Quantum Tunneling of Normal-Superconductor Interfaces in a Type-I Superconductor

QUANTUM TUNNELING OF NORMAL-SUPERCONDUCTOR

INTERFACES IN A TYPE-I SUPERCONDUCTOR

J. Tejada, S. Vélez, A. García-Santiago, R. Zarzuela, J.M. Hernández Grup de Magnetisme, Dept. de Física Fonamental, Universitat de BarcelonaGrup de Magnetisme, Dept. de Física Fonamental, Universitat de Barcelona

E. M. ChudnovskyLehman college, City University of New York, New York.

Outline

1. Introduction: 1.1 Type-I superconductivity.

1.2 Intermediate state and flux structures.

1.3 Magnetic irreversibility.

2. Experimental Results:2.1 Topological hysteresis and pinning.

2.2 Thermal and non-thermal behaviors in the magnetic irreversibility.

2.3 Quantum tunneling of Normal-Superconductor interfaces.

2.4 Phase diagram of flux motion in a type-I superconductor.

3. Model: Flattening\Bumping of NSI at the defects

4. Conclusion: A new physical phenomena discovered: QTI

Phase Diagram of a

Normal\Superconductor

1.1 Type-I superconductivity. Basics

])/(1[)( 20 ccc TTHTH

A superconductor, aside to has zero resistance, it is characterized by the Meissner state: In the superconducting state any flux line cannot penetrate inside the sample. Perfect screening of the external applied magnetic field

The superconducting state only can exist below a certain critical temperature T<Tc if any.

However, for strong enough applied magnetic fields H>Hc (or even for strong applied currents), the superconducting state is suppressed.

Magnetic properties

1.1 Type-I superconductivity. Basics

HcH

M

At different temperatures

Hc(T1)HM Hc(T2)Hc(T3)

)(0

)(

THHforM

THHforHM

c

c

Geometry of the sample

Non uniformity of external magnetic field over the space (around the sample)

Free energy reach SC-N transition at certain H’c<Hc

SC-N transition becomes gradual between H’c<H<Hc

Coexistence of SC and N regions: Intermediate state

Hc

H

M Hc’

Hc’ = (1 – N) Hc

1.2 Intermediate state. Geometric effects

N : Demagnetizing factor

Formation of N-SC strips in a plane. First idea introduced by Landau (1938)

1.2 Intermediate state. Magnetic properties

N ~ 1 infinite slab with H applied perpendicular to the surface

N = 1/2 infinite cylinder with H applied perpendicular to the revolution axis

N = 1/3 sphere

N~0 infinite cylinder with H applied parallel to the revolution axis or

infinite slab with H applied parallel to the surface

H

M

-Hc

N ~1 N =1/2 N =1/3 N ~0 H

B

Hc

N ~1 N =1/2 N =1/3 N ~0

)()(

)(1

THHTHforN

HHM

THHforN

HM

ccc

c

Important points:

1) All “new” properties can be described through N

2) Reversible system is expected. Penetration an expulsion of magnetic flux in the intermediate state

should follow same states

Yu. V. Sharvin, Zh. Eksp. Teor. Fiz. 33, 1341 (1957).

1.2 Intermediate state. Flux structures

Magneto-optical imaging of the flux structures formed in the intermediate state: Thin Slabs

Laminar patterns Landau description of the IS

T. E. Faber, Proc. Roy. Soc. (London) A248, 460 (1958).

Applied magnetic field in planeRegular strip patterns!

Applied magnetic field is perpendicular to the plane

Laberinthic patters: Random growth/movement

However, irreversibility was mostly observed in slab-shaped samples when the applied magnetic field was perpendicular to the plane of the surface… WHY?

Would be a correlation between different flux structures observed, magnetization dynamics and the shape of the sample against the direction of the applied magnetic field?

1.3 Magnetic irreversibility. Historical point of view

J. Provost, E. Paumier, and A. Fortini, J. Phys. F: Met. Phys. 4, 439 (1974)

R. Prozorov, Phys. Rev. Lett. 98, 257001 (2007).

1.3 Magnetic irreversibility. Prozorov’s point of view:

Topological hysteresis

Flu

x pe

ne

tratio

n: b

ub

ble

s

Flu

x e

xpu

lsio

n:

lam

ella

eInterpretation: there is a GEOMETRICAL BARRIER

which controls both the penetration and the

expulsion of the magnetic flux in the intermediate

state and is the responsible of both the intrinsic

irreversibility of a pure defect-free samples and

the formation of different flux patterns.

