the mysterious metallic phase in 2d superconductors and ... · 3. unexpected metallic phase in...

The Mysterious Metallic Phase in 2D Superconductors and the Resulting Phase Diagram

Yoon’s GroupDepartment of PhysicsUniversity of Virginia

Yize (Stephanie) Li

Xiaogan, Hubei, China, People’s Republic of

Outline1. Lab Tour.

2. Conventional Treatments of Electronic Transport in 2D Superconducting films.

3. Unexpected Metallic Phase in B-induced Suppression of Superconductivity. Is the Metallic Phase Real? What’s the Origin?

4. Mapping the Phase Diagram in B-T-Disorder Space (Based on the Nonlinear Transport Characteristics). Fundamental Issues Related with the Phase Diagram.

5. A Possible Signature for the Localized Cooper Pairs in B-Induced Insulating Phase.

6. Conclusions

Properties of Tantalum

General: 181Ta, column 5B , transition metal, hard material, high melting point, slow oxidation in the air

Bulk: T =4.5K

73

Bulk: Tc=4.5K

Film: Excellent wetting on most of the substrates

Ta films are dc sputter deposited on Si substrates

1. Base pressure ~10-8 Torr before deposition.

2. Clean the chamber and Ta source by presputtering.

3. Films are grown at a rate of ~0.05nm/s at an Ar pressure of 4 mTorr.mTorr.

4. Films are patterned into a bridge for 4-leads measurement

5. Up to 12 films per batch

The Ta films we grown are highly amorphous, as demonstrated(1) by the x-ray diffraction pattern (no sign of local atomic correlation)(2) by the fact that Tc decreases with decreasing thickness

Helium: The Coolant

Firstly created in the Big Bang; Then created as a result of the nuclear fusion of hydrogen in stars.

Rare on earth; Mainly created by the radioactive decay of much heavier elements (alpha particles are helium nuclei).

Trapped with natural gas in concentrations up to 7% by volume, from which it is extracted commercially by fractional distillation.distillation.

ScienceDaily (Jan.5, 2008)Helium Supplies Endangered, Threatening Science And Technology

The element that lifts things like balloons, spirits and voice ranges is being depleted so rapidly in the world's largest reserve, outside of Amarillo, Texas, that supplies are expected to be

depleted there within the next eight years.

“All should make better efforts to recycle it."

Low temperature measurements are carried out in 3He – 4He Dilution Refrigerator

3He concentration (%)

0.0 .2 .4 .6 .8 1.0

Tem

pera

ture

(K

)

0.0

.5

1.0

1.5

2.0

Normal 3He/4Heλ line

Superfluid 3He/4He

Two-phase region

(Bath) 4.2K

(1K pot) 1.5K

(Still pot) 0.6K

(50mK/100mK stage) 0.1K

(Mixing chamber) 0.02K

He concentration (%)

Low temperature measurements are carried out in 3He – 4He Dilution Refrigerator

For our Dilution Refrigerator

Base Temperature (Tmin) : 40mK (It takes ~12 hours to reach Tmin from 600mK)

Maximum Magnetic Field (B ) : 9T

Transport Measurements:

T-dependence of resistance

B-dependence of resistance

V dependence of I Maximum Magnetic Field (Bmax) : 9T

Provided by superconducting magnets(It takes ~ 12 hours to reach Bmax from 0T without apparent heating to the samples)

Caution

If you do it within 3 hours, heating effect is significant !If you do it within 1 minute, a PHD (short for “Permanent Head Damage” ) may be produced !!

dV/dI dependence of I

Outline1. Lab Tour.




5. A Possible Signature for the Localized Cooper Pairs in B-induced Insulating Phase.

6. Conclusions

Conventional Treatments for 2D Superconductors(Cooper Pairs)

• At low temperatures, lattice-mediated attractive interactions between electrons produce a resistanceless state in which the charge carriers are electron pairs called Cooper pairs (charge 2e bosons).

• Superconducting state can be characterized by the complex order parameter Ψ= Ψ0eiΦ.Here Ψ is a macroscopic wavefunction for the superconducting electrons.electrons.

• Superconductivity is destroyed by either breaking the Cooper pairs or disrupting phase coherence . An insulating state will obtain in either case.

• Phase and particle number are conjugate variables , so their simultaneous measurement is limited by the Heisenberg uncertainty principle .

• Bosons can either be in an eigenstate of particle number or phase : the eigenstate of phase is a superconductor and that of particle number is an insulator.

