1.12　Specific characteristics of HTSC

From the London theory, GL theory to BCS theory, the theory of superconductivity has experienced a long history. Although the BCS theory can explain the character istic properties of conventional superconductors, the HTSC materials still have no widely accepted theory to explain their properties.The HTSCs with their layered structures have strong anisotropy and giant flux creep effects.It is complicated and difficult to study high temperature superconductivity.Although the properties of HTSCs are in many respects similar to those of conventional superconductors, the HTSCs have a series of special characteristics compared with LTSCs.The critical temperatures Tc are higher by almost one order of magnitude, and the supercon ducting energy gaps 2Δ are also larger by one order of magnitude.In addition, the penetration depthsλare also larger for one order of magnitude, and the su perconducting coherence lengths ξ are much shorter, thus, the Ginzburg-Landau parametersκare larger（on the order of 100）.The superconducting wave function has d-wave symmetry in HTSCs, but that of LTSCs shows s-wave symmetry.A se ries of the differences and problems between HTSCs and LTSCs have posed serious challenges for theoretical explanation of the physical mechanisms of HTSCs.

Axial symmetry is assumed for the case of in-plane a and b directions, so that the screening currents in a and b directions are equivalent to each other. Such an assumption is a good approximation for orthorhombic HTSCs.Thus, there are two different penetration depths λab ，λc ，and coherence lengths ξ ab ， ξ c .The penetration depthλab and the coherence length ξ ab are in the a, b plane, and λc and ξ c are along the c direction.Two different GL parameters κab and κc as25，26for the applied field in the a-b plane and along the c direction, respectively，

The thermodynamic critical field Hc is given by

There are expressions for the lower and upper critical fields. For the particular case of axial symmetry the critical fields in the a-b plane and along the c direction24are

whereμ0 is the permeability of free space and Φ0 is the quantized flux expressed by Φ0 =hc/2e.

The following relations hold generally for the characteristic length scales in HTSC：

therefore，