HTSC Yuval Lubashevsky Prof. Amit Keren The superconductor energy - - PowerPoint PPT Presentation

The origin of pseudogap in HTSC

Yuval Lubashevsky

• Prof. Amit Keren

The superconductor energy gap

The BCS superconductor

The pseudogap temperature

Specific heat

Loram J W Physica C 282-287 1405 1997

• verdoped

underdoped

NMR

Bankay M PRB 50 6416 1994

Resistivity

Takagi H PRL 69 2975 1992 Timusk Rep. Phys. 62 61-122 1999

T* Tc T*

ARPES measurements

Kanigel

Theory Normal state Theory dSC state Experiment dSC Experiment PG state

Main question

What are the interactions that affect the T*?

The CLBLCO system

• Similar structure as the

well known YBCO

• 1:2:3 atomic ratio
• The main structure

doesn’t change with the families

• Controllable doping

level (y parameter)

• Controllable magnetic

coupling (x parameter)

  

1 1.75 0.25 3 x x x x y

Ca La Ba La Cu O

  

CLBLCO phase diagram

• Similar phase

diagrams

• The family with the

highest Tc have the highest TN on the lowest doping.

• Big difference at Tc

max

between the families

6.6 6.9 7.2 40 80 200 250 300 350 400 450 Tc TN Tg x=0.1 x=0.2 x=0.3 x=0.4 T (K)

y

Ofer PRB 73 220508 2006

Transformation of the entire doping range.

( )

• pt
• pt

m x x

p p p K y y     

The scaling works in the entire doping range apart for x=0.1?

6.4 6.6 6.8 7.0 7.2 20 40 60 80 180 240 300 360 420 TN,Tg Tc x 0.1 0.2 0.3 0.4

TN, g, C (K) y

TC Tg TN

• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

0.0 0.1 0.0 0.5 1.0 2 3 4 5 6 7 x 0.1 0.2 0.3 0.4

TN, g, C / TC

max

Pm

(CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy

y x K y T T T T T T T

c c g N c g N

   ) ( / , , , ,

max

Ofer PRB 73 220508 2006

The role of anisotropies

• We extracted J out of TN.
• TN is determined by the in-plane J and out of plane coupling.

J

Unified Phase Diagram

• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

0.0 0.1 0.0 0.4 0.8 1.2 10 15 20

x=0.1 x=0.2 x=0.3 x=0.4

( J, Tg,c ) / Tc

max

Pm

The in-plane J is extracted from TN

.

Ofer PRB 73 220508 2006

Scaling Conclusion

• We found that Tc scale like the in-plane J

therefore is a consequence of a 2D magnetic interaction.

• Question: Does T* scales with J as Tc does,
• r with some other magnetic parameter?

c

T J 

The experimental methods

• The SQUID

(Superconducting QUantum Interference Device)

• The temperature range

is 1.2K to 310K

• The field range is up to

6.5T.

Susceptibility

• Practice
• Where D is known as the demagnetizing factor, and it get different values

for different geometries.

• For needle like sample D=0, then:

dc

M H  

1

dc

D     

limH M H 



  

dc

  

• Definition

Measurement condition

• 4.0x10

0.0 4.0x10

• 6

6

• 40

• 1.0
• 0.5

M[10

• 9 emu]

H [G]

H10

• 2kG=2.571

[cm

3/gm]

H10

[cm

3/gm]

1 2 3 4 5 3 4 5 6 7 8 9  [10

• 7cm

3/gr]

h/2R

Field dependence Geometric dependence

Raw data

60 120 180 240 300 2 4 6 8 10 12 y=7.007 y=6.93 y=6.87 y=6.75

 [10

• 7 cm

3/gr]

T [K]

X=0.2

180 240 300 2.8 3.0 3.2 3.4 3.6 3.8

y=7.007 y=6.93 y=6.87 y=6.75

 [10

• 7 cm

3/gr]

T [K]

• The minimum point

drop systematically with the doping- first clue of pseudogap effect ( T* behavior).

200 250 300 3.32 3.34 3.36 3.38 y=6.93

 [10

• 7 cm

T [K]

This phenomena has been noticed by D C Johnston

• n 1988

• The value of is increasing with the doping (Pauli

susceptibility).



( ) f y  

6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 2.0 2.5 3.0 3.5 4.0 4.5 x=0.1 x=0.2 x=0.3 x=0.4

 [10

• 7cm

3/gr]

T299

• K

Y

Susceptibility types

• Isolated spin: Langevin paramagnetism, Curie law
• Weakly coupled spins: Curie-Weiss
• Pauli spin (Landau ) :
• Core: Van Vleck and Langevin

2

3

B B

N C k T T    

C T    

2 0( )

( ) D

B f

T const     

0( )

T const  

There is no traditional theory about increasing susceptibility with T

Strongly coupled spins

• Two coupled spins according to Heisenberg

model.

• shrinking arcs phenomena.
• The fitting term.

2 2

cosh 2

J

J e



  



            

2

2 ( ) * * T T A T T T                 

* cosh const T T        

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 kBT/J J pseodogaped fitting function strong coupled spins function shrinking arcs function

The fitting function

C.W. + PG + CORE



T C.W. Peudogap core

1 2 3

* cosh C C C T T T            

100 200 300 4 6 8 10 12

[10

• 7 cm

3/gr]

T [K]

Curie-Weiss temperature

6.80 6.85 6.90 6.95 7.00 7.05 7.10 10 20 30 40

[K]

y x=0.1 x=0.2 x=0.3 x=0.4



TN



T

Antiferromagnetic susceptibility

 

2 1 3

i i i B

S S Z J K         

• 0.25
• 0.20
• 0.15
• 0.10
• 0.05

0.0 0.1 0.2 0.3 0.4 0.5 0.6

/Tc

max

Pm

x=0.1 x=0.2 x=0.3 x=0.4

T*

6.85 6.90 6.95 7.00 7.05 200 400 600 T* [K] y x=0.1 x=0.2 x=0.3 x=0.4

• 0.25
• 0.20
• 0.15
• 0.10
• 0.05

6 8 10 12 14 16 18 20 22 24 T*/Tc

max

Pm

x=0.1 x=0.2 x=0.3 x=0.4

The T* doesn’t scale well with Tc.

• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

TN, g, C / TC

• 0.2
• 0.1

0.0 1 2 3 4 T*/TN

max

Pm

x=0.1 x=0.2 x=0.3 x=0.4

T* scale with TN

Very similar to the Tc/TN scaling.

Conclusions

• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

0.0 0.1 0.0 0.1 0.2 0.6 0.8 1.0 1.2 Tc, TN, Tg, T

*/TN max

Pm x TN/Tg T

0.4 0.3 0.2 0.1

6.3 6.6 6.9 7.2 40 80 200 300 400 500 600 700 Tc TN Tg T

*

x=0.1 x=0.2 x=0.3 x=0.4 T (K)

y

We added the T* to the phase diagram T* scale like TN, and it is a 3D magnetic phenomena. Tc is a 2D magnetic phenomena.

Acknowledgment

I’m grateful to Prof. Amit Keren Thanks to:

• Dr. Arkady Knizhnik, Avi Post, Dr.Michael Reisner,
• Dr. Leonid Iomin

And the lab’s fellow-students: Orenstein, Oren, Eran, Meni, Oshri, Daniel, Maniv, Gil, Yoash, Ana

Specially to Rinat Ofer for her help