Disordered Elastic s s y t s em e s stems T. Giamarchi h c / h/gr_gi hi/ amarc
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1 Disordered Elastic sstems systems T. Giamarchi h/ i hi/
2 P. Le Doussal (ENS) S. SB Barnes (Miami iu) U.) S. Bustingorry (Bariloche Bariloche) D. Carpentier (ENS Lyon) P. Chauve (Orsay/ENS) R. Chitra (Jussieu) L. Cugliandolo (Jussieu) J. P. Eckmann (Geneva) A. AKl Kolton (Bariloche Bariloche) W. Krauth (ENS) V. Lecomte (Geneva) E. Orignac (ENS) A. Rosso (LPTMS) G. Schehr (ENS) S. Lemerle (Orsay) J. Ferré (Orsay) J.P. Jamet (Orsay) TKli T. Klein (Grenoble) bl) I. Joumard (Grenoble) J.M. Triscone (Geneva) P. Paruch (Geneva/Cornell) T. Tybell (Trondheim)
3 Common denominator of:
4 Common denominator of:
5 Common denominator of: Superconductor
6 Common denominator of: Superconductor
7 Common denominator of: Superconductor Magnet Ferroelectric
8 Common denominator of: Superconductor Magnet Ferroelectric
9 Common denominator of: Superconductor Magnet Ferroelectric
10 Common denominator of: Superconductor Magnet Ferroelectric
11 Common denominator of: Superconductor Magnet Ferroelectric Contact line
12 Common denominator of: Superconductor Magnet Ferroelectric I V Contact line
13 Common denominator of: Superconductor Magnet Ferroelectric I V Contact line Two dimensional electron gas
14 Common denominator of: Superconductor Magnet Ferroelectric I V Contact line Two dimensional electron gas
15 Magnetic domain wall
16 Magnetic domain wall
17 Magnetic domain wall S. Lemerle et al. PRL (98)
18 Vortices in superconductors Magneto-optics NbSe 2 Y. Baselevitch T. Johansen Oslo Bitter decoration NbSe 2 Scanning SQUID Nb C. Veauvy, D. Mailly, & K Hasselbach CRTBT Grenoble M Marchevsky J Aarts P H Kes M. Marchevsky, J. Aarts, P.H. Kes (Kamerlingh Onnes Laboratorium, Leiden University)
19 Two dimensional electron gas V I Strong repulsion : Wigner crystal Quantum fluctuations instead (in addition to) thermal fluctuations
20 Wigner Crystal E.Y. Andrei, et al PRL (1988) R.L. Willett, et al. PRB 38 R7881 (1989)
21 Disordered Elastic Systems Interfaces (magnetic domain walls, ferroelectrics, growth interfaces, contact lines, crack propagation,...) Periodic systems (vortex lattice, Charge density waves, colloids, magnetic bubbles, charges spheres, es,...) Quantum systems (Wigner crystal, Luttinger liquids, Spin density waves,...)
22 Basic Features
23 Basic Features
24 Basic Features
25 Basic Features c Z H = dz( u(z)) ( Z dzv (u(z),z)( )
26 Should we care about disorder
27 Should we care about disorder
28 Should we care about disorder Larkin (1970 ) :Yes!!!
29 Very difficult stat-mech problem
30 Very difficult stat-mech problem
31 Very difficult stat-mech problem
32 Very difficult stat-mech problem
33 Very difficult stat-mech problem Optimization : many solutions
34 Very difficult stat-mech problem Optimization : many solutions Glass!
35 Very difficult stat-mech problem Optimization : many solutions Glass!
36 Very difficult stat-mech problem Optimization : many solutions Glass!
37 Very difficult stat-mech problem Optimization : many solutions Glass!
38 Very difficult stat-mech problem Optimization : many solutions Glass!
39 Very difficult stat-mech problem Optimization : many solutions Glass!
40 Very difficult stat-mech problem Optimization : many solutions Glass!
41 Very difficult stat-mech problem Optimization : many solutions Glass!
42 Questions Competition ``Order / ``Disorder
43 Questions Competition ``Order / ``Disorder Statics (what does it looks like)
44 Questions Competition ``Order / ``Disorder Statics (what does it looks like) Dynamics (how does it responds when one pulls on it)
45 Domain walls
46 What to measure (statics) Br () [() ur u(0)] 2 Positional order
47 Mean field arguments c 2 d Hel ( u( r)) d r 2 V( z, x) V( z', x') D ( x x') ( z z') u H dis V(, r u()) r d d r 2 d 2 cu L 1/2 d/2 m/2 RB urf L 4 d 4 m 4 d L4 m D L u Flory argument (mean field)
