ABSTRACT
As the coherence length xc(T), perpendicular to the ab planes of the highTC superconductors, is very low at low temperature, these materials can be described by a continuum model only at a temperature range defined by xc(T) >> d (d is the distance between the planes). In this temperature range near TC, these materials with the laminated structures can be adequately described by the anisotropic Ginzburg-Landau model. To go from the isotropic model to this model, it is sufficient to replace the electron mass m in the expression of the energy by a tensor of effective masses (m)ij describing the electronic anisotropy of the material1. In a superconductor with a uniaxial symmetry, supposed case of the high-TC materials, the orthogonal system of Oxyz axes is chosen such that the Oz axis is parallel to the c-axis of the crystal. The tensor of the masses is then reduced to a diagonal tensor whose principal values are: ma = mb = mab, effective masses of the Cooper pairs in the superconductor’s planes, and mc effective mass in the direction perpendicular to the planes:
m
m
m
00 00 00
(4.1)
The free energy is written:
h d A
2i
z2m
Φ
2i
2m
( )Td( )TF
r
A
r
where A// = (Ax, Ay), Ñ// = (¶/¶x, ¶/¶y) and h = Ñ ´ A. The minimization of this energy leads to the anisotropic Ginzburg-Landau equations:
c
e i
2m
c
zAe
zi 2m
A
(4.3)
cm
e
)( mi2
e
A
(4.4a)
A cm
e
mi
j (4.4b)
In the absence of field, one obtains the value of the order parameter:
)(
T (4.5)
where a(T) = a0 (T – TC), and the expression of the condensation energy:
)(
)( 22 TTH
which are both similar to the isotropic case (see Eq. 4.39 and Eq. 4.41).
