Effects of symmetry breaking in low dimensional materials

Resumen

The dimensionality of the system plays a decisive role in the behavior of the electronic dynamics of interacting electrons. In particular, the quasi-2D dimensionality is responsible for the unusual behavior observed in graphene-like materials and layered van-der-Waal systems. Moreover, such effects are also observed for superconducting materials of high critical temperature, even in the normal state, due to their low-dimensionality. The experimental study of graphene triggered a growing attention to respective electronic properties, because the honeycomb lattice defines a band structure with two nodal points in the Brillouin zone which determines a relativistic Dirac-type electronic dynamics. Within a theoretical framework, many properties of single-layer graphene have been studied to allow further characterization of this material. These properties are unconventional due to the unique band structure of graphene, which is described in terms of Dirac fermions, creating links with certain theories of particle physics. In fact, several theoretical groups have employed phenomenological models inspired in quantum cromodynamics (i.e. Nambu-Jona Lassino and Gross-Neveu models) applied to the study of graphene properties. These properties are responsible for the unusual phenomena, such as the fractional Hall effect, which allows the possibility for magnetic catalysis of an excitonic gap, ferromagnetism and superconductivity. The research of high critical temperature superconductors with impurity centers is significant for understanding the underlying physics of such disordered systems. While the cuprate family present insulating properties in the pristine state, the undoped iron pnictides (i.e. LaOFeAs) show a semi-metallic behavior. Inspite these diferences, both compounds are layered structures, where the superconducting state is supported by a quasi-2D square lattice. While for iron pnictides this state is formed by the FeAs layer, the cuprate superconducting state is formed by the CuO layer. The current work focuses on the theoretical study of the structural, electronic and optical properties of graphene-type materials, such as bilayer graphene; and also of s- and d-wave superconductors, more specifically iron pnictides and cuprates, respectively. Furthermore, disordered systems will be focused upon since these (quasi-)2D systems are quite sensitive to disorder. Such properties have major importance for technological device applications, as can be observed in the increasing technological fields of high temperature superconductores and electronic devices. The type of perturbations applied to the systems of interest are chemical impurities and/or external electric bias, and these show variations of the electronic and optical properties when compared to the pristine systems.