Anisotropy of the gap parameter in the hole-doped cuprates

Abstract

The structure of the gap parameter (∆ k ) for the hole-doped cuprates has been studied. The obtained results indicate that the antinodal part of ∆ k is very weakly temperature dependent and above the critical temperature (TC), it extends into the anomalous normal state to the pseudogap temperature. On the other hand, the values of ∆ k , which are close to the nodal part, are strongly temperature dependent. The model has been tested for the YBa2Cu3O 7−δ superconductor. It has been shown that the theoretical results agree with the experimental data.Keywords: High-temperature superconductors; Anisotropy; Energy gap. [20]. So far, the obtained results have been interpreted in the framework of the two different approaches.In the first case, the difference between the doping and temperature dependence of the gap in the nodal and antinodal region suggests that the pseudogap and the superconducting gap are independent [21], [22]. Additional support comes from the strong deviation from the standard d-wave form of the energy gap in the underdoped region. The above fact is interpreted as composition of the d-wave superconducting gap and the remnant pseudogap [23], [24].In the second case, the pseudogap is considered as the precursor of the superconducting gap [25], [26]. The d-wave symmetry deviation in the underdoped region is connected with the existence of the high-harmonic pairing terms [27].In the presented paper, we have studied the anisotropy of the gap parameter for the hole-doped superconductors in the framework of the recently introduced theory [28], [29].Our main purpose was to derivation the thermodynamic equation for the anomalous thermal average, which determines the structure of the gap parameter. Next, the temperature dependence of the nodal and the antinodal part of the energy gap has been calculated. We have assumed that the theory should be simple enough as far as possible. However, the good agreement between the theoretical predictions and the experimental results has been also required.The model is based on three postulates: (i) In the superconductivity domain of the cuprates the fundamental role is played by the electrons on the CuO 2 planes. (ii) The conventional electron-phonon (EPH) interaction exists in the cuprates, which does not have to be strong. (iii) Strong electronic correlations exist in the cuprates, but the electron-electron scattering in the superconductivity domain is inseparably connected with absorption or emission of the vibrational quanta.The first postulate emphasizes the importance of the quasi two-dimensionality of the system. The second one refers to the classical pairing mechanism given by Fröhlich [30], [31]. The third postulate states that the strong electron correlations in the cuprates are inseparably coupled with the phonon subsystem. The first two postulates define the van Hove scenario [32], [33]. The third postulate requires further discussion because it is far more subtle. In particular, it should be noted that the postulated electron correlations generalize the Hubb...

Superconducting properties of lithium-decorated bilayer graphene

“…In order to determine precisely the physical value of the energy gap at the Fermi level, and supplement results obtained in the previous section, the Eliashberg equations are solved in the mixed representation (for more details please see [26], [37] and [38]). This procedure allows to obtain the solutions of the Eliashberg equations on the real axis (ω), which provide the quantitative values of the energy gap at the Fermi level (2∆(T )) from:…”

“…This is a general trend in the domain of superconductivity which aims to achieve the highest possible value of critical temperature (T C ) in the given material (please see for example [30], [31], [32]). In particular, proposition given in [29] should be of crucial interest for the scientific community, since bilayer lithium-decorated graphene structures are already experimentally proved to be thermodynamically stable [33].…”

Detailed study of the superconducting properties in compressed germane

“…Wherein the measured critical temperature (T C ) of 203 K in hydrogen sulfide is among the highest over allknown superconductors [5]. The theoretical studies have revealed a significantly more superconducting hydrogenrich materials such as PtH [7,8], H 2 S [9], GaH 3 [10,11], ScH 3 [12,13], SnH 4 [14], GeH 4 [15,16], NbH 4 [17,18], CaH 6 [19], MgH 6 [20] of which the highest critical temperature equal to 263−271 K was estimated for MgH 6 compound at a pressure range from 300 to 400 GPa [20]. As it turns out pressure (p) can have a very large impact on the critical temperature and thermodynamics of superconducting state.…”

Phonon-mediated superconductivity in compressed NbH4 compound

“…In particular, in the family of hydrogenated silicon: Si 2 H 6 at 275 GPa and SiH 4 (H 2 ) 2 at 250 GPa, application of the Allen-Dynes modified McMillan equation gives the highest superconducting transition temperatures amounts 153 K and 107 K, respectively [13,14]. In hydrogenated germane GeH 4 (H 2 ) 2 at 250 GPa, T C is equals to 90 K [15] and hydrogenated gallane GaH 3 at 120 GPa is characterized by T C = 102 K [16] (T C rises to 123 K when calculations are conducted in the framework of the Eliashberg formalism [17]). …”

“…A proper treatment of those effects was developed in Eliashberg theory which allows to reproduce the superconducting properties of a conventional superconductor within an experimental accuracy. This approach has been described in paper [24] and successfully used in the study of other hydrogen-rich compounds [17,19,25], and also in the study of materials for which is a possibility of comparison of the theoretical and experimental results (e.g. simple elements: Ca, S, Li, and compounds: CaLi 2 , K 3 C 60 , Rb 3 C 60 , MgB 2 ) [26][27][28][29][30][31].…”