Disordered Elastic Systems T. Giamarchi - - PowerPoint PPT Presentation

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Disordered Elastic Systems T. Giamarchi - - PowerPoint PPT Presentation

Jun 02, 2023 115 likes •515 views

Disordered Elastic Systems T. Giamarchi http://dqmp.unige.ch/gr_giamarchi/ E. Agoritsas (Geneva) S. Lemerle (Orsay) S. Barnes (Miami U.) J. Ferr (Orsay) S. Bustingorry (Bariloche) J.P. Jamet (Orsay) D. Carpentier (ENS Lyon) V. Jeudy

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SLIDE 1

Disordered Elastic Systems

  • T. Giamarchi

http://dqmp.unige.ch/gr_giamarchi/

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SLIDE 2
  • E. Agoritsas (Geneva)
  • S. Barnes (Miami U.)
  • S. Bustingorry (Bariloche)
  • D. Carpentier (ENS Lyon)
  • P. Chauve (Orsay/ENS)
  • R. Chitra (ETHZ)
  • L. Cugliandolo (Jussieu)
  • J. P. Eckmann (Geneva)
  • L. Foini (Geneva)
  • A. Kolton (Bariloche)
  • W. Krauth (ENS)
  • V. Lecomte (Jussieu)
  • P. Le Doussal (ENS)
  • E. Orignac (ENS)
  • A. Rosso (LPTMS)
  • G. Schehr (LPTMS)
  • S. Lemerle (Orsay)
  • J. Ferré (Orsay)

J.P. Jamet (Orsay)

  • V. Jeudy (Orsay)

J.M. Triscone (Geneva)

  • P. Paruch (Geneva)
  • T. Tybell (Trondheim)
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SLIDE 3

General References

Domain walls:

  • E. Agoritsas, V. Lecomte, TG,

Arxiv:1111.4899, Physica B 407 1725 (2012) Disordered Elastic Media: TG, Encyclopedia of Complexity and Systems Science (Springer)

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SLIDE 4

Common denominator of:

Superconductor Ferroelectric Magnet Contact line

I V

Two dimensional electron gas

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SLIDE 5

Basic Features

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SLIDE 6

Very difficult stat-mech problem

  • Optimization :

many solutions

Glass !

E

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SLIDE 7

What to measure (statics)

2

( ) [ ( ) (0)] B r u r u  

Amplitude: new questions (Calabrese, Le Doussal, Quastel, etc.)

  • E. Agoritsas et al. PRE 87 042406 (13)

Positional order

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SLIDE 8
  • S. Lemerle et al. PRL

80 849 (98)

u L

Theory:  = 2/3

Magnetic systems

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SLIDE 9

Dynamics

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SLIDE 10

+ 50 m

Dynamics

  • Groupe J. Ferre/J.P. Jamet; Exp: V. Repain
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SLIDE 11

Equation of motion

2

( , ) ( , ) [ ( , )] ( , )

t z pin

u z t c u z t F u z t F z t        

 : friction  : thermal noise

pin ( , )

( , )

x u z t

V x z F x

   

( , ) ( , ) ( ) ( ) z t z t T z z t t            

(x,z)V(x',z') Df(x x') ( z') V z      

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SLIDE 12

Questions for dynamics

  • Disorder = pinning

Large v: Nature of moving phase ? Depinning:

 

c

v F-F

Fc F v T0 T=0 f  0 v = ????

  • Finite temperature probes barriers
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SLIDE 13

2

[ ]

t pin

u c u F u f     

2

ˆ( ....)

ˆ

t

iu u c u

DuDue

   

D

u

Correlator of disorder

How to study microscopically

Study by RG

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SLIDE 14

Usual vs Functional RG

2 4

( ) .... u a bu cu D    

Needs only to keep b and c (higher powers are irrelevant)

  • Disorder: all powers are important

Renormalize the whole function Review: P. Le Doussal + K. Wiese arXiv:cond-mat/0611346

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SLIDE 15

D’’

u

D’’

u

  • Nonanalyticity at a finite lengthscale Rc such that

u(Rc) ~lc

  • Cusp signals metastability and glassy states

(A. Larkin, D. Fisher)

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SLIDE 16

Example: static

  • Periodic system (crystal): D(u) = A cos(u)
  • Fixed point:

 = 0

TG + P. Le Doussal, PRB 52 1242 (95)

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SLIDE 17
  • P. Chauve, T. Giamarchi, P. Le Doussal EPL 44 110 (98);

PRB 62 6241 (2000)

Dynamics from FRG

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SLIDE 18

thermal flat flat depinning

RT Rv

D

u

D

u

D

u

Small force response

Phenomenological derivation: Ioffe + Vinokur; Nattermann

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SLIDE 19

Motion different from phenomenological picture (two regimes)

RT Slow RV

Fast: Avalanche

Thermal activation Depinning like

New lengthscale: avalanches

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SLIDE 20

Tests

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SLIDE 21

Numerical study d=1

Molecular dynamic simulations:

  • A. B. Kolton, A. Rosso, TG, PRL 91 056603 (03)

Exact enumeration algorithm: A.B. Kolton, A. Rosso, TG, W . Krauth PRL 97 057001 (06); PRB 79 184207 (09)

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SLIDE 22

Experiments

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SLIDE 23
  • S. Lemerle et al. PRL 80 849 (98)

(1/ ) B

v e

 

2 2 2 / 3 1/ 4 2 d          

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SLIDE 24

Ferroelectrics

  • P. Paruch et al.

cond-mat/0411178

10 m

  • T. Tybell et al. PRL 89 097601 (02)
  • P. Paruch et al. PRL 94 197601 (05)
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SLIDE 25

Lenthscales

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SLIDE 26
  • V. Repain et al. EPL 68 460 (04)

RT » 1  m

Probing RT and Rv

Rv » 17  m

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SLIDE 27

Probe the lengthscale RT

K.J. Kim et al. Nature 458 540 (09)

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SLIDE 28

Open challenges

 Thermal rounding; Depinning  Out of equilibrium issues (aging)  Defects (overhangs, bubbles)  Quantum systems (bosons, magnets etc.)  Internal degrees of freedom (spintronic etc.)

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SLIDE 29

Thermal rounding; Depinning

  • J. Gorchon et al. PRL (14)
  • S. Bustingorry, A. B.

Kolton, TG, EPL 81 26005 (2008)

Not understood yet !!

( ) 0.15 0.01

c

v F T    

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SLIDE 30

Aging

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SLIDE 31

Out of equilibrium

  • A. B. Kolton, A. Rosso, TG, PRL 95 180604 (05)
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SLIDE 32

Defects

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SLIDE 33

210 m

Pt/Co(0,5 nm)/Pt/SiO2

(V. Repain et al. (Orsay))

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SLIDE 34

Internal degrees of freedom

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SLIDE 35

Wall with internal degree of freedom

  • V. Lecomte, S. Barnes, J.P. Eckmann, TG PRB 80 054413 (09)

Nonlinearity 25 1427 (12)

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SLIDE 36

Rigid wall approximation

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SLIDE 37

Different from standard depinning

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SLIDE 38

Yamanouchi et al. Science 317 1726 (2007); H. Ohno Nature Materials 9 952 (2010)

Drive with magnetic field or current