
170 K
85 KTc= 80 Kp ~ 0.11
ρ ~ T2
ρ ~ T2~
ρ ~ T
~
~
Tc
T´
SC
AF
Hole doping (%)
T (K
)
T*T**
0 10 20 300
100
200
300
Nature of the state between T´ and T**
Hg1201
[
.
YBCO
LSCO
0 2 4 6 8
16
18
20
LSCO 1%
ρ (mΩc
m-1)
T2 (104K2)
ʌ ∝ T 2Fermi liquid
Frequency dependence of the scattering rate
S. I. Mirzaei et al., PNAS 110, 5774 (2013)
Sheet-conductance of the CuO2 layers:
For Fermi liquids: a ≈ 1.6a
1/τ
(ξ)
[meV
]
M2
(ω)
[meV
]
Magnetotransport
– Kohler's rule
Kohler’s rule
• from Boltzmann equation
z assuming single scattering time τ
z (Hτ) appears together
z τ ∝ 1/ρ0
⇒ δρ/ρ0 = F (H/ρ0) only
• in weak field limit, MR ∝ H2
⇒ δρ/ρ0 ∝ (H/ρ0)2
100 K125 K150 K175 K200 K225 K
J. M. Harris et al., Phys. Rev. Lett. 75, 1391 (1995)
δρ/ρ
0 (1
04 )
(H/ρ0)2 (109 T2/(Ω·cm)2)
Tc = 60K
Magnetotransport in YBCO
– Kohler's rule violated
Kohler’s rule
• from Boltzmann equation
z assuming single scattering time τ
z (Hτ) appears together
z τ ∝ 1/ρ0
⇒ δρ/ρ0 = F (H/ρ0) only
• in weak field limit, MR ∝ H2
⇒ δρ/ρ0 ∝ (H/ρ0)2
p у 0.1
Tc = 60K
T ** уϮϮϬ<
Samples with Tc 70 K, 81 K
ρ0 ∝ T2, Fermi liquid-like
ρres ≈ 0 : high sample quality
“Strange” Metal
Hg1201 - Resistivity
N. Barišić et al., PNAS 110, 12235 (2013) 00
• Pulsed field measurements at LCNMI-Toulouse.
• δρ/ρ0 = aH2
• ρ0 changes by a factor of 6
Magnetotransport in Hg1201
– Kohler's rule obeyed
M. K. Chan et al., Phys. Rev. Lett. 113, 177005 (2014)
Max. field - 30 Tj ∥ ab, H ∥ c
• Pulsed field at LCNMI-Toulouse
• δρ/ρ0 = aH2
• ρ0 changes by a factor of 6
• Kohler’s rule is valid
Magnetotransport in Hg1201 – Kohler's rule obeyed
M. K. Chan et al., Phys. Rev. Lett. 113, 177005 (2014)
z δρ/ρ0 = aH2 ∝ (H/ρ0)2
z a∝ 1/ρ02
z ρ0∝ T2
⇒ a ∝ T –4
Tc = 70KTc = 70KTc = 81K
Temperature dependence of MR coefficient – Hg1201
M. K. Chan et al., Phys. Rev. Lett. 113, 177005(2014)
Y. Ando et al. PRL 88, 167005 (2002)
Resistivity• ρ = A2T2
measured perpendicular to
the chains
MR Coefficient• δρ/ρ0 = aH2
• a ∝ T –4
Temperature dependence of MR coefficient – YBCO
YBa3CuO6.6 , p ≈ 0.085, Tc ≈ 50K
M. K. Chan et al., Phys. Rev. Lett. 113, 177005(2014)
Y. Ando et al. PRL 88, 167005 (2002)
Temperature dependence of MR coefficient – YBCO
⇒ Kohler's rule is valid
⇒ Fermi liquid
YBa3CuO6.6 , p ≈ 0.085, Tc ≈ 50K
M. K. Chan et al., Phys. Rev. Lett. 113, 177005(2014)
Doping dependence of A1
and A2
ρ ~ A1T
ρ ~ A2T
2
ρ ~ A2T
2~
Tc
T´
SC
AF
Hole doping (%)
T (K
)
T*T**
~
~
0 10 20 300
100
200
300
N. Barišić et al., PNAS 110, 12235 (2013)
..
