Majorana Nanostructures and Their Electrostatic Environment

Abstract

Majorana zero modes (MZMs) are zero-energy excitations emerging in one- and two-dimensional topological superconductors. These exotic modes have attracted much attention in the last decade due to their topological protection and non-Abelian statistics, which make them possible building blocks for topological quantum computation. In particular, semiconductor-superconductor (SM-SC) nanostructures have attracted the most attention with several measurements being consistent with the presence of MZMs. Debate continues, however, whether MZMs or topologically-trivial Andreev bound states are responsible for such measurements. In order to interpret experimental results distinguishing MZMs from Andreev bound states and gain a better understanding of what conditions need to be met in order for MZMs to be achieved in semiconductor-superconductor nanostructures, detailed modeling is required. In this thesis, work is presented that addresses this need with particular focus placed on understanding the electrostatic environment. A formalism is developed to solve the Schrodinger-Poisson equations for large systems. Additionally, effective models are constructed that accurately capture the low-energy physics governing Majorana devices while significantly reducing the computational complexity. Various problems currently of importance to the community are addressed. As a first example, we study subband occupation in Majorana nanowires as a function of device parameters. We find that moderate values of surface charge density dramatically limits the parameter space lying in the optimal regime in which only a few well-separated subbands are occupied. As a second example, we study how the electrostatics affects the magnetic proximity effect in SM-SC-magnetic insulator nanostructures. The geometric layout of the three material components is shown to play a key role in determining the magnitude of the magnetic proximity effect and whether topological superconductivity is achievable. A detailed study of charge impurity disorder within Majorana nanowires is presented. We show that rather low charge impurity densities ( ∼ 10^{15} cm^{− 3} ) destroy the topological superconductivity and resulting MZMs, indicating that significant improvements in material purity should be a top community priority. We also show that inter-subband coupling arising from disorder or other non-uniformities, can pin trivial Andreev bound states near zero-energy, mimicking the phenomenology of MZMs. Lastly, original device designs in planar SM-SC nanostructures are presented. Periodic modulations of the superconductor are shown to significantly increase the topological gap and improve the robustness of MZMs against disorder and other non-uniformities.