From Local Elements to Globally Ordered TOPological states of matter

Project Information

LEGOTOP

Grant agreement ID: 788715

DOI

10.3030/788715

Project closed

EC signature date 24 April 2018

Start date 1 October 2018

End date 30 September 2024

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 532 163,00

EU contribution

€ 1 532 163,00

Coordinated by

WEIZMANN INSTITUTE OF SCIENCE
Israel

Periodic Reporting for period 4 - LEGOTOP (From Local Elements to Globally Ordered TOPological states of matter)

Reporting period: 2023-04-01 to 2024-09-30

Summary of the context and overall objectives of the project

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.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

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 interferometers in the fractional quantum Hall effect, in Majorana wire networks, and in time-domain set-ups.

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

7. Discovery of a class of experimental set-ups in which 1D topological superconductivity may be generated with no application of a Zeeman magnetic field, thus finding a solution to an experimentally timely problem.

8. Analyzing an extension of this set-up to 2D.

9. Employing composite fermion theory to analyze the phases of the half-filled Chern band.

10. Developing an online course on Topological Quantum Matter that is followed by thousands of researchers, including students and faculty members. See https://www.youtube.com/watch?v=q0ELfyrvnbQ&t=55s&ab_channel=Topologicalquantummatter-Weizmannonline%7d and https://www.youtube.com/@topologicalquantummatter-w4105/featured.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

We consider the project to be very successful, as explained in our response to the various questions in this report. Its value is demonstrated by the publications, by its contribution to the professional development of a young cohort of physicists, and by the dissemination of knowledge acquired.

Many of the research directions developed in this project will continue in the years to come. In particular, the research of 1D topological superconductivity with no application of a magnetic field may have an applied angle that we will pursue.

Proposed finite-temperature phase diagram of $\nu\approx 5/2$ quantum Hall states.Hatched regions d

exact-pd-snsns.jpg