**1. Introduction**

44 Superconductors – Materials, Properties and Applications

& Yokoya, T. (2009). Electronic Structure of Superconducting FeSe Studied by High-

Resolution Photoemission Spectroscopy. *The Physical Society of Japan*, 78: 034708. Zaanen, J., Sawatzky, G.A. & Allen, J.W. (1985). Band gaps and electronic structure of

transition-metal compounds, *Physical Review Letters*, 55: 418-421.

More than 24,000 inorganic phases are known. Of these phases approximately 16,000 are binary or pseudobinary while about 8,000 are ternary or pseudo-ternary. However, it is surprising to note that the observation of superconductivity in these alloys is a rare phenomenon. Superconductivity is ubiquitous but sparsely distributed and can be considered a rare phenomenon among the known alloys. BCS theory has been enormously successful in explaining the superconducting phenomena from the microscopic view point. The fundamental idea of this theory is the formation of Cooper pairs of electrons, mediated by phonons, the quantum of vibration of the crystal lattice [1]. Thus maximizing the critical temperature is involved with maximizing the electron-phonons coupling. Among the intermetallic materials, the binary cubic (A3B) so-called A15 compounds displayed the highest Tc, until the discovery of superconducting cuprates. Among these materials in particular, Nb3Sn and V3Si with critical temperatures of 18.0 K and 17.1 K respectively have lattice instabilities of martensitic-type occurring at temperatures Tm very close to the maximum Tc. In the phase diagram of Tm and Tc versus Pressure (P) of V3Si, the martensitic phase line intersects and stops exactly at the superconducting phase boundary. A qualitative example of this kind of the behavior can be observed in the Figure 1. Data exists beyond the extrapolated intersection shown and finds that there is no martensitic distortion occurring below Tc in this pressure regime. One way to think about this behavior is in terms of a lattice softening arising from strong electron-phonon coupling. Both the martensitic distortion and superconductivity arise from this coupling, and when the superconductivity Tc occurs at higher temperature than that of the lattice distortion, the energy gap that opens in the superconducting state gaps out at the same time phonon fluctuations that give rise to the lattice distortion [2-3]. One has, then, two phases that are competing for the same resource.

© 2012 Machado et al., 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, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Machado et al., 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.

A similar type behavior is observed in heavy Fermion (HF) superconducting materials. Here antiferromagnetic order competes with the superconducting transition, both phases arising from electronic coupling to magnetic fluctuation in the heavy electron liquid.

Defect Structure Versus Superconductivity in MeB2 Compounds (Me = Refractory Metals) and One-Dimensional Superconductors 47

transition temperatures intersect the superconducting transition temperature curve in the phase diagram versus pressure and/or composition. At the pressure suppressing the structural or SDW transition down to the superconducting Tc superconductivity does not appear to coexist with the SDW or structurally distorted phase. However, the data are not sufficient to say that the critical temperature of the superconducting transition is maximized at the intercept of the SDW transition, but the results seem to suggest that this may occur. In addition, the organic superconductors show similar behavior to that which occurs in high critical temperature cuprates. In all these cases maximizing the superconducting temperature appears to involve suppressing a secondary phase which competes with the phenomenon of superconductivity, whether CDW, SDW, Tm or other competitive instability. These experiments all suggest that superconducting pairs are utilizing the same fluctuation spectrum that supports the order of the phases it competes with. The key to superconductivity is to be found in frustrating the competing order so that the superconducting instability of the Fermi surface can gap out parts of the fluctuation spectrum favoring the second phase. Even in one-dimensional systems instabilities play a role in the superconducting behavior [4-5]. The superconducting critical temperature increases upon applying hydrostatic pressure while simultaneously suppressing the electronic CDW. Within this general scenario is the superconductivity of compounds which can crystallize in AlB2 prototype structure. Our discussion of superconductivity in this

structure-type is based on the defect structures that these compounds may have.

The first superconductor found to crystallize in the AlB2 prototype structure was discovered by A. S. Cooper et. al. [6] In this paper the authors showed that NbB2 as well MoB2 can exhibit superconductivity. However, stoichiometric NbB2 was not superconducting, but adding excess boron for a nominal composition of NbB2.5 yielded bulk superconductivity observed at 3.87 K, determined from the measurement of the specific heat. In the same article the authors discussed the high temperature phase MoB2. When a nominal composition MoB2.5 was splat-melted forcing excess boron into lattice the material had a superconducting transition close to 7.45 K. These results were not confirmed by other authors and remained of little interest to the scientific community until the discovery of superconductivity in MgB2 with critical temperature close to 40.0 K [7]. In the Nb-B system the NbB2 phase shows a wide range of boron stoichiometry where a defect structure can explain this large range of solubility. Recently C. A. Nunes et. al. [8] made a systematic study of the B-solubility in NbB2. The homogeneity of the phases obtained was determined by neutron diffraction and a maximum critical temperature was found to be 3.9 K. This study raises anew the question of the nature of defects that can be generated in these compounds. The stability of the phase NbB2 spans a wide range of composition as shown in

At the solubility limit the Nb-B inter-atomic distance in NbB2 phase is constant. This indicates that variations in lattice parameters "a" and "c" inside of the stability range do not occur randomly but are such as to maintain a constant Nb-B distance of 2.43Å. To explain the wide

**1.1. Superconductivity in compounds with AlB2 prototype structure** 

the diagram in Figure 2.

**Figure 1.** Schematic representation of the temperature dependence with pressure showing the critical temperature and martensitic temperature for V3Si.

With the heavy Fermions, all superconductors are found in the vicinity of a quantum critical point, where the antiferromagnetic order has been driven to zero Kelvin (T = 0K). The general characteristics of high critical temperature cuprates are often discussed in terms of the kind of phase diagram found in the HF materials. A line known as the pseudogap intersects the maximum Tc in a superconducting dome in the temperature control parameter phase diagram, in general doping level being the control parameter [3]. There continues debate as to whether the pseudogap line represents a true phase transition. However, it is arguably the temperature setting the critical superconducting transition temperature upper limit. Again, the similarities with other instabilities discussed here are evident, with the temperature of the pseudogap intercepting the maximum of Tc against a control parameter that in this case is the doping level. This same discussion is also relevant to recent Fe-based pnictide superconductors. In this set of materials two competing phases are observed in the phase diagram, the non-superconducting one a structural instability or an SDW. Their transition temperatures intersect the superconducting transition temperature curve in the phase diagram versus pressure and/or composition. At the pressure suppressing the structural or SDW transition down to the superconducting Tc superconductivity does not appear to coexist with the SDW or structurally distorted phase. However, the data are not sufficient to say that the critical temperature of the superconducting transition is maximized at the intercept of the SDW transition, but the results seem to suggest that this may occur. In addition, the organic superconductors show similar behavior to that which occurs in high critical temperature cuprates. In all these cases maximizing the superconducting temperature appears to involve suppressing a secondary phase which competes with the phenomenon of superconductivity, whether CDW, SDW, Tm or other competitive instability. These experiments all suggest that superconducting pairs are utilizing the same fluctuation spectrum that supports the order of the phases it competes with. The key to superconductivity is to be found in frustrating the competing order so that the superconducting instability of the Fermi surface can gap out parts of the fluctuation spectrum favoring the second phase. Even in one-dimensional systems instabilities play a role in the superconducting behavior [4-5]. The superconducting critical temperature increases upon applying hydrostatic pressure while simultaneously suppressing the electronic CDW. Within this general scenario is the superconductivity of compounds which can crystallize in AlB2 prototype structure. Our discussion of superconductivity in this structure-type is based on the defect structures that these compounds may have.
