**6. References**


18 Will-be-set-by-IN-TECH

The obtained anisotropy of superconducting current around the single vortex in AFA theory agrees reasonably with that found from the Eilenberger equations [96]. Extending electronic states also results in the observed field dependent flattening of *λeff*(*B*) at low temperatures [73]. Thus, our microscopical consideration justifies the phenomenological AFA model and

The core structure of the vortices is studied for *<sup>s</sup>*±, *dx*<sup>2</sup>−*y*<sup>2</sup> symmetries (connected with interband and intraband antiferromagnetic spin fluctuation mechanism, respectively) and *s*++ symmetry (mediated by moderate electron-phonon interaction due to Fe-ion oscillation and the critical orbital fluctuation) using Eilenberger approach and compared with the experimental data for iron pnictides. It is assumed [99] that the nodeless *s*± pairing state is realized in all optimally-doped iron pnictides, while nodes in the gap are observed in the over-doped KFe2As2 compound, implying a *dx*<sup>2</sup>−*y*<sup>2</sup> -wave pairing state, there are also other points of view [10, 13]. The stoichiometrical LiFeAs, without antifferomagmetic ordering, is considered as a candidate for the implementation of the *s*++ symmetry. Different impurity scattering rate dependences of cutoff parameter *ξ<sup>h</sup>* are found for *s*<sup>±</sup> and *s*++ cases. In the nonstoichiometric case, when intraband impurity scattering (Γ0) is much larger than the interband impurity scattering rate (Γ*π*) the *ξh*/*ξc*<sup>2</sup> ratio is less in *s*<sup>±</sup> symmetry. When Γ<sup>0</sup> ≈ Γ*<sup>π</sup>* (stoichiometric case) opposite tendencies are found, in *s*<sup>±</sup> symmetry the *ξh*/*ξc*<sup>2</sup> rises above the "clean" case curve (Γ<sup>0</sup> = Γ*<sup>π</sup>* = 0) while it decreases below the curve in the *s*++ case. In *d*-wave superconductors *<sup>ξ</sup>h*/*ξc*<sup>2</sup> always increases with <sup>Γ</sup>. For *dx*<sup>2</sup>−*y*<sup>2</sup> pairing the nonlocal generalized London equation and its connection with the Eilenberger theory are also considered. The problem of the effective penetration depth in the vortex state for *d*-wave superconductors is discussed. In this case, the field dependence of *λeff* is connected with the extended

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© 2012 De Luca, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

= *LIJ*/Φ<sup>0</sup> ≈0, where Φ0 is the elementary flux quantum and *IJ* is the

1 and *φ*2

, across the

distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 De Luca, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Effective Models of Superconducting** 

It is well known that the electrodynamic properties of SQUIDs (Superconducting Quantum Interference Devices) are obtained by means of the dynamics of the Josephson junctions in these superconducting system (Barone & Paternò, 1982; Likharev, 1986; Clarke & Braginsky, 2004). Due to the intrinsic macroscopic coherence of superconductors, r. f. SQUIDs have been proposed as basic units (qubits) in quantum computing (Bocko et al., 1997). In the realm of quantum computing non-dissipative quantum systems with small (or null) inductance parameter and finite capacitance of the Josephson junctions (JJs) are usually considered (Crankshaw & Orlando, 2001). The mesoscopic non-simply connected classical devices, on the other hand, are generally operated and studied in the overdamped limit with negligible capacitance of the JJs and small (or null) values of the inductance parameter. Nonetheless, r. f. SQUIDs find application in a large variety of fields, from biomedicine to aircraft maintenance (Clarke &

As for d. c. SQUIDs, these systems can be analytically described by means of a single junction model (Romeo & De Luca, 2004). The elementary version of the single-junction model for a d. c. SQUID takes the inductance *L* of a single branch of the device to be

average value of the maximum Josephson currents of the junctions. In this way, the Josephson junction dynamics is described by means of a nonlinear first-order ordinary differential equation (ODE) written in terms of the phase variable *φ*, which represents the

junctions in the d. c. SQUID. By considering a device with equal Josephsons junction in each of the two symmetric branches, the dynamical equation of the variable *φ* can be written as

**Quantum Interference Devices** 

Additional information is available at the end of the chapter

Braginsky, 2004), justifying actual scientific interest in them.

average of the two gauge-invariant superconducting phase differences, *φ*

R. De Luca

http://dx.doi.org/10.5772/48483

**1. Introduction** 

negligible, so that

β

follows (Barone & Paternò, 1982):

