Guanhai Wang, Minglu Li and Chuliang Weng Shanghai Jiao Tong University, China. SVM09, Wuhan, China.
Dingping Li School of Physics, P eking University , China
description
Transcript of Dingping Li School of Physics, P eking University , China
IVW2005, TIFR, India Jan.11(2005) 1
Dingping Li School of Physics, Peking University, China
Baruch Rosenstein, NCTS&NCTU, Hsinchu, Taiwan,
Weizmann Institute&Bar Ilan, Israel
QUANTITATIVE THEORY OF THERMAL FLUCTUATIONS AND DISORDER IN THE
VORTEX MATTER
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Symmetry breaking pattern of vortex phase diagram.
replicatranslation
unbroken
unbroken
broken
broken
liquid
solid
Vortex glass
Bragg glass
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Vortex glass
liquid
solidBragg Glass
structural (square-rhomb)
ODO
(melting
+s.p.)
Glass (irreversibility)
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Thermal fluctuations are taken into account using the
statistical sum
with the GL energy in 2D (for simplicity)
Ginzburg – Landau theory and the LLL approximation
22
2 43 ( ) ( ) ( )2 2
2 1 ( ) 1 ( )F d x T Tc x xm
ie W x V xc
A
[ ] /( ) ( ) F TZ D x D x e
with variances
( ) ( ) ( ) ( )( ); ( )x y x yW W n x y V V q x y
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Within the LLL approximation the gradient term is combined with the quadratic.
1/ 2
2 2 14 2
DT
t b G i t ba
2 / 3
3 14 2
DT
t b G i t ba
Therefore without disorder physical quantities depend on a single parameter:
Ruggeri, Thouless,1975
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Thermal fluctuations
Vortex liquid
1. We constructed the Optimized
gaussian series, which are
convergent rather than asymptotic.
Radius of convergence is
Spinodal
2. Using gaussian approximation one finds that the
solid becomes unstable at (spinodal).
BR PRB60,4268 (1999)DPL, BR PRB65,024514(2001)
Vortex Solid:
1. For the free energy we get to the required precision (.1%) at the two loop
order (the IR divergencies due to “supersoft” phonons cancel exactly) :
5.5spinodalTa
4.5Ta
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9.5m
Ta
However it allowed us to verify unambiguously the validity of Borel-
Pade method which provided a convergent scheme everywhere down
to T=0.
The melting is obtained by
comparing liquid and solid free
energy:
DPL, BR, PRB, 2004.
13.2mTa
in 3D
in 2D
H
TT/Tc
T/TcCC
MM
5288.16 , 175.9 , 7.0 10c cT K H T Gi 2 3 7YBa Cu O Shibata et.al.,
PRB66,214518(02)
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Point disorder, Unified ODO line, Kauzmann points
1. Disorder breaks the LLL scaling. Using perturbation around the
zero disorder overcooled liquid and solid, we find that there is a
single order – disorder line combining the melting line and the second
peak line. Liquid gains more than solid from pinning and the line
“curves down” at Kauzmann point in which the entropy jump
vanishes.
2. The continuation of the “clean” melting line becomes a crossover
(Hx) between liquid I and a viscous liquid II which we characterize as
strongly correlated (deeply supercooled). Tricritical point is
reinterpreted as a Kauzmann point.
3. In 3D the line has a “wiggle”.
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The unified order –disorder and Hx lines
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65 70 75 80 85 90
5
10
15
20
25
30
2 3 7YBa Cu O
mH
xH
H
T*H
3D theoretical fitting of the optimally doped YBCO in DPL,BR, PRL90,167004(03)
Exp. inBouquet et al, Nature 414, 448 (2001)
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Circles taken from Shibata et. al., PRB66, 214518 (02)
Triangles taken fromBouquet et al, Nature 414, 448 (2001)
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Replica symmetry breaking-Glass transition
To calculate disorder averages we can use replica trick to integrate
over disorder. Then we use the Mezard –Parisi Gaussian variational
method to study the RSB. Lopatin Europhys. Let. 51,635 (00)
DPL, BR, cond-mat (04), unpublished.
Replica symmetry breaking solution means there is a hierarchy of
relaxation times in dynamics (reflecting the logarithmically diverging
energy barriers).
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0 2 4 6 8 10 12
0
1
2
3
4
6 7 8 9 10 11
0
5
10
15
20
mH
gH
M MG
Shibauchi, PRB57, R5622 (1998)
2 2 - ( - ) [ ( ) ] kappa BEDT TTF Cu N CN Br
2D fitting of
Replica symmetry breaking line (or glass transition line) with small q
in 3D is given by4 / 3
1/ 3
3 4 5 43T
na n qn n
The glass transition line
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xH liquid I to liquid II transition line. (black points – exp, pink - th)
60 65 70 75 80 85 90
5
10
15
20
25
30
Hupg
H lowg
H theg
mH
xHth
xH
The upper part of glass line of Shibata et.al., PRB66,214518(02) Hupg
H lowg
The low upper part of Taylor et alPRB68,054523 (03)
Phase diagram of optimally doped YBCO
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Conclusion
The LLL GL theory allows qualitative and quantitative comparison with
experiment in a wide variety of type II materials in surprisingly wide range
of fields and temperatures. It include the melting and the glass lines, in some
cases magnetization and specific heat jumps and other quantities.
The generic phase diagram contains four
phases: liquid, solid, vortex glass and
Bragg glass experimentally and
theoretically in our approach.Divakar et al, PRL92,237004 (04) LaSCO
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Fuchs et al PRL80,4911
(2002)
Sasagawa et al PRB61,1610 (00)
BSCCO LaSCO YBCO
Taylor et al PRB68,054523 (03)
Open question: glass line in solid
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See our posters for details in
Theory (P56) and Experimental Fitting (P35)