This irreversibility is called TOPOLOGICAL

HYSTESRESIS and vanishes when H tends to 0

R. Prozorov et al., Phys. Rev. B 72, 212508 (2005)

1.3 Magnetic irreversibility. Prozorov’s point of view:

Topological hysteresis

Upper panel, sample with stress defects

Lower panel, defect-free sample

Different thin slab samples of Pb where studied. H was always applied perpendicular to the surface.

Different flux structures appear in the Intermediate

state depending on the history: Tubs/bubbles are

formed during magnetic field penetration and

laberinthic patterns appear upon expulsion

1.3 Topological hysteresis. Suprafroth state

The growth of flux bubbles in the IS in a defect-free sample resembles the behavior of a froth.

Minimation of the free energy when the Suprafroth grows:

tends to 6 interfaces for each bubble:

hexagonal lattice!

2. Experimental Results. Set-up

MPMS SQUID Magnetometer

All magnetic measurements were performed in a commercial

superconducting quantum interference device (SQUID)

magnetometer (MPMS system) which allows to work at

temperatures down to T = 1.80 K and it is equipped with a

continuous low temperature control (CLTC) and enhanced

thermometry control (ETC) and showed thermal stability

better than 0.01 K.

In all measurements the applied magnetic field does not

exceed H = 1 kOe strength.

The samples studied were: a sphere (Ø = 3 mm), a cylinder

(L = 3 mm, Ø = 3 mm) and several disks (L ~ 0.2 mm, Ø = 6

mm) of lead prepared using different protocols (cold rolling,

cold rolling+annealing, melting and fast re-crystallization) and

were studied over different orientations.

2.1 Topologycal hysteresis and pinning

S Vélez et al., Phys. Rev. B 78, 134501 (2008).

H

H

The effect of the geometrical barrier strongly depend

on the orientation of the applied magnetic field with

respect to the sample geometry.

Topological irreversibility appears in disk (cylinder)-

shaped samples only when the applied magnetic

field is parallel to the revolution axis.

h = Ø = 3 mm

t = 0.2 mm, S = 40 mm2

same as B, annealed(glycerol, 290ºC, 1h, N2)

Ø = 3 mm

A

B

C

D

H

-750 -500 -250 0 250 500 750

-1.0

-0.5

0.0

0.5

1.0 Sample ASample BSample CSample D

M/M

max

H (Oe)

No zero M when H0

Defects are the reason for the observation of a remnant

magnetization at zero field. Enhancement of the

irreversibility of the system.

2.1 Topological hysteresis and pinning

S Vélez et al., Phys. Rev. B 78, 134501 (2008).

h = Ø = 3 mm

t = 0.2 mm, S = 40 mm2

same as B, annealed(glycerol, 290ºC, 1h, N2)

Ø = 3 mm

A

B

C

D

H

Non-annealed sample exhibit higher remnant flux. Defects

enhance the capability of the system to trap magnetic flux

-750 -500 -250 0 250 500 750

-1.0

-0.5

0.0

0.5

1.0 Sample ASample BSample CSample D

M/M

max

H (Oe)

Non zero M when H0

In conclusion, defects act as a pinning centers that avoids the

complete expulsion of the magnetic flux as is expected in the

defect-free case.-800 -600 -400 -200 0 200 400 600 800

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

Sample BT = 3 K

M (

em

u)

H (Oe)

H

Parallel configuration. No irreversibility

Absence of vortices: No type-II

superconductivity

The resemblances of domain walls in ferromagnets and the

movement on Normal-Superconductor Interfaces in type-I

superconductors points to pinning of NS interfaces at the

defects

Schematic view of the texture of a NS Interface in presence of structural defects. Around the defects, a bump in the NS Interface could be generated. For a strong enough

pinning potential, the interface must not move freely through the sample when the external magnetic field, H, is swept:

Enhancement of the magnetic irreversibility of the system.

E. M. Chudnovsky et al., Phys. Rev. B 83, 064507 (2011).



M(H) data of a disk with stress defects.

Effect of pinning potentials upon expulsion?

0.0 0.1 0.2 0.3 0.4 0.5 0.6

-0.6

-0.4

-0.2

0.0

0.2

Solid simbols: M(H) loopOpen simbols: FC data

m (

arb.

uni

ts)

h

Topological equilibrium Points correspond to

the FC data, whereas line is the whole M(H) cycle

obtained

REMEMBER

R. Prozorov et al., Phys. Rev. B 72, 212508 (2005)




0.0 0.1 0.2 0.3 0.4 0.5 0.6

-0.6

-0.4

-0.2

0.0

0.2


m (

arb

. u

nits

)

h


Topological equilibrium?

