Topological superconductivity in Chern insulators

This dissertation presents studies of topological superconductivity in Chern insulator systems. In particular, when a Chern insulator such as a quantum Hall or a quantum anomalous Hall system is proximity coupled to a trivial s-wave superconductor. While quantum anomalous Hall based system is investigated in detail in both one and two dimensions, the focus is solely on two dimensions in quantum Hall bases system. Both quantum Hall and quantum anomalous Hall break time reversal (T)-symmetry. Hence throughout this thesis, we focus on the T-symmetry broken topological superconductor systems, which fall in the class [double struck D] of the Altland-Zirnbauer classification. After a brief introduction to thesis in chapter 1 and review of topological superconductivity in chapter 2, in chapter 3, a realistic system motivated from the experimental observation of the quantum anomalous Hall effect is considered. The focus of this chapter is on one dimensional (1D) topological superconducting phase in thin ribbon geometries [Phys. Rev. B 97, 081102(R)]. It identifies the quantum anomalous Hall based system as highly controllable platform for Majorana zero modes, which can be potentially used as Majorana braiding device. In chapter 4, two dimensional (2D) topological superconducting phase in the quantum Hall based system is studied [arXiv:1903.12249]. Because of the inherent requirement of the external magnetic field to achieve quantum Hall physics, this system requires consideration of vortex lattice phase in the parent superconductor. It is shown that the topological superconducting phase is determined by the type of vortex lattice. Hence, making quantum Hall based system different than quantum anomalous Hall based system, giving much richer phase diagram. Experimental protocol to engineer and observe Majorana edge modes in this system is also discussed. In chapter 5, reentrant superconductivity under magnetic fields beyond semiclassical critical magnetic field is discussed. It is argued that recently discovered superconductivity in magic angle twisted bilayer graphene (MATBG) can be a promising ground to observe this phase. In chapter 6, recent transport experiments in quantum anomalous Hall/superconductor devices are discussed. The two main experiments on this system have contradictory results and there is widespread debate on possible explanations of the experimental observations, which can born out of chiral Majorana mode (i.e. topological) or disorder (i.e. trivial). The main arguments on both sides are summarized and some strategies to resolve the debate are proposed.Physic