New paradigms for correlated quantum matter: Hierarchical topology, Kondo topological metals, and deep learning

Project Information

PARATOP

Grant agreement ID: 757867

DOI

10.3030/757867

Project closed

EC signature date 24 August 2017

Start date 1 January 2018

End date 30 September 2023

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 362 401,00

EU contribution

€ 1 362 401,00

Coordinated by

UNIVERSITAT ZURICH
Switzerland

Periodic Reporting for period 4 - PARATOP (New paradigms for correlated quantum matter:Hierarchical topology, Kondo topological metals, and deep learning)

Reporting period: 2022-07-01 to 2023-09-30

Summary of the context and overall objectives of the project

We study quantum materials with properties that were previously unknown. Understanding quantum materials is of foundational importance for the future developments of in electronics, be it for data storage, electronic chip architectures, sensors, quantum computers and more. In recent years, materials with so-called topological properties came into the focus of research. They are characterized by stable conducting states on their boundary (edge or surface), while their interior is insulating. Due to these properties, they are envisioned for low-power electronic devices and for various applications in metrology.

In PARATOP we studied theoretically materials with qualitatively new behaviors. One of the main new directions are so-called higher order topological insulators, which are three-dimensional crystals that are insulating in the bulk, on the surface, but not on the hinges. Rather, on the crystal hinges we find one-dimensional conducting channels. These channels have the special property that current running through them is dissipationless, that means no power ist lost when the current flows. Such channels may be useful in future ultra-low-power electronics. Aside from predicting new materials with these intriguing properties, we developed numerical methods to study the hardest problems of crystals with many strongly interacting electrons. To be able to compute their properties with unprecedented precision, and to predict quantum phase diagrams, we employed neural networks. The neural network represents the quantum mechanical state of the system.

We have succeeded in finding higher-order topology in very common materials, such as elementary bismuth and the compound bismuth bromide. Such materials could indeed see lend themselves to future applications in 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

For higher-order topological insulators, we developed a mathematical framework that allows to predict which materials have this property. Based on our prediction we found that elementary bismuth is an iconic representative of this new phase of matter. Together with experimental groups, we collected evidence that our prediction is actually true. From this starting point, we developed the concept of higher-order topology in many further directions. Among others, we found criteria under which two-dimensional crystals (like graphene) have corner charges (the lower dimensional version of the conducting hinge modes). Furthermore, we studied higher-order topological superconductors, which have corner or hinge modes that are called Majorana fermions and may be relevant for building quantum computers. These developments are flanked by many other subprojects and methodological progress. Most prominently, we work on a code package called Wannier Berri, which allows to calculate response functions of real materials, based on band structure calculations, with extremely high precision. We tested the code on several occasions in collaboration with experimental groups or when we predict new topological quantum materials.

For the numerical investigation of strongly interacting phases of matter, we have mostly focused on code development and benchmarking of the method of neural network quantum states. In that way, PARATOP team members contributed to NetKet, the most prevalent software package in this filed. The results are very promising. We tested the new method on 1D systems, and on the 2D J1-J2 Heisenberg model on the square lattice, which is a iconic model of frustrated magnetism. We found that ground state energy and low-lying excitation energies with new records in numerical precision. Even more challenging was the study of a three-dimensional quantum magnet, the Heisenberg model on the pyrochlore lattice. We established the existence of symmetry broken states in this model. More broadly, we studied various applications of machine learning technology to condensed matter physics.

Finally, in close collaboration with experimental groups, we were able to study unconventional orders in a new class of materials, so-called Kagome-metals. The name derives from a lattice motive, the Kagome structure, which provides a background for studying the interplay of topology, electronic correlations and strong frustration.

Dissemination of the project results was achieved through many talks of PARATOP team members at renown conferences (e.g. three invited talks at APS march meetings), public code packages including lectures and tutorials (NetKet, Wannier Berri), and towards an interest public via popular science and review articles.

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)

PARATOP reached new frontiers in numerically simulating quantum many-body systems using variational methods. Furthermore, the discovery of higher-order topology and its realization in concrete materials is a very concrete result that pushed the boundaries of our knowledge.

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