Giamarchi

Vortex Phases: 

Vortex Phases T. Giamarchi (Orsay) P. Le Doussal (ENS)

Slide3: 

J v E Bad conductor F Need to pin the vortices: Disorder Disorder needed to have good superconductors !

Questions: 

Questions Effect of disorder on the vortex crystal I-V characteristic ? Linear response ? How to describe such a phase (GL ? Elastic ?) Phase diagram ? Nature of moving system

Elastic description of vortices: 

Elastic description of vortices R0i : crystal ui : displacements n=2 d=3 vortices Elastic hamiltonian

Slide6: 

Simplest elastic hamiltonian : c(q) = c q2 Long range forces ; bulk, shear and tilt

Slide7: 

Anisotropy: lxlz Very anistotropic materials : pancakes z Josephson or electromagnetic coupling between planes

Thermal fluctuations : Melting: 

Thermal fluctuations : Melting

Phase Diagram: 

Phase Diagram T B Solid Liquid

Slide10: 

u r

Disorder (point like defects): 

Disorder (point like defects)

Loss of translational order (Larkin): 

Loss of translational order (Larkin) No crystal below four spatial dimensions

Larkin Model: 

Larkin Model Exactly solvable Not valid at large distance

Slide14: 

Not valid when : New length Rc Larkin model has no metastable states and pinning

How to describe the vortex phase: 

How to describe the vortex phase Loss of translational order beyond Ra (Wrong) argument: disorder induces dislocations at Ra

Slide16: 

T B Solid Liquid Ignore the lattice (Fisher,Fisher,Huse) Continuous transition

Problems with this approach: 

Problems with this approach Experimental : Transition Neutrons Decorations

Quantitative theory of DES: 

Quantitative theory of DES TG +P. Le Doussal PRL 72 1530 (94); PRB 52 1242 (95) n=2; d=3 vortices Also: CDW Random XY Wigner crystal Magnetic bubles

How to solve ?: 

How to solve ? Other method: Functional Renormalization Group in d=4-

Slide20: 

r Rc Ra B(r) Larkin Random manifold Asymptotic RSB: many metastable states glass ! Quasi long range translational order ! Power law Bragg peaks; Ad = 4-d

Absence of dislocations: Bragg Glass: 

Absence of dislocations: Bragg Glass Look at stability to injection of dislocations Because QLRO in elastic theory: Stable to unpaired dislocations ! Existence of a thermodynamically stable glassy phase with quasi long range translational order and power law Bragg peaks [Bragg Glass]

Consequences: 

Consequences No dislocations in decoration; B(r) Phase diagram

Slide23: 

A. Van Otterlo et al. PRL 81 1497 (98)

Slide24: 

P. Kim PRB 60 R12589 (99)

Unified phase diagram: 

Unified phase diagram T H, Bragg glass No dislocations Dislocations Liquid

Peak Effect: 

Peak Effect V J J1 BrG J2 (disordered) TG +P. Le Doussal PRB 55 6577 (97) Peak at « melting » of the Bragg glass : second peak in magnetization Peak effect in transport

Slide27: 

B. Khaykovich et al. PRL 76 2555 (96) K. Deligiannis et al. PRL 79 2121 (97) Hardy et al. Physica C 232 347 (94)

Slide28: 

Y. Nonomura and X. Hu cond-mat 0002263 Transport studies in a Corbino disk geometry suggest that the Bragg glass phase undergoes a first-order transition into a disordered solid. Y. Paltiel et al. cond-mat 0008092

Neutrons: 

Neutrons Collapse of intensity without broadening

Slide30: 

I. Joumard et al. PRL 82 4930 (99); T. Klein et al. (01)

Creep: 

Creep D.T. Fuchs et al. PRL 81 3944 (98) C. Van der Beek et al. cond-mat 9912282 Bragg glass:

Dynamics: 

Dynamics Competition between disorder and elasticity Statics: glassy properties Dynamics ?

