CORDIS - EU research results

From Local Elements to Globally Ordered TOPological states of matter

Periodic Reporting for period 3 - LEGOTOP (From Local Elements to Globally Ordered TOPological states of matter)

Reporting period: 2021-10-01 to 2023-03-31

In the last four decades there have been tremendous progress in the study of topological states of matter, starting from the integer and the fractional quantum Hall effects at the 1980’s and expanding into topological insulators and superconductors in the last two decades. In parallel, there has been much progress in the understanding of the great potential of quantum computers, in particular for the solution of computational problems that are inaccessible to classical computers. Standing between this potential and its realization is the difficult problem of de-coherence. This project attempts to advance the comprehension of topological states of matter and examine their suitability for the construction of quantum bits that have a good level of protection from the effects of de-coherence. In particular, we study Majorana zero modes in topological superconductors, anyons in the fractional quantum Hall effect, and other systems of fractionalized nature.

Our overall objectives in this project are the discovery of systems suitable for realization of novel topological states of matter, the proposal of experiments designed to unravel their topological properties, the analysis of experimental results and the search for their use as quantum information devices.
A selected list of main achievements within the project include:

1. Analysis of measurements of thermal conductance of edge states in putative non-abelian fractional quantum Hall states.

2. Theoretical analysis of the effect of disorder on the phase diagram of the \nu=5/2 FQHE state and the way it is reflected in measurements of thermal Hall conductance.

3. Proposals for new experimental set-ups for the realization of Majorana zero modes in the normal part in planar SNS junctions, and participation in the analysis of the experimental systems realizing the proposal.

4. Study of interacting one dimensional systems and the circumstances under which they exhibit fractional conductances and fractional charge. The fate of these wires in presence of a nearby strongly correlated system inducing attractive interaction between the electrons in the one dimensional system.

5. Study of interference effects in the ultraclean materials of delafossites family, in Fabry-Perot interferometer in the fractional quantum Hall effect and in Majorana wire networks.

6. Constructing a model describing the evolution of the correlated quantum states in twisted bi-layer Graphene systems and employing it to understand a set of experimental measurements of thermodynamic quantities conducted by colleagues at MIT and Weizmann institute
In the future part of the project, we plan to:

• Expand our studies of novel experimental setups for observing and manipulating Majorana zero modes in topological superconductors. In particular, we will focus on set-ups in which the relative phase between different superconducting elements will play an important role.

• Expand our studies to new engineered material systems with interesting topological properties. In particular, these will include twisted bi-layer graphene, transition metal dichalcogenides (TMDs), epitaxially grown systems combining metals, semi-metals, insulators and superconductors, as well as their combinations.

• Expand our studies to novel types of topology, including fragile topology and its derivatives.

• Expand our studies of interference effects in fractionalized states of matter, in particular those engineered on the basis of Majorana boxes and quantum Hall systems.

• Continue and enhance our ongoing collaboration with experimental groups.
Proposed finite-temperature phase diagram of $\nu\approx 5/2$ quantum Hall states.Hatched regions d