1 The Peak Effect Gautam I. Menon IMSc, Chennai, India.
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Transcript of 1 The Peak Effect Gautam I. Menon IMSc, Chennai, India.
1
The Peak Effect
Gautam I. Menon
IMSc, Chennai, India
2
Type-II Superconductivity
Structure of a vortex line
The mixed (Abrikosov) phase of vortex lines in a type-II
superconductor
The peak effect is a propertyof dynamics in the mixed
phase
3
How do vortex lines move under the action of an external force?
How are forces exerted on vortex lines?
4
Lorentz Force on Flux Lines
Magnetic pressureTension along lines of force
Force/unit volume
Local supercurrent density Local induction
5
Dissipation from Line MotionViscous forces oppose
motion, damping coefficient lines move with velocity v
Competition of applied and viscous forces
yields a steady state, motion of vortices
produces an electric field
Power dissipation from EJ, thus nonzero
resistivity from flux flow
6
Random Pinning Forces
• To prevent dissipation, pin lines by quenched random disorder
• Line feels sum of many random forces
• Summation problem: Adding effects of these random forces.
How does quenched randomness affect the crystal?
7
Elasticity and Pinning compete
In the experimental situation, a random potential from pinning sites
The lattice deforms to accommodate to the pinning, but pays elastic energy
Pinning always wins at the largest length scales: no translational long-range order (Larkin)
8
Depinning
• From random pinning: critical force to set flux lines into motion
• Transition from pinned to depinned state at a critical current density
• Competition of elasticity, randomness and external drive
9
The Peak Effect
The Peak Effect refers to thenon-monotonic behavior of
the critical force/currentdensity as H or T are varied
Critical force to set the fluxline system into motion
10
How is this critical force computed?
11
Larkin Lengths
• At large scales, disorder induced relative displacements of the lattice increase
• Define Larkin lengths
12
Estimating Jc
Larkin and Ovchinnikov
J. Low Temp. Phys 34 409
(1979)
Role of the Larkin
lengths/Larkin Volume
collective pinning theory
Pinning induces Larkin domains. External drive balances gain from domain formation.
13T.G. Berlincourt, R.D. Hake and D.H. Leslie
No peak effect
14
Surface Plot of jc
The peak effect in
superconducting response
Rise in critical currents implies
a drop in measured resistivity
15
Why does the peak effect occur?
Many explanations …
16
The Pippard Mechanism• Pippard: Softer
lattices are better pinned [Phil. Mag. 34 409 (1974)
• Close to Hc2, shear modulus is vastly reduced (vanishes at Hc2), so lines adjust better to pinning sites
• Critical current increases sharply
17
PE as Phase Transition?
• Shear moduli also collapse at a melting transition
• Could the PE be signalling a melting transition? (In some systems …)
• Disorder is crucial for the peak effect. What does disorder do to the transition?
18
Peak Effects in ac susceptibility measurements
Dips in the real part of ac susceptibility translate to peaks in the critical current
Sarkar et al.
19
Will concentrate principally on transport measurements
G. Ravikumar’s lecture: Magnetization, susceptibility
20
Peak Effect in Transport: 2H-NbSe2
Fixed H, varying T; Fixed T varying H
Peak effectprobed in resistivity
measurements
21
Nonlinearity, Location
A highly non-linear phenomenon
Transition in relation to Hc2
22
In-phase and out-of-phase response
• Apply ac drive, measure in phase and out-of-phase response
• Dip in in-phase response, peak in out-of-phase response: superconductor becomes more superconducting
• Similar response probed in ac susceptibility measurements
23
Systematics of I-V Curves
I-V curves away from the peak
behave conventionally.
Concave upwards. Such curves are non-trivially different
in the peak regime
24
IV curves and their evolution
Differential resistivityEvolution of dynamics
IV curves are convex upwards in the peak region
Peak in differential resistivity in the peak
region
25
Fingerprint effect• Differential resistivity
in peak regime shows jagged structure
• Reproducible: increase and lower field
• Such structure absent outside the peak regime
• Power-laws in IV curves outside; monotonic differential resistivity
26
Interpretation of Fingerprints?
• A “Fingerprint” of the structure of disorder?
• Depinning of the flux-line lattice proceeds via a series of specific and reproducible near-jumps in I-V curves
• This type of finger print is the generic outcome of the breaking up of the flux-line lattice due to plastic flow in a regime intermediate between elastic and fluid flow (Higgins and Bhattacharya)
27
Noise
• If plastic flow is key, flow should be noisy
• Measure frequency dependence of differential resistivity in the peak region
• Yes: Anomalously slow dynamics is associated with plastic flow. Occurs at small velocities and heals at large velocities where the lattice becomes more correlated.
• A velocity correlation length Lv
28
Dynamic Phase Diagram
• Force on y-axis, thermodynamic parameter on x-axis (non-equilibrium)
• Close to the peak, a regime of plastic flow
• Peak onset marks onset of plastic flow
• Peak maximum is solid-fluid transition
29
Numerical Simulations
• Brandt, Jensen, Berlinsky, Shi, Brass..