0.0 0.1 0.2 0.3

-0.6

-0.4

-0.2

0.0

0.2


m (

arb

. u

nits

)

h

Enhanced irreversibility along the descending branch due to the existence of defects.

Pinning of Normal-Superconductor Interfaces!




M(H) data of a disk with stress defects.

Effect of pinning potentials upon expulsion?

cc HHhHMm //

The magnetic properties of any reversible type-I superconductor scale with the thermodinamical crytical field Hc. Using the so-called reduced magnitudes:

S. Vélez et al., arxiv:cond-mat.suprcon/1105.6218

2.2 Magnetic irreversibility at different temperatures

all the M(H) curves measured at different temperatures collapses in a single m(h) curve.

Actually, the magnetic properties of an irreversible sample are also related to Hc. Therefore, any deviation between the different (and hysteretic) m(h,T) curves should be related to other thermal effects than those

related to Hc.

A defect-free sample does not exhibit thermal effects in the magnetic irreversibility.

The topological hysteresis is thermally

independent!

Equivalent flux structures should be

formed for a given h-1.0 -0.5 0.0 0.5 1.0-1.0

-0.5

0.0

0.5

1.0

2.00 K 3.00 K 4.00 K 5.00 K 6.00 K

m

h

Cylinder Pb

H


0.0 0.2 0.4 0.6

-0.6

0.0

0.6

4.5 K 5.0 K 5.5 K 6.0 K

2.0 K 2.5 K 3.0 K 3.5 K 4.0 K

m

h

All curves stick togheter during penetration

Thermaly dependent upon flux expulsion

1) Thermal dependencies appear only during flux expulsion.

2) Flux penetration is quite similar for all samples and resembles how must be the defect free one

3) At fixed T, irreversibility increases from (a) to (c) in accordance with the expected strength of the pinning potentials

4) For a given sample, as higher T is, smaller the irreversibility becomes.

Thermal effects should be related to the thermal activation of the NSI when they are pinned by the defects.

The pinning potentials should follow an inverse functionality with h

2.2 Magnetic irreversibility at different temperatures.

FC data

-1.0

-0.5

0.0

0.5

1.0

-1.0

-0.5

0.0

0.5

1.0

-1.0 -0.5 0.0 0.5 1.0

-1.0

-0.5

0.0

0.5

1.0

m

(a)

4.5 K 5.0 K 5.5 K 6.0 K

2.0 K 2.5 K 3.0 K 3.5 K 4.0 K

(b)

m

4.5 K 5.0 K 5.5 K 6.0 K

2.0 K 2.5 K 3.0 K 3.5 K 4.0 K

(c)

m

h

4.5 K 5.0 K 5.5 K 6.0 K

2.0 K 2.5 K 3.0 K 3.5 K 4.0 K

Annealead disk

Cold rolled disk

Recristalized disk

H

H

H

2.3 Magnetic relaxation experiments. Basics.

One simple experiment to test the metastability of a system: Magnetic relaxation

0.0 0.1 0.2 0.3 0.4 0.5 0.6

-0.6

-0.4

-0.2

0.0

0.2


m (

arb.

uni

ts)

h

1

2

1

2

1) We keep T fixed and we apply H>Hc. Then the magnetic field is reduced to a desired H and

subsequently, the time evolution of the magnetic moment, M(t), is recorded .

2) Keeping constant h, the temperature is increased above Tc and then reduced to a desired T.

When it is reached, time evolution of the magnetic moment, M(t) is recorded

2.3 Magnetic relaxation experiments. Basics.

One simple experiment to test the metaestability of a system: Magnetic relaxation

0.0 0.1 0.2 0.3 0.4 0.5 0.6

-0.6

-0.4

-0.2

0.0

0.2


m (a

rb.

un

its)

h

1

2

1

1 (Metastable state) relax towards 2 (stable state).

We can study the magnetic viscosity at several points along Mdes (h) and repeat the process at different T

1

2

0.0 0.1 0.2 0.3-0.2

0.0

0.2


m (

arb

. u

nits

)

h

1 Metastable states

2 Stable states

2.3 Magnetic relaxation experiments: Magnetic viscosity S.

1

2

1

This law is followed for any system which has a broad distribution of energy barriers as the sources of both the metastability and any normalized magnetic relaxation rate

obtained, S.