P. Phillips and D. Dalidovich, Science 302, 243 (2003)

Conventional Treatments for 2D Superconductors(Vortices)

• For thin films, one can experimentally transform a superconductor into an insulator by either (1) decreasing the film thickness or (2) applying a perpendicular magnetic field.(1) Decreasing the thickness increases boundary scattering and hence disorder drives the transition.(2) In the application of a magnetic field, resistive topological excitations called vortices frustrate the onset of global phase coherence.

• If a Cooper pair moves around the vortex, the quantum phase of the system winds by ±2π. Associated with this gradient in the phase is a circulating current much like a whirlpool in an ordinary fluid.

• Vortices and Cooper Pairs are related by a duality transformation. In 2D superconductors this transformation interchanges Cooper Pairs and vortices and maps the insulating and superconducting phases onto each other.

S.M.Girvin, Science 274, 524 (1996)

Conventional Treatments for 2D Superconductors(“Dirty Bosons” Model Proposed by M. P. A. Fisher)

Superconducting Phase:A condensate of Cooper pairs with localized vortices

free “Cooper pair” localized “vortex” localized “antivorte x”

Insulating Phase:A condensate of vortices with localized Cooper pairs

localized “Cooper pair” free “vortex” free “antivortex”

+ +

Conventional Treatments for 2D Superconductors(General Conclusion)

Bosonic Picture: (For the strong disorder regime, where quantum fluctuations have the dominant effect)

M. P. A. Fisher, Phys. Rev. Lett. 65, 923 (1990).M. P. A. Fisher, G. Grinstein, and S. M. Girvin, Phys. Rev. Lett. 64, 587 (1990).A. Larkin, Ann. Phys. 8, 785 (1999).

Fermionic Picture: (For the weak disorder regime, where the conductivity is mostlydetermined by the weakly decaying fermionic excitations)

A. Finkelshtein, JETP Lett. 45, 46 (1987).A. Larkin, Ann. Phys. 8, 785 (1999).

General ConclusionThere is no true metallic behavior in 2D supercondu ctors.

The suppression of the superconductivity leads to a direct SIT at T=0.

Outline1. Lab Tour.





6. Conclusions

SIT vs. SMITSuperconductor-Insulator

TransitionSuperconductor-Metal-Insulator

Transition

InO(Bi, Be, MoSi, …)

MoGe

V. F. Gantmakher et al, JETP 71, 160 (2000)

Mason and Kapitulnik, PRL 81, 5342 (1999)

Ta

Y.Qin, C.Vicente, and J.Yoon, PRB 73, 100505(R) (2006)

T (K)0.0 0.1 0.2 0.3

ρ (K

Ω)

0

1

2

3

0 T

0.46 T0.27 T0.21 T0.16 T0.13 T0.06 T

Ta

I (µA)-0.5 0.0 0.5

dV/d

I (K

Ω)

8

10

12

14

16

0.46 T0.27 T0.16 T

(b)

M-I boundary2

20

d V

dI<

2

0d V >

ρ (K

Ω)

1

2

3

0.46 T0.27 T0.21 T0.16 T0.13 T0.06 T

Nonlinear I-V Characteristics in Three Different Ph ases

Insulating phase 0d

dT

ρ <

( )finiteρ =Metallic phase

20

dI>

I (µA)0.0 0.5 1.0

V (

mV

)

0

5

10

15

I (µA)-0.5 0.0 0.5

V (

mV

)

-5

0

5

20 mKB = 0.06 T 20 mK

B = 0

dV/d

I (K

Ω)

(a)

S-M boundary

hysteretic I V−

T (K)0.0 0.1 0.2 0.3

00 T

0.06 T

Superconducting phase ( )0ρ =

Q: Is the metallic phase real? Can it be due to electron heating?

A: The Metallic Phase Is Real!

