José Carlos Egues de Menezes.

In this proposal we present research plans to study Majorana Fermions in topological superconductors. We will address the problem by investigating the properties of the Kitaev toy model in the presence of metallic contacts and a more realistic quantum wire system. To investigate the Kitaev model with metallic contacts, we will employ the Green's function method that allows us to obtain the spectral properties of the Majorana modes in the system. In studying the Majoranas in quantum wells we will start from the basic ingredients necessary for the appearance of Majorana zero modes, namely the spin-orbit coupling, the superconducting proximity effect and an external magnetic eld. We will also include the electron-electron interaction in a 2D system, and investigate how the e-e induced gap affects the condition for the appearance of Majorana modes. Our proposal involves topics that are at the frontier of condensed matter research and are actively being investigated by the corresponding international scientific community.

This project consists essentially of four subprojects describing in detail research plans involving many challenging and outstanding problems in the recent literature. Our proposal identifies many relevant problems of common interest to be carried out jointly within recently created (virtual) Research Support Center in Quantum NanoPhysics, Q-NANO. We have grouped the topics in four main themes: (i) Quantum spintronics: novel spin effects in nanosystems, (ii) Electronic correlation effects in nanostructured materials, (iii) Quantum information processing with nanocavity networks, and (iv) Ab initio calculations in nanoalloys and nanoclusters. More specifically, we shall tackle problems involving topics such as: 1) quantum transport in and out of equilibrium in interacting quantum dots, 2) the Kondo effect in 
magnetic dots and molecular complexes, 3) spin orbit interaction in wires and dots with and without magnetic atoms, 4) correlation effects in model many-body systems, 5) topological insulators, 6) graphene nanostructures, 7) majorana fermions in wires with spin orbit interaction, 8) electronic structure of nanoclusters for nanocatalysis, 9) light-matter interaction in nanocavity networks (circuit QED), and 10) cold atoms in optical lattices simulating condensed matter systems. We emphasize that each of these topics offers a rich variety of research possibilities for us. Many of them are interconnected and will be approached using different theoretical/numerical complementary techniques mastered by our team. Our collaborative efforts proposed here should prove instrumental in boosting our research capacity and our ability to carry out competitive and impacting research with a higher international visibility.

CIAM/CNPq -- Colaboração Interamericana em Materiais

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