Majorana Fermions In Topological Superconductors

The Majorana fermion is a particle that is its own antiparticle. Because of its special nature has great application prospect in the topological quantum computer. People have paid great effort to find the Majorana fermions in theoretical research and experimental research. Although people have not found any fundamental particles belonging to Majorana fermions, in recent year people in condensed matter systems have found the evidence of Majorana fermions. In theory, the Majorana fermions can be simulated by the system including topological insulator—superconductor, S wave superconductor semiconductor heterostructure and s wave superconductor heterostructure, cold atom.In our work, mainly research on topology properties in the induction of Coulomb potential impurities numerical study of Majorana fermions in a superconductor. First, we establish the theoretical model and write the Hamiltonian. We use the solution of the BDG equations to obtain the required data. Last, we can use the data to summary. The specific work is as follows:1. Topological superconductors. We first establish a simple model of topological superconductors to explain the nature of topological superconductors.2. The Majorana fermions of the topological superconductors. We establish a theoretical model to analyze the Majorana fermions of topological superconductors.3. The impurity effect of the topological superconductors. Through the introduction of prior experimental and theoretical research results, combined with the work we have done in this paper to analyze the impurity effect of the topological superconductors.4. We here investigate the effect of an off-plane charged impurity in a topological superconductor with the impurity term being simulated by an additional Coulomb potential. The research results show that: We study numerically Majorana fermions induced by a charged impurity in topological superconductors. It is revealed from the relevant Bogoliubov-de Gennes equations that for quasi-one dimensional systems, a pair of Majorana fermions are bounded at the two sides of one charge impurity and well separated; and for a two dimensional square lattice, the charged-impurity-induced Majorana fermions are similar to the known pair of vortex-induced Majorana fermions, in which one Majorana fermions is bounded by the impurity while the other appears at the boundary. Moreover, the corresponding local density of states is explored, demonstrating that the presence of Majorana states may be tested experimentally.