Helical states and Majorana fermions in topological nanostructures – TOPONANO

The mathematical concept of topology applied to condensed matter has been very helpful to understand the transport properties of certain materials. This description was responsible for the discovery of new states of matter called topological insulators. These are insulating in the bulk of the material, but conducting at the edge. Their band structure is dominated by the spin-orbit interaction and is characterized by one or more topological invariants that distinguish them from traditional insulators. In two dimensions, they give rise to the quantum spin Hall effect and spin states are characterized by helical one-dimensional spin-polarized edge channels. The emergence of these new states of matter is a fundamental topic, but because of their spin properties, they could also have implications in spintronics.

Similar concepts have led to the superconducting counterpart of topological insulators: topological superconductors. The topological character manifest itself in the excitation spectrum of the superconducting state and gives rise to quasiparticles analog to Majorana fermions. Majorana particle is known to be its own antiparticle, have no charge or spin and are therefore very well isolated from the environment and are ideal for storing quantum information. The existence of Majorana fermions was predicted and intensely studied in particle physics but this quest was unsuccessful. The experimental realization of topological superconductivity in superconductor-semiconductor hybrid structures allowed to reproduce the experimental conditions for the creation of Majorana fermions and the first experimental signatures in transport was obtained recently. Since then, the search around the Majorana fermions has become a major theme in condensed matter physics. However, most of these theoretical predictions about these excitations have not received any experimental confirmations.

While traditional methods of characterization of materials such as ARPES or STM have convincingly shown the existence of topological insulators and topological superconductors, the few experimental signatures obtained in transport are the subject of discussions in our community. The main sticking point is related to the low crystalline quality materials available. To use topological insulators in electronic circuits and make the most of their unique structure of bands, a major effort is nowadays devoted to optimize the growth of materials with strong spin-orbit.

We have assembled a consortium with strong expertise in the fields of topological superconductivity, semiconductor-superconductor hybrid structures and growth of materials with strong spin-orbit coupling. We propose initially to optimize the growth of two recently identified material for their extremely important spin-orbit coupling compared to traditional semiconductor materials (GaAs, Si) nanowires based on germanium (Ge) and quantum wells based of antimonide (GaSb) and arsenide (InAs). We intend to highlight clearly and study the helical spin states. In a second step, we will use these developments to integrate these components in nanoelectronic superconductor-semiconductor hybrid circuits. The expected high quality of the semiconductor structures developed in our consortium will then allow us to demonstrate the unique properties of Majorana fermion excitations predicted theoretically but so far with no experimental demonstrations.