1.12 Specific characteristics of HTSC Ë 17Axial symmetry is assumed for the case of in-planeaandbdirections, so that
the screening currents inaandbdirections are equivalent to each other. Such an
assumption is a good approximation for orthorhombic HTSCs. Thus, there are two
different penetration depths휆ab,휆c, and coherence lengths휉ab,휉c. The penetration
depth휆aband the coherence length휉abare in thea,bplane, and휆cand휉care along
thecdirection. Two different GL parameters휅aband휅cas for the applied field in the
a-bplane and along thecdirection, respectively, [25, 26]
휅ab=휆ab휆c
휉ab휉c
1 / 2
, (1.46)휅c=휆ab
휉ab. (1.47)The thermodynamic critical fieldHcis given by
Hc=훷 0
2 $ 2 휋휇 0 휆ab휉ab. (1.48)
There are expressions for the lower and upper critical fields. For the particular case of
axial symmetry, the critical fields in thea-bplane and along thecdirection [24] are
Hc1,ab= 훷^0 ln휅
4 휋휇 0 휆ab휆c, (1.49)
Hc1,c=훷 0 ln휅
4 휋휇 0 휆^2 ab, (1.50)
Hc2,ab= 훷^0
2 휋휇 0 휉ab휉c, (1.51)
Hc2,c=훷 0
2 휋휇 0 휉^2 ab, (1.52)
where휇 0 is the permeability of free space and훷 0 is the quantized flux expressed by
훷 0 =hc/2e.
The following relations hold generally for the characteristic length scales in HTSC:
휉c<휉ab≪휆ab<휆c,therefore,
Hc1⊥c<Hc1‖c≪Hc2‖c<Hc2⊥c.