• Koshelev, Vinokur• Faleski, Marchetti,
Middleton• Nori, Reichhardt,
Olson• Scalettar, Zimanyi,
Chandran ..
And a whole lot more …
30
Simulations: The General Idea• Interaction – soft
(numerically easy) or realistic
• Disorder, typically large number of weak pinning sites, but also correlated disorder
• Apply forces, overdamped eqn of motion, measure response
• Depinning thresholds, top defects, diff resistivity, healing defects through motion,
• Equilibrium aspects: the phase diagram
31
Numerical Simulations
Depinning as a function of pinning strengths. Differential resistivity
Faleski, Marchetti, Middleton: PRE (1996)
Bimodal structure of velocity distributions: Plastic flow
32
FMM: Velocity Distributions
Velocity distributions appear to have two components
33
Chandran, Zimanyi, Scalettar (CZS)
More realistic models for interactions
Defect densities Hysteresis
Dynamic transition in T=0 flow
34
CSZ: Flow behaviour
Large regime of Disordered flow
All roughly consistent with the physical ideas of
the dominance of plasticity at depinning
35
Dynamic Phase Diagram
• Predict a dynamic phase transition at a characteristic current
• Phase at high drives is a crystal
• The crystallization current diverges as the temperature approaches the melting temperature
• Fluctuating component of the pinning force acts like a “shaking temperature”
Koshelev and Vinokur, PRL(94).. Lots of later work
36
Simulations: Summary
• We now know a lot more about the depinning behaviour of two-dimensional solids in a quenched disorder background.
• Variety of new characterizations from the simulations of plastic flow phenomena
• Dynamic phase transitions in disordered systems
• Yet .. May not have told us much about the peak effect phenomenon itself
37
Return to the experiments
38
History Dependence in PE region
Critical Currents differ between FC and ZFC routes
Henderson, Andrei, Higgins, Bhattacharya
Two distinct states of the flux-line lattice, one relatively ordered one highly disordered. Can anneal the disordered state into the ordered
one
39
Peak Effect vs Peak Effect Anomalies
The Peak Regime
Tpl Tp
Let us assume that the PE is a
consequence of an order-disorder transition in the flux line system
Given just this, how do we understand the
anomalies in the peak regime?
40
Zeldov and collaborators: Peak Effect anomalies as a consequence of the
injection of a meta-stable phase at the sample boundaries and annealing within
the bulk
Boundaries may play a significant role in PE physics
41
The Effects of Sample Edges
• Role of barriers to flux entry and departure at sample surfaces
• Bean-Livingston barrier• Currents flow near
surface to ensure entry and departure of lines
• Significant dissipation from surfaces
42
Corbino geometry:Zeldov and collaborators
Surface effects can be
eliminated by working in a
Corbino geometry. Peak effect sharpens, associated with
Hp
43
Relevance of Edges
• Both dc and ac drives• Hall probe
measurements• Measure critical
currents for both ac and dc through lock-in techniques
• Intermediate regime of coexistence from edge contamination
44
Direct access to currents
• Map current flow using Maxwells equations and measured magnetic induction using the Hall probe method
• Most of the current flows at the edges, little at the bulk
• Dissipation mostly edge driven?
46
Andrei and collaborators
• Start with ZFC state, ramp current up and then down
• Different critical current ..
• “Jumpy” behavior on first ramp
• Lower threshold on subsequent ramps
47
Plastic motion/Alternating Currents
• Steady state response to bi-directional pulses vs unidirectional pulses
• Motion if bi-directional current even if amplitude is below the dc critical current
• No response to unidirectional pulses
Henderson, Andrei, Higgins
48
Memory and Reorganization I
Andrei group
49
Memory and Reorganization II
Response resumes
where it left off
Andrei group
50
Generalized Dynamic Phase Diagram
More complex intermediate “Phases” in a
disordered system under
flow
51
Reentrant Peak Effect
• Reentrant nature of the peak effect boundary at very low fields
• Connection to reentrant melting?
• See in both field and temperature scans
• Later work by Zeldov and collaborators
TIFR/BARC/WARWICK/NEC COLLABORATION
52
Phase Behaviour: Reentrant Melting
54
The phase diagram angle
and a personal angle ….
55
Phase Behaviour of Disordered Type-II superconductors
The ordered phase
The disordered phase
The conventionalview
57
Phase Behaviour in the Mixed Phase
The conventional picture An alternative view
58
Properties of the Phase Diagram
• Peak effect associated with the sliver of glassy phase which is the continuation of the high field glassy state to low fields
• Domain-like structure in the intermediate (multi-domain) state
• Domains can be very large for weak disorder and high temperature
• A generic two-step transition
Lots of very suggestive data from TIFR/BARC etc
59
The Last Word ..
• Alternative approaches: Critical currents may be dominated by surface pinning, effects of surface treatment (Simon/Mathieu). PE seems to survive, though
• How to compute the transport properties of the multi-domain glass?
• If the Zeldov et al. disordered phase injection at surfaces scenario is correct, what about the simulations?
• More theory which is experiment directed• Other peak effects without transitions?