. .
0
0,2
0,4
0,6
0,80 2 4 6
190 K
Tc= 47 Kp ~ 0.055ρ(
mΩc
m)
Hg1201100 K
0
0,2
0,4
0,6 218 K
84 K
Tc= 67 Kp ~ 0.075ρ(
mΩc
m)
0 2 4 60
0,2
0,4
T2 (104 K2)
ρ(mΩc
m)
170 K
85 KTc= 80 Kp ~ 0.11
ρ ~ T2
ρ ~ T2~
ρ ~ T
~
~
Tc
T´
SC
AF
Hole doping (%)T
(K)
T*T**
0 10 20 300
100
200
300
Nature of the State Between T´ and T**
Hg1201
[
.
YBCO
LSCO
0 2 4 6 8
16
18
20
LSCO 1%
ρ (mΩc
m-1)
T2 (104K2)
ʌ ∝ T 2Fermi liquid
Doping dependence of A1
and A2
0
1,3
2,6
3,9
5,2
A 1 (µΩ
cm/K
)
A
0 5 10 15 20 25 30 350,0
9,8
19,6
29,4
D
p (%)
A 2 (nΩ
cm/K
2 )
0 5 10 15 20 25 30 350
0,12
0,24
0,36
E
p (%)
A 2 (Ω
/K2 )
0 5 10 15
3
6
9
A2
(Ω/K
2 )p (%)
0,6 0,9 1,2 1,5
0
1
2
C
Log ((p-p1) (%))
Log
(A1
(Ω/K
))
Hg1201 YBCO
Tl2201 LSCO
Polycrystalline LSCO
-1,0 -0,5 0,0 0,5 1,0 1,5-2,0
-1,5
-1,0
-0,5
0,0
0,5
1,0
F
Log(
A 2 (Ω
/K2 ))
Log ((p-p2) (%))
ρ ~ A1T
ρ ~ A2T
2
ρ ~ A2T
2~
Tc
T´
SC
AF
Hole doping (%)
T (K
)
T*T**
~
~
0 10 20 300
100
200
300
ρ ∝ A1T
ρ ∝ A2T2
N. Barišić et al., PNAS 110, 12235 (2013)
Doping dependence of A1 and A
2
ρ ~ A1T
ρ ~ A2T
2
ρ ~ A2T
2~
Tc
T´
SC
AF
Hole doping (%)
T (K
)
T*T**
~
~
0 10 20 300
100
200
300
ρ ∝ A1T
ρ ∝ A2T2
a, b, c - are the unit cell dimensions N - number of CuO2 planes in the unit cell
ρ = ρ _______ ab (c/N)
0
1,3
2,6
3,9
5,2
A 1 (µΩ
cm/K
)
A0
20
40
60
80
B
A 1 (Ω
/K)
0 5 10 15 20 25 30 350,0
9,8
19,6
29,4
D
p (%)
A 2 (nΩ
cm/K
2 )
0 5 10 15 20 25 30 350
0,12
0,24
0,36
E
p (%)
A 2 (Ω
/K2 )
0 5 10 15
3
6
9
A2
(Ω/K
2 )
p (%)
0,6 0,9 1,2 1,5
0
1
2
C
Log ((p-p1) (%))
Log
(A1
(Ω/K
))
Hg1201 YBCO
Tl2201 LSCO
Polycrystalline LSCO
-1,0 -0,5 0,0 0,5 1,0 1,5-2,0
-1,5
-1,0
-0,5
0,0
0,5
1,0
F
Log(
A 2 (Ω
/K2 ))
Log ((p-p2) (%))N. Barišić et al., PNAS 110, 12235 (2013)
Doping dependence of A1 and A
2
ρ ~ A1T
ρ ~ A2T
2
ρ ~ A2T
2~
Tc
T´
SC
AF
Hole doping (%)
T (K
)
T*T**
~
~
0 10 20 300
100
200
300a, b, c - are the unit cell dimensions N - number of CuO2 planes in the unit cell
ρ = ρ _______ ab (c/N)
0
1,3
2,6
3,9
5,2
A 1 (µΩ
cm/K
)
A0
20
40
60
80
B
A 1 (Ω
/K)
0 5 10 15 20 25 30 350,0
9,8
19,6
29,4
D
p (%)
A 2 (nΩ
cm/K
2 )
0 5 10 15 20 25 30 350
0,12
