Abstract:
Point-contact spectroscopy was originally developed for the determination of the electron-phonon spectral function in normal metals. However, in the past 20 years it has become an important tool in the investigation of superconductors. As a matter of fact, point contacts between a normal metal and a superconductor can provide information on the amplitude and symmetry of the energy gap that, in the superconducting state, opens up at the Fermi level. In this paper we review the experimental and theoretical aspects of point-contact spectroscopy in superconductors, and we give an experimental survey of the most recent applications of this technique to anisotropic and multiband superconductors.

Abstract:
Iron-based superconductors (FeSC) present an unprecedented variety of features both in the superconducting and in the normal state. Different families differ in the value of the critical temperature, in the shape of the Fermi surface, in the existence or absence of quasi-nesting conditions, in the range of doping in which the antiferromagnetic (AFM) and the superconducting phase coexist and in the structure of the order parameter in the reciprocal space, and so on. In this paper the most important results of point-contact spectroscopy (PCS) in Fe-based superconductors are reviewed, and the most recent advances are described with the aim to discuss the future perspectives and challenges of this spectroscopic technique in the characterization of the superconducting properties of these complex compounds. One of the main challenges, faced so far only by a few researchers in the PCS field, is to fully explore the phase diagram of these materials, as a function of doping or pressure, to understand the interplay between superconductivity and magnetism, the effect of intrinsic or extrinsic inhomogeneities, the role of spin fluctuations (SFs) in the pairing, the symmetry and the structure of the order parameter(s).

Abstract:
The experimental critical temperatures and gap values of the superconducting pnictides of both the 1111 and 122 families can be simultaneously reproduced within the Eliashberg theory by using a three-band model where the dominant role is played by interband interactions and the order parameter undergoes a sigh reversal between hole and electron bands (s+- wave symmetry). High values of the electron-boson coupling constants and small typical boson energies (in agreement with experiments) are necessary to obtain the values of all the gaps and to correctly reproduce their temperature dependence.

Abstract:
Point-contact Andreev reflection spectroscopy (PCAR) has proven to be one of the most powerful tools in the investigation of superconductors, where it provides information on the order parameter (OP), a fundamental property of the superconducting state. In the past 20 years, successive improvements of the models used to analyze the spectra have continuously extended its capabilities, making it suited to study new superconductors with "exotic" properties such as anisotropic, nodal and multiple OPs. In Fe-based superconductors, the complex compound- and doping-dependent Fermi surface and the predicted sensitivity of the OP to fine structural details present unprecedent challenges for this technique. Nevertheless, we show here that PCAR measurements in Fe-based superconductors carried out so far have already greatly contributed to our understanding of these materials, despite some apparent inconsistencies that can be overcome if a homogeneous treatment of the data is used. We also demonstrate that, if properly extended theoretical models for Andreev reflection are used, directional PCAR spectroscopy can provide detailed information not only on the amplitude and symmetry of the OPs, but also on the nature of the pairing boson, and even give some hints about the shape of the Fermi surface.

Abstract:
The real-axis direct solution of the Eliashberg equations for the retarded electron-boson interaction in the half-filling case and in the presence of impurities is obtained for six different symmetries of the order parameter: $s$, $s+\mathrm{i}d$, $s+d$, $d$, anisotropic-$s$ and extended-$s$. The spectral function is assumed to contain an isotropic part $\alpha_{is}^{2}F(\Omega) $ and an anisotropic one $\alpha_{an}^{2}F(\Omega)$ such that $\alpha_{is}^{2}F(\Omega)=g\cdot\alpha_{an}^{2}F(\Omega)$, where $g$ is a constant, and the Coulomb pseudopotential $\mu^{\ast}$ is set to zero for simplicity. The density of states is calculated for each symmetry at $T= 2, 4, 40$ and 80 K. The resulting curves are compared to those obtained by analytical continuation of the imaginary-axis solution of the Eliashberg equations and to the experimental tunneling curves of optimally-doped Bi 2212 crystals.