48 Magnetic systems u L S. Lemerle et al. PRL (98)
49 Magnetic systems u L S. Lemerle et al. PRL (98)
50 Magnetic systems u L S. Lemerle et al. PRL (98)
51 Magnetic systems u L Theory: = 2/3 S. Lemerle et al. PRL (98)
52 Magnetic systems u L Theory: = 2/3 S. Lemerle et al. PRL (98)
53 How to see it is a glass?
54 How to see it is a glass? Statics ti not a good criterium i (can look ordered!)
55 How to see it is a glass? Statics ti not a good criterium i (can look ordered!) Look at the dynamics
56 + Dynamics 50 m - Groupe J. Ferre/J.P. Jamet; Exp: V. Repain
57 Questions for dynamics Disorder = pinning Finite temperature probes barriers
58 Questions for dynamics Disorder = pinning Finite temperature probes barriers v T 0 Large v: Nature of moving phase? Fc T=0 F Depinning: v v F-FF c
59 Questions for dynamics Disorder = pinning Finite temperature probes barriers v T 0 Large v: Nature of moving phase? Fc T=0 F Depinning: v v F-FF c
60 Questions for dynamics Disorder = pinning Finite temperature probes barriers v T 0 Large v: Nature of moving phase? f 0 v =???? Fc T=0 F Depinning: v v F-FF c
61 Questions for dynamics Disorder = pinning Finite temperature probes barriers v T 0 Large v: Nature of moving phase? f 0 v =???? Fc T=0 F Depinning: v v F-FF c
62 Response to a small force v T 0 T=0 Fc F v e F
63 Response to a small force v T 0 T=0 Fc F TAFF : typical barrier v e F Linear response
64 Response to a small force v T 0 E Fc T=0 F x TAFF : typical barrier v e F Linear response
65 Response to a small force v T 0 E Fc T=0 F x TAFF : typical barrier v e F Linear response
66 Creep Glassy system (L. Ioffe + V. Vinokur; T. Nattermann) c ( ( )) el 2 H () d el Fu r d r 2 d Hel u r d r R d 2 2 cr FR d 2 U ( L ) 2 opt L F v e opt U( L ) opt F d 2 2 2
67 Strong hypothesis
68 Strong hypothesis Barriers scale as minima
69 Strong hypothesis Barriers scale as minima Dominated by tpicalmo typical move
70 Strong hypothesis Barriers scale as minima Dominated by tpicalmo typical move Exponents are equilibrium ones
71 How to study microscopically u c u F u f 2 [ ] t pin 2 t DuDue ˆ iu ˆ( u c u...)
72 How to study microscopically u c u F u f 2 [ ] t pin 2 t DuDue ˆ iu ˆ( u c u...)
73 How to study microscopically u c u F u f 2 [ ] t pin 2 t DuDue ˆ iu ˆ( u c u...)
74 How to study microscopically u c u F u f 2 [ ] t pin 2 t DuDue ˆ iu ˆ( u c u...)
75 How to study microscopically u c u F u f 2 [ ] t pin 2 t DuDue ˆ iu ˆ( u c u...)
76 How to study microscopically u c u F u f 2 [ ] t pin 2 t DuDue ˆ iu ˆ( u c u...)
77 How to study microscopically u c u F u f 2 [ ] t pin 2 t DuDue ˆ iu ˆ( u c u...)
78 How to study microscopically u c u F u f 2 [ ] t pin 2 t DuDue ˆ iu ˆ( u c u...) u
79 How to study microscopically u c u F u f 2 [ ] t pin 2 t DuDue ˆ iu ˆ( u c u...) Correlator of disorder d u
80 How to study microscopically u c u F u f 2 [ ] t pin 2 t DuDue ˆ iu ˆ( u c u...) Correlator of disorder d u
81 How to study microscopically u c u F u f 2 [ ] t pin 2 t DuDue ˆ iu ˆ( u c u...) Correlator of disorder d u Study by RG