0,24
0,36
E
p (%)
A 2 (Ω
/K2 )
0 5 10 15
3
6
9
A2
(Ω/K
2 )
p (%)
0,6 0,9 1,2 1,5
0
1
2
C
Log ((p-p1) (%))Lo
g (A
1 (Ω
/K))
Hg1201 YBCO
Tl2201 LSCO
Polycrystalline LSCO
-1,0 -0,5 0,0 0,5 1,0 1,5-2,0
-1,5
-1,0
-0,5
0,0
0,5
1,0
F
Log(
A 2 (Ω
/K2 ))
Log ((p-p2) (%))
ρ ∝ A1T
A1 ∝ 1/p
ρ ∝ A2T2
A2 ∝ 1/p
N. Barišić et al., PNAS 110, 12235 (2013)
Doping dependence of A2
ρ ~ A1T
ρ ~ A2T
2
ρ ~ A2T
2~
Tc
T´
SC
AF
Hole doping (%)
T (K
)
T*T**
~
~
0 10 20 300
100
200
300a, b, c - are the unit cell dimensions N - number of CuO2 planes in the unit cell
ρ = ρ _______ ab (c/N)
0
1,3
2,6
3,9
5,2
A 1 (µΩ
cm/K
)
A0
20
40
60
80
B
A 1 (Ω
/K)
0 5 10 15 20 25 30 350,0
9,8
19,6
29,4
D
p (%)A 2 (
nΩcm
/K2 )
0 5 10 15 20 25 30 350
0,12
0,24
0,36
E
p (%)
A 2 (Ω
/K2 )
0 5 10 15
3
6
9
A2
(Ω/K
2 )
p (%)
0,6 0,9 1,2 1,5
0
1
2
C
Log ((p-p1) (%))
Log
(A1
(Ω/K
))
Hg1201 YBCO
Tl2201 LSCO
Polycrystalline LSCO
-1,0 -0,5 0,0 0,5 1,0 1,5-2,0
-1,5
-1,0
-0,5
0,0
0,5
1,0
F
Log(
A 2 (Ω
/K2 ))
Log ((p-p2) (%))
ρ ∝ A2T2
A2 ∝ 1/p
Hg1201 YBCO
Tl2201 LSCO
Polycrystalline LSCO
N. Barišić et al., PNAS 110, 12235 (2013)
Doping dependence of A2
ρ ~ A1T
ρ ~ A2T
2
ρ ~ A2T
2~
Tc
T´
SC
AF
Hole doping (%)
T (K
)
T*T**
~
~
0 10 20 300
100
200
300
ρ = m*/(p e2τ)
0
20
40
60
80
A 1 (Ω
/K)
0 5 10 15 20 25 30 350
0,12
0,24
0,36
p (%)
A 2 (Ω
/K2 )
0 5 10 15
3
6
9
A2
(Ω/K
2 )
p (%)
Doping dependences
ρ ∝ A2T2 ∝ m*/(p e2τ 2)
A2 ∝ 1/p m* and τ 2 doping independent
N. Barišić et al., PNAS 110, 12235 (2013)
Doping dependence of A1 and A
2
ρ ~ A1T
ρ ~ A2T
2
ρ ~ A2T
2~
Tc
T´
SC
AF
Hole doping (%)
T (K
)
T*T**
~
~
0 10 20 300
100
200
300
Doping dependences
ρ ∝ A2T2 ∝ m*/(p e2τ 2)
A2 ∝ 1/p m* and τ 2 doping independent
ρ = m*/(p e2τ)
1/τ2 ∝ T2
Temperature dependences
m* and p temperature independent
-Scattering mechanism
same at 1% and 33% -Fermi liquid
T 2- ω2 scalingKohler rule
N. Barišić et al., PNAS 110, 12235 (2013)
0
20
40
60
80
A 1 (Ω
/K)
0 5 10 15 20 25 30 350
0,12
0,24
0,36
p (%)
A 2 (Ω
/K2 )
0 5 10 15
3
6
9
A2
(Ω/K
2 )
p (%)
"Strange" metal regime - ρ∝ A1T
ρ = m*/(p e2τ)
What changes upon crossing the T*, T** ?
