View
214
Download
1
Category
Tags:
Preview:
Citation preview
Knotted field distributions of order parameters
in pseudogap phase states
L. Martina
Dipartimento di Fisica, Università del Salento
Sezione INFN - Lecce
• A. Protogenov, V. Verbus , RAS - Nizhny Novgorod, Russia•EINSTEIN – RFBR •cond-mat.str-el/0706.0639 Nonlinear Physics V
2-components Ginzburg – Landau Model
3D
•Two – Higgs doublet model (T.D. Lee, Phys. Rev. D 8 (1973) 1226)
•Spin – Charge decomposition in Yang – Mills (L. Faddeev A. Niemi (2006)•Spin – density waves in cuprate •two charged condensates .•two charged condensates of tightly bounded fermion pairs, • two-band superconductor •(Nb, T , V , Nb-doped SrT iO3, hT MgB2 ) (E. Babaev, L.V. Faddeev, A.J. Niemi,
Phys. Rev. B 65 (2002) 10051)
221, C
Mermin – Ho vorticity
the densities of the Cooper pairs
paramagnetic current
Gauge-invariant vector field
mass
Nonlinear Physics V
the magnetic order (Néel) vector
Group Theoretical Classification
of the Local Minima of V(, n) I.P. Ivanov, cond-mat/0802.2107
b d
Phases
Skyrme – Faddeev
1 component Ginzburg-Landau in E.M.
Inhomogeneous Superconductor
Quasi-1 dim distribution b
dL
24
bGL
2
Nonlinear Physics V
A.F. Vakulenko and L.V. Kapitanskii, Sov. Phys. Dokl. 24, 433 (1979)L. Faddeev, A. Niemi, Nature 387, 1 May (1997) 58..R.S. Ward, Nonlinearity 12 (1999) 241 V. M. H. Ruutu et al, Nature 382 (1996) 334.
Skyrme – Faddeev model
Hopf Invariant
Stability of large-Q configurations
/1min
L. Faddeev, Quantisation of Solitons, preprint IAS-75-QS70, 1975;
Nonlinear Physics V
/2,/1 knotknot RR
Q=1
M.F. Atiyah, N.S. Manton, Phys. Lett. A 222 (1989) 438
nvrin ,exp 22:, SSv
QvWinding ,
0,20
Trial function
r
tghr 12
5.4
min SFS 7.116 2
min
SFS
L. Faddeev, A.J. Niemi, Nature 387 (1997),59 Nonlinear Physics V
y
x
-2 -1 0 1 2
-2
-1
0
1
2
x
z
Q=1
Nonlinear Physics V
-2 -1 0 1 2
-2
-1
0
1
2
n-field
H-field
-2 -1 0 1 2
-2
-1
0
1
2
y
x
-2 -1 0 1 2
-2
-1
0
1
2
x
z
r
hr
Ok4
2
2
2
22 sec
2cos1
8n
,
/
/11
2g
r
rfb d
bb
Inhomogeneous Superconductor Vconst min
V. I. Arnold and B. A. Khesin: Topological methods in hydrodynamics..A. P. Protogenov Physics-Uspekhi 49, 667 (2006).
Hoelder
Ladyzhenskaya
2
4/32 132
Q
LQS h
QL
SFh SS Nonlinear Physics V
216
Quasi 1- dim distribution
0,, ndbBB
Compressible fluid
X.G. Wen, A. Zee, Phys. Rev. B 46 (1992) 2290
Nonlinear Physics V
General Case
Closed quasi 1-dimdistribution
Packing parameter
cnh SSS 0 TOROID STATE
V.M. Dubovik, V.V. Tugushev Phys. Rep. 187, 145 (1990).
Dense packing, anti-chirality Nonlinear Physics V
Toroid Moment
T
Toroid distributions:Near inhomogeneous superconductorQuasi – planar knotsAntiferromagnetic ordering
Topological phase transition : hom. SuperC. Toroid order
mrdxTmdx 33
2
1,0
Nonlinear Physics V
Conclusions
2-component Ginzburg – Landau ModelSpecial class of phasesTopological classificationEstimate of parametersAppearence of nets of toroi solutionsAnalogy with Dimeric system on the Lattice
Open problemsExplicit construction of solutions (approximated)Discretization schemes based on group invarianceFractional – Statistics of toroid distributionRoksar-Kivelson type Hamiltonian
Recommended