TAFF vs Creep: 

TAFF vs Creep F v Fc T0 T=0 TAFF (Anderson+Kim) : typical barrier Linear response

Creep: 

Creep Glassy system (Nattermann, Ioffe+Vinokur, Feigelman et al.) Slow dynamics determined by static arguments No linear response Phenomenological derivation

Large V: 

Large V Interfaces reorder at large V Rv Naively: periodic structure is the same ! Crystal at large v ?? (T changed by disorder) (Koshelev+Vinokur)

Moving glass: 

Moving glass Need to Retain transverse degrees of freedom TG + P. Le Doussal PRL 76 3408 (1996); P. Le Doussal + TG PRB 57 11356 (1998).

Channels: 

Motion via static channels Channels are rough No shaking temperature Channels provide a natural framework to study dislocations  coupling/decoupling of the channels Channels

Dynamical Phase Diagram: 

Dynamical Phase Diagram

Slide40: 

K. Moon, R. T. Scalettar and G.T. Zimanyi PRL 77 2778 (1996) M. Marchevsky at al. PRL 78 531 (1997) A.M Troyanovski et al Nature, 399 665 (1999)

Slide41: 

A. Kolton et al PRL 83 3061 (1999) F. Pardo et al. Nature, 396 348 (1998)

Transverse critical force: 

Transverse critical force Crystal

Slide43: 

H. Fangohr, P. de Groot, S. Cox cond-mat 0005263 C.J. Olson, C. Reichhardt PRB 61 R3811 (1999)

Other elastic systems: 

Other elastic systems Disordered elastic systems cover many physical situations Interfaces Correlated disorder Quantum systems: quantum solids ; Luttinger Liquids

Columnar defects: 

Columnar defects Related to quantum problems (z is « time ») Vortex : Bose glass (Nelson+Vinokur)

Magnetic domains: 

Magnetic domains S. Lemerle et al. PRL 80 849 (98)

Slide47: 

Creep

Charge density Waves: 

Charge density Waves N. Markovic, N. Dohmen, H. van der Zant PRL 84 534 (2000) Electrons + Phonons: Electronic crystal

Wigner Crystal: 

Wigner Crystal E.Y. Andrei, et al PRL 60 2765 (1988) R.L. Willett, et al. PRB 38 R7881 (1989)

Slide50: 

C.-C. Li, et al. PRB 61 10905 (2000)

Absence of Hall voltage: 

F. Perruchot et al. Physica B 256 587 (1998) Absence of Hall voltage Flor < Ftran : no hall voltage Compatible with the existence of a transverse threshold

Luttinger Liquids: 

Luttinger Liquids t

Conclusion: 

Conclusion Periodicity crucial for disordered elastic systems Static: Bragg Glass, topologically ordered Field induced transition: destruction of BrG; universal phase diagram Dynamics: Moving system remains a Moving Glass (Moving Bragg glass or Smectic) Transverse pinning force

The future: 

The future Nature of field driven transition Nature of large field phase (DISLOCATIONS) Dynamics (noise, aging etc.) Similarities and differences with elastic and plastic systems

Slide55: 

General on vortices : G. Blatter et al. Rev. Mod. Phys 66 1125 (1994). Bragg glass : T.G. + P. Le Doussal Phys. Rev. B 52 1242 (1995). T.G. + P. Le Doussal Phys. Rev. B 55 6577 (1997). P. Le Doussal + T.G. Physica C 331 233 (2000). Review: T.G. + P. Le Doussal In ``Spin Glasses and Random Fields'', ed. A.P. Young, World Scientific (Singapore) 1998, p. 321, cond-mat/9705096 Moving glass: T.G. + P. Le Doussal Phys. Rev. Lett. 76 3408 (1996). P. Le Doussal + T.G. Phys. Rev. B 57 11356 (1998). Creep from RG: P. Chauve + T.G. + P. Le Doussal Phys. Rev. B 62 624 (2000).

Slide56: 

Quantum problems: T.G. + P. Le Doussal Phys. Rev. B 53 15206 (1996). R. Chitra + T.G. + P. Le Doussal Phys. Rev. Lett. 80 3827 (1998). R. Chitra + T.G. + P. Le Doussal cond-mat/0103392. T.G. + P. Le Doussal + E. Orignac cond-mat/0104583. Review: T.G. + E. Orignac cond-mat/0005220 And references therein...