10-1 Ta 30.5 K

Ta 3 0.5 K102

Strong increase of PcSmooth evolution across S-M boundary

I (µA)7 15 2010

V (

V)

10-4

10-3

10-2

0.10 T0.05 T0.02 T

0.5 K

(Ic, Vc)

0.5 K

B (T)0.00 0.05 0.10

Pc

(nW

)

101

102

Y. Seo, Y. Qin, C. Vicente, K. Choi and J. Yoon, Phys. Rev. Lett. 97, 057005 (2006)

Proposed Origins for the Metallic Phase

• Bosonic interactions in the nonsuperconducting phaseD. Dalidovich and P. Phillips, Phys. Rev. B 64, 052507 (2001)

D. Dalidovich and P. Phillips, Phys. Rev. Lett. 89, 027001 (2002)

• Contribution of fermionic quasiparticles to the conductionV. M. Galitski, G. Rafeal, M. P. A. Fisher, and T. Senthil, Phys. Rev. Lett. 95, 077002 (2005)V. M. Galitski, G. Rafeal, M. P. A. Fisher, and T. Senthil, Phys. Rev. Lett. 95, 077002 (2005)

• Quantum phase fluctuationD. Das and S. Doniach, Phys. Rev. B 60, 1261 (1999)

D. Das and S. Doniach, Phys. Rev. B 64, 134511 (2001)M. V. Feigelman and A. I. Larkin, Chem. Phys. 235, 107 (1998)B. Spivak, A. Zyuzin, and M. Hruska, Phys. Rev. B 64, 132502 (2001)

An agreement is yet to be achieved!

Outline1. Lab Tour.





6. Conclusions

Superconducting-Metallic Phases Boundary

V vs. I (T=0.10K)

0.04

0.05

Superconducting - Metallic Phases Boundary

0.10

0.12

0.140.15 T0.14 T0.13 T0.12 T0.11 T

I(µA)

6.5 7.0 7.5 8.0 8.5 9.0 9.5

V(V

)

0.00

0.01

0.02

0.03

T(K)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

B(T

)0.00

0.02

0.04

0.06

0.08

0.100.11 T0.10 T0.09 T0.08 T

SuperconductingPhase

Quantum Metal, Insulator, and Normal Metal “Phases” Boundaries

dV/dI vs. I (B=0.6T)

6.6

6.8

7.0

7.2

dV/dI vs. I (B=6T)

7.56

7.58

7.60

7.62

0.20K0.26K0.32K0.42K0.52K

I(µA)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

dV/d

I(K

Ω)

5.6

5.8

6.0

6.2

6.4

6.6

1.00K0.62K0.50K0.42K0.36K0.32K0.28K

I(µA)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5dV

/dI(

KΩ

)7.46

7.48

7.50

7.52

7.54

7.56 0.52K

Identifying the Boundaries Quantitatively

• We found that the measured differential IV can be fitted to a quadratic form,

dV/dI=a(I-b)2+c, where “a”, “b” & “c” are fitting parameters.

dV/dI vs. I (B=0.6T)

dV/d

I(K

Ω)

5.6

5.8

6.0

6.2

6.4

6.6

6.8

7.0

7.2

1.00K0.62K0.50K0.42K0.36K0.32K0.28K

• The sign of parameter “a” can be used to identify phases:a>0: quantum metallic phasea<0: insulating phase

a=0 (or a≈0): normal metal phase

I(µA)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.55.6

dV/dI vs. I (B=6T)

I(µA)

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

dV/d

I(K

Ω)

7.46

7.48

7.50

7.52

7.54

7.56

7.58

7.60

7.62

0.20K0.26K0.32K0.42K0.52K

Stephanie’s former Brute force approach on data analysis.

Stephanie’s C program helps her to achieveunbelievable efficiency boost on data analysis&& makes the analyzing process much moreenjoyable.

Phase Diagrams on B-T plane

0.4

0.5

0.8

1.0

10

Sample 1 (high disorder)Norminal film thickness : 4.1nmNormal state sheet resistivity : 2.3KΩTc (B=0) : 0.26K

Sample 2 (low disorder)Norminal film thickness: 5.6nmNormal state sheet resistivity: 1.4KΩTc (B=0) : 0.65K

T(K)

0.0 0.1 0.2 0.3 0.4

B(T

)

0.0

0.1

0.2

0.3

0.0 0.1 0.2 0.3 0.4

0.01

0.1

1

10

T(K)

0.0 0.2 0.4 0.6 0.8

B(T

)

0.0

0.2

0.4

0.6

0.0 0.2 0.4 0.6 0.8

0.01

0.1

1

Phase Diagram in B-T-Disorder Space

• Outstanding questions to be answered:A. Nature of the Metal-Insulator Transition ?B. The Fate of Kosterlitz-Thouless Transition ?C. Is There Disorder-Induced Metallic Phase ?

Insulator

B

AA

T

disorder

Insulator

QuantumMetal

SC

normal metal(linear I-V)

AA

BBCC

A. Nature of the Metal-Insulator Transition ?Percolation Type

dV/d

I (K

Ω) 6.0

6.1

6.2

6.3

T = 60 mKAt B < Bc, isolated insulating puddles exist in the background of the metallic region and d2V/dI2 > 0 at all currents.

