Quantum Tunneling of Normal-Superconductor Interfaces in a Type-I Superconductor
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Transcript of 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).
2.1 Topological hysteresis and pinning
2.1 Topological hysteresis and pinning
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)
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.
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
. u
nits
)
h
2.1 Topological hysteresis and pinning
Topological equilibrium?
0.0 0.1 0.2 0.3
-0.6
-0.4
-0.2
0.0
0.2
Solid simbols: M(H) loopOpen simbols: FC data
m (
arb
. u
nits
)
h
Enhanced irreversibility along the descending branch due to the existence of defects.
Pinning of Normal-Superconductor Interfaces!
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.
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
S. Vélez et al., arxiv:cond-mat.suprcon/1105.6218
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
Solid simbols: M(H) loopOpen simbols: FC data
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
Solid simbols: M(H) loopOpen simbols: FC data
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
Solid simbols: M(H) loopOpen simbols: FC data
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).
S. Vélez et al., arxiv:cond-mat.suprcon/1105.6222
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
S Vélez et al., arxiv:cond-mat.suprcon/1105.6222
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?
S Vélez et al., arxiv:cond-mat.suprcon/1105.6222
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
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