**1. Introduction**

The discovery of superconductivity in copper oxides with an active *CuO*<sup>2</sup> plane [1] at temperatures of the order of 100 K is undoubtedly one of the most important achievements of the modern solid state physics. However, even more than twenty six years later since the discovery the physics of the electronic processes and interactions in high-temperature superconductors (HTS's) and, in particular, the superconducting (SC) pairing mechanism, resulting in such high *Tc*'s, where *Tc* is the superconducting transition (critical) temperature, still remain controversial [2]. This state of affairs is due to the extreme complexity of the electronic configuration of HTS's, where quasi-two-dimensionality is combined with strong charge and spin correlations [3, 4, 6–12].

Gradually it became clear that the physics of superconductivity in HTS's can be understood, first and foremost, by studying their properties in the normal state, which are well known to be very peculiar [4, 6–12]. It is believed at present that the HTS's possess at least five specific properties [2, 7, 8, 11–13]. First of all it is the high *Tc* itself which is of the order of 91 K in optimally doped (OD, oxygen index (7 − *<sup>δ</sup>*) ≈ 6.93) *YBa*2*Cu*3*O*7−*<sup>δ</sup>* (YBCO, or Y123), of the order of 115 K in OD *Bi*2*Sr*2*Ca*2*Cu*3*O*8+*<sup>δ</sup>* (Bi2223) and in corresponding Tl2223 [8, 9, 12], and arises up to *Tc* ≈ 135*K* in OD *HgBa*2*Ca*2*Cu*3*O*8+*<sup>δ</sup>* (Hg1223) cuprates [14]. The next and the most intrigueing property is a pseudogap (PG) observed mostly in underdoped cuprates below any representative temperature *T*<sup>∗</sup> � *Tc* [2, 8]. As *T* decreases below *T*∗, these HTS's develop into the PG state which is characterized by many unusual features [2, 8, 12, 13, 15, 16]. The other property is the strong electron correlations observed in the underdoped cuprates too [3, 5, 12, 16]. However, existence of the such correlations in, e.g., FeAs-based superconductors still remains controversial [17–21]. The next property is pronounced anisotropy [6–9, 11, 12] observed both in cuprates [2, 9, 12] and FeAs-based superconductors (see Refs. [17–19] and references therein). As a result, the inplane resistivity, *ρab*(*T*) is much smaller than *ρc*(*T*), and the coherence length in the *ab* plane, *ξab*(*T*), is about ten times of the coherence length along the c-axis, *ξc*(*T*). The last but not least property is a reduced density of charge carriers *n <sup>f</sup>* . *n <sup>f</sup>* is zero in the antiferromagnetic (AFM) parent state of HTS's and gradually increases with

©2012 Solovjov, 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 Solovjov, 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.

doping [2, 8, 9, 11, 12]. But even in an optimally doped YBCO it is an order of magnitude less than in conventional superconductors [2, 8, 9, 11, 12, 15]. There is growing evidence that just the reduced density of charge carriers may be a key feature to account for all other properties of HTS's [2, 6, 7, 13, 22–26].

still not been finally established, the density of quasiparticle states at the Fermi level starts to

The number of papers devoted to the problem of the pseudogap in HTS's is extraordinarily large (see Refs. [6–8, 12, 15, 84] and [40, 49, 50, 53, 54, 56, 59] and references therein) and new papers are constantly appearing [38, 41, 47, 60–63]. It seems to be reasonable as it is completely clear that a correct understanding of this phenomenon can also provide an answer to the question of the nature of high-temperature superconductivity as a whole. Among many other papers it is worth to mention the most radical model as for the nature of high-temperature superconductivity and a PG in cuprates. It is the Resonating Valence Bonds (RVB) model proposed by Anderson [64, 65], which describes a spin liquid of singlet electronic pairs. In this model, largely relies on the results obtained using one-dimensional models of interacting electrons, the low-temperature behavior of electrons differs sharply from the standard behavior in ordinary three-dimensional (3D) systems. An electron possessing charge and spin is no longer a well-defined excitation. So-called charge and spin separation occurs. It is supposed that spin is transferred by an uncharged fermion, called a spinon and charge - a spinless excitation - by a holon. In the RVB model both types of excitations - spinons and holons - contribute to the resistivity. However, the holon contribution is considered to be determining, while spinons, which are effectively coupled with a magnetic field **H**, must determine the temperature dependence of the Hall effect. Even though the RVB model led to a series of successes [65, 66], it is dificult to think up the physics behind the processes which could lead to the charge and spin separation especially in quasi-two-dimensional systems, which cuprate HTS's are. Nevertheless, the RVB model contains at lest one rational idea, namely, it is supposed that two kinds of quasi-particles with different properties have to exist in the high-temperature superconducting (HTS) system at *T* below *T*∗. In the RVB model such

However, even though researchers have made great efforts in this direction, the physics of the PG phenomenon is still not entirely understood (see Ref. [2] and references therein). That is why, we have eventually to propose our own Local Pair (LP) model [13, 27] developed to study a pseudogap Δ∗(*T*) in high-temperature superconductors and based on analysis of the excess conductivity derived from resistivity experiments. We share the idea of the RVB model as for existence of two kinds of quasi-particles with different properties in HTS's below *T*∗. But in our LP model these are normal electrons and local pairs, respectively. I will frame our discussion in terms of the local pairs, and try to show that this approach allows us to get a set

There are several considerations leading to the understanding of the possibility of paired fermions existence in HTS's at temperatures well above *Tc* which I am going to discuss now. It is well known, that a pseudogap in HTS's is manifested in resistivity measurements as a downturn of the longitudinal resistivity *ρxx*(*T*) at *T* ≤ *T*<sup>∗</sup> from its linear behaviour above *T*<sup>∗</sup>

Here *ρ*(*T*) = *ρxx*(*T*) and *ρN*(T)=*α*T+b determines the resistivity of a sample in the normal

(*T*) = *σ*(*T*) − *σN*(*T*), which can be written as

Pseudogap and Local Pairs in High-Tc Superconductors 139

(*T*)=[*ρN*(*T*) − *ρ*(*T*)]/[*ρ*(*T*)*ρN*(*T*)]. (1)

of reasonable and self-consistent results and clarify many of the above questions.

**2.2. The main considerations as for local pair existence in HTS's**

(Fig.1). This results in the excess conductivity *σ*�

state extrapolated toward low temperatures.

*σ*�

decrease [57–59]. That is why the phenomenon has been named a "pseudogap"

particles are spinons and holons.

The Chapter addresses the problem of the PG which is believed to appear most likely due to the ability of a part of conduction electrons to form paired fermions (so-called local pairs) in a high-*Tc* superconductor at *T* ≤ *T*<sup>∗</sup> [6, 13, 22–27]
