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

The recent classification of symmetry-indicated band structure topologies for all crystallographic structures has led to the prediction that one third of all materials are topological.

We are thus at a very exciting crossroad where the theory of topological materials (TM) is gaining enough maturity to transform material science, opening the way to real settings and potential long term applications. There are however key challenges remaining for the building of efficient topological quantum devices.

Indeed, little is known on the microscopic origin of topology in TM because (i) the general analytical conditions for nontrivial topology is unknown even for simple tight-binding models, (ii) there is a big jump in complexity towards the modeling of real materials (including all sub-lattices, orbitals, and spins), and (iii) the quantum interactions are hidden in the effective one-body (tight-binding) parameters.

The aim of this “Inverse Problem for Topological Materials” (IPTM) proposal is to address these issues concretely and practically; (A) by establishing the inverse map for generic few-band lattice models, and then by refining to the most representative crystalline symmetric structures; (B) by establishing the inverse map in real settings through the state-of-the-art modeling of (families of) real materials from the combination of first principles computational results (Density Function Theory and optimized wannierization) and with lattice models systematically derived from group theory; (C) by extracting the contributions of the quantum interactions (electron-electron, electron-phonon, exchange) to the microscopic tight-binding parameters.

Aiming at a fundamental understanding of topology in materials, this proposal aims to culminate in the prediction of completely new physics and functionalities, allowing the design of future quantum technology. Consequently this timely action is anticipated to start a new chapter in this active and impactful branch of science.