The Inverse Problem for Topological Materials, towards new topologies and new functionalities in real settings

Project Information

IPTM

Grant agreement ID: 101025315

DOI

10.3030/101025315

Project closed

EC signature date 31 August 2021

Start date 1 January 2022

End date 23 January 2024

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 224 933,76

EU contribution

€ 224 933,76

Coordinated by

THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE
United Kingdom

Periodic Reporting for period 1 - IPTM (The Inverse Problem for Topological Materials, towards new topologies and new functionalities in real settings)

Reporting period: 2022-01-01 to 2023-12-31

Summary of the context and overall objectives of the project

The recent classification of symmetry-indicated band structure topologies for all space groups has led to the prediction of thousands of topological materials (TM). We are thus at a very exciting crossroad where the theory of TM is gaining enough maturity to impact material science, opening the way to real settings and potential long-term applications. There are however key challenges remaining towards the building of functional topological quantum devices. Indeed, the microscopic origin of topology in TM is not well understood because (i) the general analytical conditions for nontrivial topology are hidden by the eigenvalue problem for which no closed-form exists beyond very low-rank matrices, (ii) there is a jump in complexity when considering the many-band models that include all relevant physical degrees of freedom of real materials (sub-lattices, orbitals, spins) leading to high-dimensional parameter spaces. The aim of this “Inverse Problem for Topological Materials” (IPTM) project is to address these issues concretely: (A) by establishing the inverse map from a fixed band structure topology to few-band lattice models, (B) by adding symmetry conditions (point groups and space groups) for the most representative crystalline structures, and (C) by establishing the inverse map in real settings through the state-of-the-art modeling of real materials obtained from the combination of (C.1) first principles results (Density Function Theory and optimized wannierization) and (C.2) tight-binding models systematically derived from group theory. Aiming at a fundamental understanding of topology in materials, this project aims to make significant steps in our ability to predict new TM with new functionalities.

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

This project has led to a variety of results ranging from the advancement of our fundamental understanding of topology in band structures to the prediction of material realization of new topologies in many different settings. In particular, this project has made impactful contributions to the study of new nodal topological phases associated to non-Abelian homotopy charges of nodal (Weyl) points and new topological insulating phases associated to the Euler class invariant of real Bloch Hamiltonians. A central point here is the intrinsic relation between the conversion of the non-Abelian charges of nodal points through braiding and the phase transitions between distinct gapped Euler phases. Furthermore, these theoretical considerations were systematically extended to the prediction of real systems holding the new topological phases and this for different settings. More precisely, we predicted the manifestation of the non-Abelian and Euler topologies in (1) the electronic band structures of Weyl semimetals with spin-orbit coupling, either using strain or temperature-induced structural phase transitions, (2) the phonon band structures of materials such as layered silicates and Al2O3, where the braiding of nodal points is controlled by strain and gating, (3) the vibration spectrum of spring-mass systems. Moreover, (4) these topological phases were realized experimentally in acoustic meta-materials. We also unveiled the manifestation of Euler topology and non-Abelian braiding in systems out-of-equilibrium, such as quenched cold atoms and time-periodically driven Floquet phases.

These results were presented in high-impact journals (Nature Physics, Nature Communications, Physical Review Letters, Science Bulletin) and in other more specialized high-standard journals (Physical Review B, Physical Review Research, Carbon, New Journal of Physics, etc.). They were also communicated to the scientific community in large scientific conferences, e.g. the March Meeting of the American Physical Society, workshops and invited seminars in different leading groups in the world. I participated actively in co-supervising master students and PhD students, and finalizing several collaborations with principal investigators and post-docs in Cambridge University. I have further disseminated the new knowledge accumulated during the project through invited lectureships and frequent discussions with the students in Cambridge.

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)

This project achieved to go beyond the state of art on several levels. First, on the theory side, I have made systematic use of the full geometric structure of the classifying space of gapped topological Hamiltonians, called complex and real Grassmannians. This allowed me to find the universal ansatz up to five-band Bloch Hamiltonians hosting non-Abelian and Euler topologies. This directly answers the challenge of point (i) above, namely my approach bypasses the step of diagonalization by constructing the lattice model directly from the two- or three-dimensional cells of the Grassmannians. On the side of modeling real materials, this project led to several successful collaborations with researchers specialized in density functional theory in Cambridge that led to the proposal of real material candidates. Finally, I collaborated with experimentalists in China in the realization of the new topological phases in meta-material settings. These collaborations permitted to set the new state of the art in the study of non-Abelian (e.g. Weyl semimetals) and Euler (e.g. phonons in insulators and semiconductors) topological materials, as is reflected in the high-impact journals in which the results were published.

Non-Abelian braiding rules in terms of signed Euler class and Dirac strings.

Linked nodal ring with monopole charge (red) between two distinct topological Euler phases.

figure2.jpeg

Tight-binding modeling of the gapped kagome lattice.