5 6 7 8

0.84

0.88

0.92

0.96

1.00

Mirr (

t)/M

irr (

0)

ln [t (s)]

2.0 K 2.5 K 3.0 K 3.5 K 4.0 K 4.5 K 5.0 K 5.5 K 6.0 K 6.5 K 7.0 K

From the slope S

2.3 Magnetic relaxation experiments: Quantum tunneling.

1

2

5 6 7 8

0.84

0.88

0.92

0.96

1.00

Mirr (

t)/M

irr (

0)

ln [t (s)]

2.0 K 2.5 K 3.0 K 3.5 K 4.0 K 4.5 K 5.0 K 5.5 K 6.0 K 6.5 K 7.0 K

2 3 4 5 6 70.000

0.001

0.002

0.003

0.004

0.005

S

T (K)

S tends a finite non-zero value when T0

Quantum tunneling of the Normal-Superconducting interfaces!

E. M. Chudnovsky, S. Velez, A. Garcia-Santiago, J.M. Hernandez and J. Tejada, Phys. Rev. B 83, 064507 (2011).


5 6 7 8

0.980

0.984

0.988

0.992

0.996

1.000

h = 0.323h = 0.296h = 0.269h = 0.242h = 0.215h = 0.188h = 0.161h = 0.134h = 0.108h = 0.081h = 0.054h = 0.027

mir

r(t)/

mir

r(0)

ln[t(s)]5 6 7 8

0.984

0.988

0.992

0.996

1.000

T = 3.60 KT = 3.30 KT = 3.00 KT = 2.70 KT = 2.40 KT = 2.10 KT = 1.80 K

T = 6.60 KT = 6.30 KT = 6.00 KT = 5.70 KT = 5.40 KT = 5.10 KT = 4.80 KT = 4.50 KT = 4.20 KT = 3.90 K

mirr(t

)/m

irr(0

)

ln[t(s)]

2.3 Magnetic relaxation experiments. Quantum tunneling.

Perfect logarithmic time dependence of M(t) for several T and h

S Vélez et al., arxiv:cond-mat.suprcon/1105.6222

2.3 Magnetic relaxation experiments. Quantum tunneling.

2 3 4 5 6 70.000

0.003

0.006

0.009

0.012(a)

h = 0.00h = 0.10h = 0.15h = 0.20h = 0.25

S

T (K)0.00 0.05 0.10 0.15 0.20 0.25

0.000

0.001

0.002

0.003

0.004

(b)

T = 2.00 KT = 4.00 KT = 5.00 K

S

h

We can identify the transition between two different regimes:

Quantum and thermal regimes

Experimental data suggest that the strength of the pinning potential barriers should follow a decreasing magnetic field dependence.

The phase diagram of the dynamics of NSC Interfaces is developed. It shows the Quasi-free Flux motion, Thermal Activation over the pinning potential as well as the quantum depinning regime


2 3 4 5 6 70.0

0.1

0.2

0.3

0.4

0.5

0.6

Quasi-Free Flux Motion

Thermal Activation

Quantum Tunneling

h*(T) T

Q(h), h

Q(T)

h

T (K)

2.3 Phase diagram of flux motion.

0.4 0.6

-0.4

-0.2

0.0Magnetic irreversibility developsin this region --> h*

4.5 K 5.0 K 5.5 K 6.0 K

2.0 K 2.5 K 3.0 K 3.5 K 4.0 K

m

h

T increase h* decrease

h* onset of the irreversibility) along Mdes

4. Model: Flattening\Bumping of NSI at the deffects

E. M. Chudnovsky et al., Phys. Rev. B 83, 064507 (2011).

Theoretically Experimentally Matching

K 010~)0(

K 5~

B

Q

U

T

nm 1~

~nm 90~

a

L

L increase and a decrease as h increases

TheoreticallyExperimentally

Bumps become flatter!!

4. Model: quantum tunneling of interfaces

2 3 4 5 6 70.0

0.1

0.2

0.3

0.4

0.5

0.6

Quasi-Free Flux Motion

Thermal Activation

Quantum Tunneling

h*(T) T

Q(h), h

Q(T)

h

T (K)

What happen with an applied magnetic field to the bumps?


Decreasing

function

Also a decreasing

function

The intermediate state of type-I superconductors

has been reactivated as an appealing

field of experimental and theoretical research

one century after the discovery of the superconductivity

5. Conclusion

THANK YOU VERY MUCH FOR YOUR KIND ATTENTION!!

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Quantum Tunneling of Normal-Superconductor Interfaces in a Type-I Superconductor