Competizione ed interazione tra ordini stripe e superconduttività nei superconduttori di tipo cuprato

The pairing mechanism of cuprate superconductors remains an unsolved question in condensed matter physics. In this family of high temperature superconductors (HTSC) the interaction between phonons and electrons seems to have no role, contrary to standard BCS superconductors. Coulomb repulsion, on the other hand, appears to be fundamental to understand HTSC. An undoped cuprate presents an anti-ferromagnetic order and it is a Mott insulator, while by replacing ligand atoms with doping atoms a superconductive phase may emerge. The cuprates structure consists of layers of ligand atoms alternating with layers of CuO2 where superconductivity develops allowing us to consider a 2d system. The crystal lattice structure splits the degeneracy of the Cu d orbitals, leaving the highest energetic orbital dx2−y2 half-filled. For this reason, a single band Hubbard model is appropriate to study the cuprate physics. The model presents two main terms:t is the nearest neighbour hopping term between Cu atoms and U is the on-site Coulomb repulsion. Recently, the discovery of competitive orders in cuprates superconductors has given new impetus to the research in this area. In particular, the experimental results show a minimum in the superconducting transition temperature for doping 1/8, explained with the presence of some competitive order. On the other side, the computational resolution of the Hubbard model finds a co-directional modulation of charge (with wavelength λ) and of spin (with wavelength 2λ), called linear or vertical stripe, as the ground state of the doping 1/8 point. We underline the discrepancy between the experimental ground state (doping 1/8) where λ= 4 and the computational solution where λ= 8. In order to try to obtain a state with λ= 4, in this thesis, the Hubbard model is extended by adding a realistic next-nearest neighbor hopping term t′. The computational method used is the Variational Monte Carlo (VMC): in practice, the ground state is approximated by a suitable wave function with variational parameters that have to be optimized. The wave function is built on an adequate auxiliary Hamiltonian: a standard BCS Hamiltonian plus an anti-ferromagnetic term for the uniform state and the same uniform auxiliary Hamiltonian plus the two modulation terms (charge and spin) for the stripe state. The Jastrow factor and the backflow correlation are added to the initial wave function in order to include electron-electron correlation. The minimization algorithm used is the stochastic reconfiguration that aims to minimize the expectation value of the variational energy optimizing the parameters of the wave function. The discussion underlines the energetical convenience of the stripe state as solution of the Hubbard model for different values of U and t′. Moreover, the optimal wavelengths λ of the stripe state are determined for different U and t′ values, which are within the ranges assessed for cuprates. The correlation functions show that the spin modulation is more important than the charge one for the formation of a stripe state. Subsequently, the analysis of the correlation functions defines the conductivity behavior and the possible coexistence of stripes with d-wave superconductivity (through an analysis ofthe BCS parameters). In this analysis, it turns out that t′ has a fundamental role in superconductivity, that emerges for t′/t < 0.