Jelena Klinovaja

Engineering topological phases and excitations in nanostructures with interactions

The last decade has witnessed a rapidly growing interest in quantum states in lower dimensions with non-trivial braid statistics, bound states at zero-energy in particular. A plethora of new setups that can host Majorana fermions, particles that are their own antiparticles, have motivated many experiments. These exotic particles are non-Abelian anyons with a braid statistics of Ising-type, which allow the implementation of some of the universal quantum gates but not all of them. Parafermions that feature a more powerful braid statistics could extend the class of gates. To create parafermions, one needs to gain control over strongly interacting systems both theoretically and experimentally. The main goal of this project was to advance theory by both proposing novel ways to generate fractional topological excitations in the most feasible experimental setting and improving our understanding of already known effects by extending them to the fractional regimes.

Results

The research begun with studies of fractional topological phases occurring in the presence of strong electron-electron interactions. The team proposed a tune-free scheme to realise Kramers pairs of Majorana bound states in recently discovered high-order topological insulators and demonstrated that such a topological superconductivity is stabilised by moderate electron-electron interactions. The study continued with strong electron-electron interactions to generate fractional topological phases. The found topological phases are stable against disorder as well as against parameter variations and are within experimental reach. The analytical study of an underdamped currency-based topological Josephson junction led to the following proposal: if the length of the system is finite, the transition from insulating to conducting state occurs at exponentially higher bias current due to hybridisation of the states with different parities as a result of the overlap of MBSs localised on the junction and at the edges of the topological nanowire forming the junction.

Impact

Along with their practical applications in topological quantum computing, generating parafermions will also have a strong impact on fundamental physics because they can serve as a stepping stone for even more exotic phases when they condense into a liquid. Quasiparticles with properties such as being anyons (neither bosons nor fermions) with non-Abelian braid statistics do not occur in our three-dimensional world. They were long considered purely academic constructs, quite disconnected from reality. With increasing theoretical understanding and improved experimental techniques, we are coming closer to the point where we can hope to observe such exotic quasiparticles in experiments. To bring this point even closer to reality by coming up with concrete and feasible schemes is one of the main goals of this project.