Fifty and One Shades of High Temperature Superconductors · 2017. 3. 16. · M. S. Grbić, N....

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


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


• 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


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


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

~


..

. .

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


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


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


..

. .

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


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


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


-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)


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


-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



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


-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




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



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


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


Hg1201 – cot ;ȺH)

ρ ρ

cot(ȺH) ∝m*/τ = C

2T2


Scattering rate: Fermi liquid like anddoping (m* = const.) independent

Hg1201 – cot ;ȺH)


2T2

ρ


Scattering rate: Fermi liquid like anddoping (m* = const.) independent

Single-layer compounds – cot ;ȺH)


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


Scattering rate: Fermi liquid like doping (m* = const.) and compound independent

Single-layer compounds – cot ;ȺH)


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**


Conclusions

N. Barišić et al., preprint (2015).

Resistivity Scattering rateρ = m*/(p e2τ) cot(ΘH) = C2T2 ∝ 1/τ


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

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