At B ≳ Bc, the sign of d2V/dI2 changes with increasing bias current because of narrow insulating gaps in the current flow path.

I (µA)-5 0 5

dV/d

I (K

5.6

5.7

5.8

5.9At B >> Bc, where isolated puddles of metallic phase exist in the background of the insulating region, d2V/dI2 < 0 at all currents.

C.Vicente, Y.Qin, and J.Yoon, PRB 74, 100507(R) (2006)T

disorder

Insulator

QuantumMetal

SC


B

AA

BBCC

1.30 T1.20 T1.15 T1.10 T1.05 T1.00 T0.95 T0.90 T0.85 T

V(µ

V)

140

150

160

0 1( ) exp( / )V t V V t τ= + −Logarithmic dependence

B. The Fate of Kosterlitz-Thouless Transition ?Vortex Pinning-Depinning Transition

τ (se

c)

0

2

4

6

8

I (A)10-6 10-5

dLog

(V)/

dLog

(I)

0

20

40

60

80

0 G

0.984 K0.988 K0.990 K0.992 K0.994 K1.000 K

B

time

Vol

tage

Cur

rent

t(sec)0 2 4 6 8I (A)

10-6 10-5

0

T

disorder

Insulator

QuantumMetal

SC


B

AA

BBCC

Y. Seo, Y. Qin, C. Vicente, K. Choi and J. Yoon, PRL 97, 057005 (2006)

K. Medvedyeva, B. Kim, and P. Minnhagen, PRB 62, 14531 (2000)

C. Is There Disorder-Induced Metallic Phase ?Probably Yes !

So far, the B=0 quantum metal phase, which is induced by disorderrather than B, has not been reported in amorphous superconducting films.

T

disorder

Insulator

QuantumMetal

SC


B

AA

BBCC

Outline1. Lab Tour.





6. Conclusions

Magnetoresistance (MR) Measurements

R(K

Ω)

6

8

MoSi(InO, Bi) Ta

60 mK

B(T)

0 2 4 6 8

R(K

0

2

4

Negative MR is not Sample – Independent.

S. Okuma et al, PRB 58, 2816 (1998)

The Peak Structure of Differential IV Traces in Insulating Phase Displays a Non-Monotonic Change as a Function of B

I(µA)

-1.0 -0.5 0.0 0.5 1.0

dV/d

I(kΩ

)

7.0

7.2

7.4

7.6

7.8

B(T)

0 2 4 6 8 10

a

-10

-8

-6

-4

-2

0

7.8-0.4-0.2

(a) 0.06 K

(c) 0.15 K

(b) 0.06 K

(d) 0.15 K

dV/dI = a (I - b)2 + c

9.00 T1.50 T1.20 T1.00 T0.90 T0.85 T

9.00 T

Voice of“Localized Cooper Pair”

I(µA) B(T)

I(µA)

-1.0 -0.5 0.0 0.5 1.0

dV/d

I(kΩ

)

7.0

7.2

7.4

7.6

B(T)

0 2 4 6 8 10

a-1.8-1.6-1.4-1.2-1.0-0.8-0.6-0.4

I(µA)

-1.0 -0.5 0.0 0.5 1.0

dV/d

I(kΩ

)

7.1

7.2

7.3

7.4

7.5

7.6

7.7

B(T)

0 2 4 6 8 10

a

-0.16-0.14-0.12-0.10-0.08-0.06-0.04-0.020.00

(c) 0.15 K

(e) 0.25 K

(d) 0.15 K

(f) 0.25 K

dV/dI = a (I - b)2 + c

dV/dI = a (I - b)2 + c

9.00 T2.00 T1.30 T1.10 T0.95 T0.90 T

9.00 T1.50 T1.20 T1.05 T0.90 T0.85 T

1. Real metallic behavior is observed in amorphous T a thin films.

2. Phase diagrams we have mapped for 2 samples indic ate that the superconducting phase is completely surrounded by the metallic phase on B -T plane. By studying samples with metallic phase on B -T plane. By studying samples with various disorders, we can map out the 3D phase diag ram in B-T-disorder space.

3. A sample – independent signature for the localized Cooper pairs in insulating phase might be in nonlinear tra nsport characteristics, instead of in negative MR.

the mysterious metallic phase in 2d superconductors and ... · 3. unexpected metallic phase in...

Documents