Abstract:
We theoretically investigate the effect of various symmetries of the superconducting order parameter Delta(omega) on the normalized tunneling conductance of SIN junctions by directly solving the real-axis Eliashberg equations (EEs) for a half-filled infinite band, with the simplifying assumption mu*=0. We analyze six different symmetries of the order parameter: s, d, s+id, s+d, extended s and anisotropic s, by assuming that the spectral function alpha^{2}F(Omega) contains an isotropic part alpha^{2}F(Omega)_{is} and an anisotropic one, alpha^{2}F(Omega)_{an}, such that alpha^{2}F(Omega)_{an} = g alpha^{2}F(Omega)_{is}, where g is a constant. We compare the resulting conductance curves at T=2 K to those obtained by analytical continuation of the imaginary-axis solution of the EEs, and we show that the agreement is not equally good for all symmetries. Then, we discuss the effect of non-magnetic impurities on the theoretical tunneling conductance curves at T=4 K for all the symmetries considered. Finally, as an example, we apply our calculations to the case of optimally-doped high-T_{c} superconductors (HTSC). Surprisingly, although the possibility of explaining the very complex phenomenology of HTSC is probably beyond the limits of the Eliashberg theory, the comparison of the theoretical curves calculated at T=4 K with the experimental ones obtained in various optimally-doped copper-oxides gives fairly good results.

Abstract:
We propose an analytical model devoted to explain the anisotropy of the electrical resistance observed below the critical temperature in granular high-Tc superconductors submitted to a magnetic field H. Reported experimental results obtained on a YBCO sample show that the superconducting transition occurs in two stages, with a steep drop of the resistance at Tc and a subsequent, smoother decrease. In this second stage, the resistance vs. temperature curve is strongly dependent not only on the field intensity, but also on the angle between H and the macroscopic current density j. We start from the assumption that the resistance below Tc is mainly due to the weak links between grains. In the model, weak links are thought of as flat surface elements separating adjacent grains. We calculate the probability for a weak link to undergo the transition to the resistive state, as a function of the angles it makes with the external magnetic field H and the macroscopic current density j. In doing this, an important role is given to the strong non-uniformity of the local magnetic field within the specimen, due to the effect of the screening supercurrents flowing on the surface of the grains. Finally, we calculate the electrical resistance of the sample in the two cases where H is parallel and perpendicular to j, respectively. The predictions of this simple model turn out to be in reasonable agreement with reported experimental results obtained on a YBCO granular specimen.

Abstract:
Point-contact Andreev-reflection measurements were performed in SmFeAsO_{0.8}F_{0.2} polycrystals with T_c \simeq 53 K. The experimental conductance curves reproducibly exhibit peaks around \pm 6 mV and shoulders at V \sim 16-20 mV, indicating the presence of two nodeless superconducting gaps. While the single-band Blonder-Tinkham-Klapwijk fit can only reproduce a small central portion of the conductance curve, the two-gap one accounts remarkably well for the shape of the whole experimental dI/dV. The fits of the normalized curves give Delta_1(0) = 6.15 \pm 0.45 meV and Delta_2(0) = 18 \pm 3 meV. Both gaps close at the same temperature and follow a BCS-like behavior.

Abstract:
We analyze the results of point-contact measurements in La_{2-x}Sr_{x}CuO_{4} (LSCO) previously reported as a clear evidence of the separation between gap and pseudogap in this copper oxide. Here we show that, in addition to this, the conductance curves of our point-contact junctions -- showing clear Andreev reflection features -- can be interpreted as supporting a nodeless d_{x^2-y^2}+id_{xy}-wave symmetry of the gap in LSCO. The results of our analysis, in particular the doping dependence of the subdominant d_{xy} gap component, are discussed and compared to the predictions of different theoretical models.

Abstract:
In this paper we propose a model to reproduce superconductive and normal properties of the iron pnictide LiFeAs in the framework of the four-band spm wave Eliashberg theory. A confirmation of the multiband nature of the system rises from the experimental measurements of the superconductive gaps and resistivity as function of temperature. We found that the most plausible mechanism is the antiferromagnetic spin fluctuation and the estimated values of the total antiferromagnetic spin fluctuation coupling constant in the superconductive and normal state are lambda{tot}=2.00 and lambda{tot,tr}=0.77.