From Andreev to Majorana bound states in hybrid superconductor–semiconductor nanowires

By E. Prada, Pablo Perez San-José, Michiel W. A. de Moor, A. Geresdi, E. J. Lee, J. Klinovaja, Daniel Loss, J. Nygård, R. Aguado, L. Kouwenhoven. 2019

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Inhomogeneous superconductors can host electronic excitations, known as Andreev bound states (ABSs), below the superconducting energy gap. With the advent of topological superconductivity, a new kind of zero-energy ABS with exotic qualities, known as a Majorana bound state (MBS), has been discovered. A special property of MBS wavefunctions is their non-locality, which, together with non-Abelian braiding, is the key to their promise in topological quantum computation. We focus on hybrid superconductor–semiconductor nanowires as a flexible and promising experimental platform to realize one-dimensional topological superconductivity and MBSs. We review the main properties of ABSs and MBSs, state-of-the-art techniques for their detection and theoretical progress beyond minimal models, including different types of robust zero modes that may emerge without a band-topological transition. Topological Majorana bound states have potential for encoding, manipulating and protecting quantum information in condensed-matter systems. This Review discusses emergence and characterization of Majorana bound states in realistic devices based on hybrid semiconducting nanowires and their connection to more conventional Andreev bound states. Non-uniform superconductors and hybrid normal metal–superconducting systems can develop discrete bound states inside the superconducting gap, known as Andreev bound states (ABSs), through Andreev reflection processes. Andreev bound states are a superposition of electrons and holes, and can also develop a non-trivial spin structure if the system exhibits spin–orbit coupling and low densities, as is the case in proximitized semiconducting nanowires. Precise experimental characterization of ABSs in proximitized nanowires is now possible through a range of spectroscopic techniques, including tunnelling transport, quantum dot spectroscopy and microwave cavity spectroscopy. The interplay of spin–orbit coupling, Zeeman fields and low densities in proximitized semiconducting nanowires can induce a quantum phase transition into a topological superconducting phase, whereupon ABSs transform into zero-energy, topologically protected Majorana bound states (MBSs) with exotic properties, promising for quantum computation purposes. The experimental search for MBSs in proximitized nanowires has encountered a rich and complex phenomenology that has required standard theoretical models to be extended substantially, revealing in the process a host of mechanisms for the emergence of zero-energy bound states beyond the original band-topological framework. These states are known in the field as quasi-MBSs, partially separated MBSs or non-topological MBSs.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/5adf45d9b54a3965c1593ae49536cc701eb86650