82 Usual vs Functional RG
83 Usual vs Functional RG In usual RG : 2 4 ( u ) a bu cu...
84 Usual vs Functional RG In usual RG : 2 4 ( u ) a bu cu... Needs only to keep b and c (higher powers are irrelevant)
85 Usual vs Functional RG In usual RG : 2 4 ( u ) a bu cu... Needs only to keep b and c (higher powers are irrelevant) Disorder: all powers are important
86 Usual vs Functional RG In usual RG : 2 4 ( u ) a bu cu... Needs only to keep b and c (higher powers are irrelevant) Disorder: all powers are important Renormalize the whole function
87 u
88 u u
89 u u Nonanalyticity at a finite lengthscale Rc such that u(rc) ~lc
90 u u Nonanalyticity at a finite lengthscale Rc such that u(rc) ~lc (A. Larkin, D. Fisher) Cusp signals metastability and glassy states
91 u u Nonanalyticity at a finite lengthscale Rc such that u(rc) ~lc (A. Larkin, D. Fisher) Cusp signals metastability and glassy states
92 u u Nonanalyticity at a finite lengthscale Rc such that u(rc) ~lc (A. Larkin, D. Fisher) Cusp signals metastability and glassy states
93 Example: static
94 Example: static Periodic system (crystal): (u) = A cos(u)
95 Example: static Periodic system (crystal): (u) = A cos(u) Fixed point:
96 Example: static Periodic system (crystal): (u) = A cos(u) Fixed point: = 0 TG + P. Le Doussal, PRB (95)
97 Example: static Periodic system (crystal): (u) = A cos(u) Fixed point: = 0 TG + P. Le Doussal, PRB (95)
98 Example: static Periodic system (crystal): (u) = A cos(u) Fixed point: = 0 TG + P. Le Doussal, PRB (95)
99 Creep from FRG
100 Creep from FRG P Chauve T Giamarchi P Le Doussal EPL (98); P. Chauve, T. Giamarchi, P. Le Doussal EPL (98); PRB (2000)
101 Creep from FRG P Chauve T Giamarchi P Le Doussal EPL (98); P. Chauve, T. Giamarchi, P. Le Doussal EPL (98); PRB (2000)
102 Creep from FRG P Chauve T Giamarchi P Le Doussal EPL (98); P. Chauve, T. Giamarchi, P. Le Doussal EPL (98); PRB (2000)
103 Creep from FRG P Chauve T Giamarchi P Le Doussal EPL (98); P. Chauve, T. Giamarchi, P. Le Doussal EPL (98); PRB (2000)
104 Creep from FRG P Chauve T Giamarchi P Le Doussal EPL (98); P. Chauve, T. Giamarchi, P. Le Doussal EPL (98); PRB (2000)
105 Dynamics: rounding of cusp thermal RT depinning Rv flat u
106 Dynamics: rounding of cusp thermal RT depinning Rv flat u u
107 Dynamics: rounding of cusp thermal RT depinning Rv flat u u u
108 Dynamics: rounding of cusp thermal RT depinning Rv flat u u u
109 Dynamics: rounding of cusp thermal RT depinning Rv flat u u u
110 Dynamics: rounding of cusp thermal RT depinning Rv flat u u u
111 New lengthscale: avalanches Motion different from phenomenological picture (two regimes) R T Thermal activation i
112 New lengthscale: avalanches Motion different from phenomenological picture (two regimes) R T Slow Thermal activation i
113 New lengthscale: avalanches Motion different from phenomenological picture (two regimes) R T Slow Thermal activation i
114 New lengthscale: avalanches Motion different from phenomenological picture (two regimes) R T Slow Thermal activation i
115 New lengthscale: avalanches Motion different from phenomenological picture (two regimes) R T Slow Thermal activation i
116 New lengthscale: avalanches Motion different from phenomenological picture (two regimes) R T R V Slow Thermal activation i
117 New lengthscale: avalanches Motion different from phenomenological picture (two regimes) R T R V Slow Thermal activation i
118 New lengthscale: avalanches Motion different from phenomenological picture (two regimes) R T R V Slow Thermal activation i
119 New lengthscale: avalanches Motion different from phenomenological picture (two regimes) R T R V Slow Thermal activation i Fast: Avalanche Depinning i like
120 New lengthscale: avalanches Motion different from phenomenological picture (two regimes) R T R V Slow Thermal activation i Fast: Avalanche Depinning i like
121 New lengthscale: avalanches Motion different from phenomenological picture (two regimes) R T R V Slow Thermal activation i Fast: Avalanche Depinning i like
122 Numerical study d=1
123 Numerical study d=1 Molecular dynamics simulations
124 Numerical study d=1 Molecular dynamics simulations A. B. Kolton, A. Rosso, TG, PRL (03)
125 Numerical study d=1 Molecular dynamics simulations A. B. Kolton, A. Rosso, TG, PRL (03) A. B. Kolton, A. Rosso, TG, cond-mat/
126 Numerical study d=1 Molecular dynamics simulations A. B. Kolton, A. Rosso, TG, PRL (03) A. B. Kolton, A. Rosso, TG, cond-mat/
127 Numerical study d=1 Molecular dynamics simulations A. B. Kolton, A. Rosso, TG, PRL (03) A. B. Kolton, A. Rosso, TG, cond-mat/
128 Numerical study d=1 Molecular dynamics simulations A. B. Kolton, A. Rosso, TG, PRL (03) A. B. Kolton, A. Rosso, TG, cond-mat/
129
130
131
132 Experiments
133 Vortex Lattice Bragg glass: V e (1/ J) RM 0.5 BrG D.T. Fuchs et al. PRL (98) C. Van der Beek et al. cond-mat
134 S. Lemerle et al. PRL (98) v e (1/ B) d 2 2 2/3 1/4 2
135 S. Lemerle et al. PRL (98) v e (1/ B) d 2 2 2/3 1/4 2
136 S. Lemerle et al. PRL (98) v e (1/ B) d 2 2 2/3 1/4 2
137 Ferroelectrics P Par ch et al P. Paruch et al. cond-mat/
138 Ferroelectrics P Par ch et al P. Paruch et al. cond-mat/
139 Ferroelectrics P. Paruch et al. cond-mat/ m
140 Ferroelectrics P. Paruch et al. cond-mat/ m 500 nm
141 Questions
142 Questions What is the mechanism of propagation of domain wall (nucleation? Miller-Weinreich)
143 Questions What is the mechanism of propagation of domain wall (nucleation? Miller-Weinreich) What is the dimensionality of the films?
