Majorana fermions in topological superconductors
Topological superconductors are a newly discovered class of materials with features uniquely advantageous for quantum computing. They have lately generated an immense amount of attention due to the possibility of them having effective Majorana fermions at surfaces, vortices, and other defects. Approximately one can say that a Majorana fermion is half an electron, or more accurately, in a system with Majorana fermions the wave function of an electron has split up into two separate parts. This non-local property of two Majorana fermions can be used for exceptionally fault-tolerant quantum computing. A quantum computer uses the quantum nature of matter to represent data and preform calculations and can be exponentially faster than any classical supercomputer. However, quantum systems are generally extremely sensitive to disturbances and we are still far from being able to construct useful quantum computers. Topological superconductors with Majorana fermions avoid this extreme sensitivity by using the non-local nature of the Majorana fermions, which automatically make them very robust. The goals of this project are to theoretically 1) discover new and experimentally viable topological superconductors with Majorana fermions and 2) determine the properties of the Majorana fermions and the conditions necessary for feasible topological quantum computation in real materials. The project focuses both on the currently most promising topological superconductors found in superconducting hybrid structures of well-known spin-orbit coupled materials and on discovering new topological superconductors in graphene and related materials. We already have several years of experience studying these types of systems using a microscopic lattice tight-binding Bogoliubov-de Gennes (BdG) formalism, which is ideally suited for an accurate description of the superconducting state in topological superconductors with Majorana fermions. Thanks to medium SNIC grants, we have during the last few years investigated a number of systems, such as a vortex core structure and its Majorana fermion in superconducting hybrid strutures, spontaneous currents in superconductors with magnetic impurities, wire networks with Majorana fermions at wire intersections, and also started to incorporate high-temperature superconductors into these type of systems (see webpage for a full publication list). We are planning to continue this research, working towards the overall goals of the project. A medium-scale computing grant is necessary to cover our computational needs. Many properties of these systems are intimately linked with the superconducting coherence length, which requires large lattice systems not feasible on a desktop computer. We also often study large parameter spaces in order to pinpoint specific behaviors.