Periodic Reporting for period 4 - ETOPEX (Engineering Topological Phases and Excitations in Nanostructures with Interactions)
Berichtszeitraum: 2022-07-01 bis 2023-12-31
During the last decade we have witnessed a rapidly growing interest in quantum states in lower dimensions with non-trivial braid statistics. In particular, bound states at zero-energy have attracted a lot of attention. For instance, a plethora of new setups that can host Majorana fermions, particles that are their own antiparticles, has been suggested and motivated many experiments to test these predictions. These exotic particles are interesting not only from a fundamental point of view but also find a direct application in topological quantum computing schemes. Majorana fermions are non-Abelian anyons with a braid statistics of Ising-type. Such anyons allow the implementation of some of the universal quantum gates but not all of them. To extend the class of gates, one should work with parafermions that feature a more powerful braid statistics. Importantly, parafermions arise only in the presence of strong electron-electron interactions giving rise to fractional topological phases. Thus, to generate parafermions, one needs to get control over strongly interacting systems both theoretically and experimentally. The same is true for their higher dimensional cousins such as fractional topological insulators and superconductors or Weyl semimentals. The main goal of this project is to advance theory by both proposing novel ways to generate fractional topological excitations in the most feasible experimental settings but also by improving our understanding of already known effects by extending them to the fractional regimes.
Along with their practical applications in topological quantum computing, generating parafermions will have a strong impact on fundamental physics, also 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. For a long time they were considered as 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.
Along with their practical applications in topological quantum computing, generating parafermions will have a strong impact on fundamental physics, also 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. For a long time they were considered as 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.
The project has been dedicated to the studies of fractional topological phases occurring in the presence of strong electron-electron interactions. In particular, we studied the electrical conductance in single-mode quantum wires with Rashba spin-orbit interaction subjected to externally applied magnetic fields in the regime in which the ratio of spin-orbit momentum to the Fermi momentum is close to an odd integer, so that a combined effect of multielectron interaction and applied magnetic field leads to a partial gap in the spectrum. We studied how this partial gap manifests itself in the temperature dependence of the fractional conductance of the quantum wire and showed how the low-temperature fractional conductance can be affected by the finite length of the wire, by the properties of the contacts, and by a shift of the chemical potential, which takes the system away from the resonance condition. We proposed a tune-free scheme to realize Kramers pairs of Majorana bound states in recently discovered higher-order topological insulators (HOTIs): by bringing two hinges of a HOTI into the proximity of an s-wave superconductor, the competition between local and crossed Andreev pairing leads to the formation of Majorana Kramers pairs, when the latter pairing dominates over the former. We demonstrated that such a topological superconductivity is stabilized by moderate electron-electron interactions. In addition, we considered a Josephson junction bilayer consisting of two tunnel-coupled two-dimensional electron gas layers with Rashba spin-orbit interaction, proximitized by a top and bottom s-wave superconductor with phase difference $\phi$ close to $\pi$. In the presence of a finite weak in-plane Zeeman field, the bilayer can be driven into a second order topological superconducting phase, hosting two Majorana corner states. In the second year, we moved to the next stage of the project by including strong electron-electron interactions to generate fractional topological phases. In particular, we were interested in fractional higher-order topological insulators and superconductors, focusing on a system of weakly coupled Rashba nanowires in the strong spin-orbit interaction (SOI) regime. The nanowires were arranged into two tunnel-coupled layers proximitized by a top and bottom superconductor such that the superconducting phase difference between them is π. We showed that in such a system strong electron-electron interactions can stabilize a helical topological superconducting phase hosting Kramers partners of Z_2m parafermion edge modes, where m is an odd integer determined by the position of the chemical potential. Furthermore, upon turning on a weak in-plane magnetic field, the system is driven into a second-order topological superconducting phase hosting zero-energy Z_2m parafermion bound states localized at two opposite corners of a rectangular sample. We also considered a one-dimensional Rashba nanowire in which multiple Andreev bound states in the bulk of the nanowire form an Andreev band. We show that, under certain circumstances, this trivial Andreev band can produce an apparent closing and reopening signature of the bulk band gap in the nonlocal conductance of the nanowire. Furthermore, we show that the existence of the trivial bulk reopening signature in nonlocal conductance is essentially unaffected by the additional presence of trivial zero-bias peaks in the local conductance at either end of the nanowire. The simultaneous occurrence of a trivial bulk reopening signature and zero-bias peaks mimics the basic features required to pass the so-called “topological gap protocol.” Our results therefore provided a topologically trivial minimal model by which the applicability of this protocol can be benchmarked. This work was very well received by the community and was covered in the public media.
The goal of this project is to push forward the theoretical description of parafermions as well as other fractional topological states in higher dimensions and make their observation possible in the near future. We have advanced the description of interacting topological phases. We have developed methods to analyse higher order topological phases.