scattering rate 1/τ(appealing)
YBCO
M.A. Hossain et al., Nat. Phys. 4, 527 (2008).
or/and carrier density
Indication of change in carrier density
For a parabolic band: RH= 1/(pe)
ρ = m*/(p e2τ)
Y. Ando et al., Phys. Rev. Lett. 92,197001 (2004)
Hall effect:- Fermi liquid regime n = x/V (in agreement
with dc-resistivity and optical conductivity)- High-temperature carrier density increases
Hg1201 – resistivity and Hall effect
N. Barišić et al., arXiv:1507.07885 (2015)
ρ ρ
ρ = m*/(p e2τ)RH= 1/(p e)
Hg1201 – cot (ȺH)
ρ ρ
ρ = m*/(p e2τ)RH= 1/(p e)
cot(ΘH) = ρ/(HRH)∝ m*/τ
N. Barišić et al., arXiv:1507.07885 (2015)
Hg1201 – cot ;ȺH)
ρ ρ
cot(ȺH) ∝m*/τ = C
2T2
N. Barišić et al., arXiv:1507.07885 (2015)
Scattering rate: Fermi liquid like anddoping (m* = const.) independent
Hg1201 – cot ;ȺH)
cot(ȺH) ∝m*/τ = C
2T2
ρ
N. Barišić et al., arXiv:1507.07885 (2015)
Scattering rate: Fermi liquid like anddoping (m* = const.) independent
Single-layer compounds – cot ;ȺH)
cot(ȺH) ∝m*/τ = C
2T2 - C
0
LSCO
Y. Ando et al., Phys. Rev. Lett. 92,197001 (2004).
J. Kokalj et al., Phys. Rev. B 86, 045132 (2012).
Tl2201
N. Barišić et al., arXiv:1507.07885 (2015)
Scattering rate: Fermi liquid like doping (m* = const.) and compound independent
Single-layer compounds – cot ;ȺH)
cot(ȺH) ∝m*/τ = C
2T2
Scattering rate: Fermi liquid like doping (m* = const.) and compound independent
C 2(K
-2)
C 2(K
-2)
cot(Θ
H)-C
0
T**
N. Barišić et al., arXiv:1507.07885 (2015)
Conclusions
N. Barišić et al., preprint (2015).
Resistivity Scattering rateρ = m*/(p e2τ) cot(ΘH) = C2T2 ∝ 1/τ
N. Barišić et al., arXiv:1507.07885 (2015)
x = 0.33
Scattering rate cot(ΘH) = C2T2 ∝ 1/τ
Change in paradigm: Novel prospect!
N. Barišić et al., preprint (2015).
Resistivity ρ = m*/(n e2τ)
Localization of the ONE
Preprint, submitted to PRX 2016
1 - localized hole 1 + p - Fermi liquid holes
1 + p p - Fermi liquid holes1 - localized hole
Acknowledgements
My activities on the topic are supported by the Austrian FWF and ERC Consolidator Grant Thank you for your
attention