We present a theory describing the superconducting (SC) interaction of Dirac electrons in a quasi-two-dimensional system consisting of a stack of N planes. The occurrence of a SC phase is investigated both at T = 0 and T = 0, in the case of a local interaction, when the theory must be renormalized and also in the situation where a natural physical cutoff is present in the system. In both cases, at T = 0, we find a quantum phase transition connecting the normal and SC phases at a certain critical coupling. The phase structure is shown to be robust against quantum fluctuations. The SC gap is determined for T = 0 and T = 0, both with and without a physical cutoff and the interplay between the gap and the SC order parameter is discussed. Our theory qualitatively reproduces the SC phase transition occurring in the underdoped regime of the high-Tc cuprates. This fact points to the possible relevance of Dirac electrons in the mechanism of high-Tc superconductivity.

We derive analytic expressions for the critical temperatures of the superconducting (SC) and pseudogap (PG) transitions of the high-Tc cuprates as a function of doping. These are in excellent agreement with the experimental data both for single-layered materials such as LSCO, Bi2201 and Hg1201 and multi-layered ones, such as Bi2212, Bi2223, Hg1212 and Hg1223. Optimal doping occurs when the chemical potential vanishes, thus leading to an universal expression for the optimal SC transition temperatures. This allows for the obtainment of a quantitative description of the growth of such temperatures with the number of layers, N, which accurately applies to the Bi, Hg and T l families of cuprates. We study the pressure dependence of the SC transition temperatures, obtaining excellent agreement with the experimental data for different materials and dopings. These results are obtained from an effective Hamiltonian for the itinerant oxygen holes, which includes both the electric repulsion between them and their magnetic interactions with the localized copper ions. We show that the former interaction is responsible for the SC and the latter, for the PG phases, the phase diagram of cuprates resulting from the competition of both. The Hamiltonian is defined on a bipartite oxygen lattice, which results from the fact that only the px and py oxygen orbitals alternatively hybridize with the 3d copper orbitals. From this, we can provide an unified explanation for the d x 2 −y 2 symmetry of both the SC and PG order parameters and obtain the Fermi pockets observed in ARPES experiments.

The discovery of superconductivity in twisted bilayer graphene has triggered a resurgence of interest in flatband superconductivity. Here, we investigate the square-octagon lattice, which also exhibits two perfectly flat bands when next-nearest-neighbor hopping or an external magnetic field are added to the system. We calculate the superconducting phase diagram in the presence of on-site attractive interactions and find two superconducting domes, as observed in several types of unconventional superconductors. The critical temperature shows a linear dependence on the coupling constant, suggesting that superconductivity might reach high temperatures in the square-octagon lattice. Our model could be experimentally realized using photonic or ultracold atoms' lattices.

Recently discovered advanced materials frequently exhibit a rich phase diagram suggesting the presence of different competing interactions. A unified description of the origin of these multiple interactions, albeit very important for the comprehension of such materials is, in general not available. It would be therefore very useful to have a simple model where the common source of different interactions could be possibly traced back. In this work we consider the (AF) Heisenberg-Kondo lattice model, describing a set of localized spins on a square lattice with anti-ferromagnetic nearest neighbors interactions and itinerant electrons, which are assumed to be Dirac-like. These interact with the localized spins through a Kondo magnetic interaction. By integrating out the localized degrees of freedom we obtain a set of different effective interactions among the itinerant electrons. This includes a BCS-like superconducting term, a Nambu-Jona-Lasinio-like, excitonic term and a spin-spin magnetic term. The resulting phase diagram is investigated by evaluation of the mean-field free-energy as a function of the relevant order parameters. This shows the competition of the above interactions, depending on the temperature, chemical potential and coupling constants.

We have shown that the weak-coupling limit superconductors are well described by q ∼ 1, where q is a real parameter which characterizes the degree of nonextensivity of Tsallis' entropy. Nevertheless, small deviations with respect to q = 1 provide better agreement when compared with experimental results. We have also shown that the generalized BCS theory with q > 1 exhibit power-law behavior of several measurable macroscopic functions in the low-temperature regime. These power-law properties are found in many high-T c oxides superconductors and motivated us to extend Tsallis entropy calculations to these systems. Therefore, we have calculated the phase diagram and the specific heat and we compare our results with the experimental data for the YBa 2 Cu 3 O 7−δ family of compounds.