We review the status on Majorana bound states in condensed matter with a primary focus on hybrid materials systems consisting of superconducting and semiconducting materials. For about a decade ‘Majorana signatures’ have been reported by several groups in different devices and materials choices. A definitive unambiguous prove, however, is still lacking. Impurities and disorder in general seems to be the main hurdle in realizing robust Majorana bound states. This hurdle is circumvented by building piecewise the required materials properties by sequencing quantum dots and superconductors and thereby forming a Kitaev chain. We recently realized a minimal chain with just a single unit cell which already shows the existence of Majorana bound states, however, without the desired topological protection. We will discuss this progress in the context of quantum computing and topological quantum computing in particular.
Delft University of Technology, The Netherlands