BSc DefencesClara Neerup Breiø
Title: Intrinsic Topological Superconductors with Triplet Pairing
Abstract: This talk will present an investigation of a $p_x+ip_y$ superconductor. After a brief introduction to superconductivity, the Bogoliubov-de Gennes equation of the $p_x+ip_y$ superconductor is determined and the topology is discussed. Subsequently results obtained from self-consistent numerical solutions are presented. We first study the case with open boundary conditions yielding chiral edge states. We further impose a vortex and confirm the guaranteed zero-energy excitation in the core. Finally we display results obtained from invoking a half-quantum vortex and argue that the zero-energy excitation in the core is a topologically protected Majorana zero mode.
Hano O. M. Sura
Title: Topological superconductivity and Majorana fermions in 2D lattice models
Abstract: "A model of a 2D topological s-wave superconductor is presented. It is argued that the model belongs to the symmetry class D from which one can infer, that it has topologically non-trivial phases. It is also argued why Majorana fermions appear at the edges of the lattice in these phases. Phases and associated edge-states are explored numerically in three different settings: a semi-periodic lattice model, a open-boundary model with a vortex-like phase in the superconducting gap and a periodic-boundary model with an on-site potential impurity. An experimential signature, the local density of states, is in each case presented."
Title: Weyl semimetals in models for ultracold atoms
Abstract: The study of topological phases of matter are at the focus of both theoretical and experimental studies. Most of the efforts have been devoted to gapped phases but in recent years gapless phases, such as Weyl semimetals, have been studied theoretically and experimentally. My project is a theoretical proposal inspired by the recent experimental techniques in the ultracold atoms platform. I study the effect of a non-Abelian gauge potential on a Weyl semimetal phase appearing in a particular 3D tight-binding model of fermions. I consider a lattice characterized by a C3 rotational symmetry and staggered pi/2 fluxes on the triangular plaquettes in its horizontal planes. The energy spectrum is characterized by both single Weyl points with linear energy dispersions in all three momenta directions, and double Weyl points with quadratic energy dispersions in two directions and linear dispersion along the axis of the rotational symmetry.