144 Questions What is the mechanism of propagation of domain wall (nucleation? Miller-Weinreich) What is the dimensionality of the films? Only the surface is accessible!!
145 Ferroelectics T. Tybell et al. PRL (02) P. Paruch et al. PRL (05)
146 Ferroelectics T. Tybell et al. PRL (02) μ = d 2+2ζ d ζ P. Paruch et al. PRL (05)
147 Ferroelectics T. Tybell et al. PRL (02) 0.26 μ = d 2+2ζ d ζ Compatible with d=2 + dipolar interactions P. Paruch et al. PRL (05) p
148 Ferroelectics T. Tybell et al. PRL (02) 0.26 μ = d 2+2ζ d ζ Compatible with d=2 + dipolar interactions P. Paruch et al. PRL (05) p
149 Probe the lengthscale R T K.J. Kim et al. Nature (09)
150 Probe the lengthscale R T K.J. Kim et al. Nature (09)
151 Probing R T and R v V. Repain et al. EPL (04)
152 Probing R T and R v V. Repain et al. EPL (04) R T 1 m
153 Probing R T and R v V. Repain et al. EPL (04) R T 1 m R v 17 m
154 Tough challenges
155 Defects
156 (V. Repain et al. (Orsay)) 210 m Pt/Co(0,5 nm)/pt/sio 2
157 P. J. Metaxas et al. PRL 99, (2007)
158 P. J. Metaxas et al. PRL 99, (2007)
159 Out of equilibrium
160 Glasses : Aging T f(t1,t2) t0 t1 t2 f : Depends on both times Aging of the Bragg glass or the interfaces?
161 Aging in interfaces A. B. Kolton, A. Rosso, TG, PRL (05)
162 Aging in interfaces A. B. Kolton, A. Rosso, TG, PRL (05)
163 Creep: Exp[- L ] eq = 1/3 eq A. B. Kolton, A. Rosso, TG, PRL (05)
164 Novel systems
165 Novel systems Spintronic i
166 Novel systems Spintronic i Multiferroics
167 Yamanouchi et al. Science (2007)
168 Yamanouchi et al. Science (2007)
169 Wall with internal degree of freedom V. Lecomte, S. Barnes, J.P. JP Eckmann, TG PRB (09)
170 Wall with internal degree of freedom V. Lecomte, S. Barnes, J.P. JP Eckmann, TG PRB (09)
171 Wall with internal degree of freedom V. Lecomte, S. Barnes, J.P. JP Eckmann, TG PRB (09)
172 Rigid wall approximation
173 Rigid wall approximation
174 Different from standard depinning
175 Different from standard depinning
176 Conclusions
177 Conclusions Slow dynamics of domain walls : glassy process
178 Conclusions Slow dynamics of domain walls : glassy process Steady state: creep
179 Conclusions Slow dynamics of domain walls : glassy process Steady state: creep FRG: scaling for the velocity; two lengthscales R T and R v
180 Conclusions Slow dynamics of domain walls : glassy process Steady state: creep FRG: scaling for the velocity; two lengthscales R T and R v Relevant and testable in several experimental systems
181 Many open questions
182 Many open questions Good methods (analytical/numerical) beyond scaling or FRG
183 Many open questions Good methods (analytical/numerical) beyond scaling or FRG Out of equilibrium issues (aging aging)
184 Many open questions Good methods (analytical/numerical) beyond scaling or FRG Out of equilibrium issues (aging aging) Defects (overhangs, bubbles)
185 Many open questions Good methods (analytical/numerical) beyond scaling or FRG Out of equilibrium issues (aging aging) Defects (overhangs, bubbles) Internal degrees of freedom (spintronic etc.)
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