New frontiers in topological materials

Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is at the core of modern physics. The Quantum Geometric Tensor (QGT) is a central physical object in this regard, encoding complete information about the geometry of the quantum state. The imaginary part of the QGT is the well-known Berry curvature, which plays a fundamental role in the topological magnoelectric and optoelectric phenomena. The real part of QGT is the quantum metric, whose importance has come to prominence very recently, giving rise to a new set of quantum geometric phenomena, such as anomalous Landau levels, flat band superfluidity, excitonic Lamb shifts, and nonlinear Hall effect. Despite the central importance of the QGT, its experimental measurements have been restricted only to artificial two-level systems. In this talk, I am going to present two recent progresses in QGT measurement of Bloch states in solids. First, I will proposed a general method to extract the QGT by introducing another geometrical tensor, the quasi-QGT, who components, the band Drude weight and orbital angular momentum, are experimentally accessible and can be used for extracting the QGT. In the second part, I will report the first direct measurement of the full quantum metric tensors using black phosphorus as a representative material. The key idea is to extract the momentum space distribution of the pseudospin texture of the valence band from the polarisation dependence of angle-resolved photoemission spectroscopy measurement.

Professor Bohm Jung Yang

Seoul National University, South Korea

Professor Bohm Jung Yang

Seoul National University, South Korea

Professor Bohm Jung Yang is a theoretical condensed matter physicist interested in the study of emergent physics in quantum materials with nontrivial topology and correlative effect. He is interested in (1) the symmetry-based classification of topological phases, (2) the unconventional topological phase transitions and critical phenomena, (3) the search of novel topological superconductors, and (4) the quantum geometry driven physical properties in quantum materials.

Topology is a branch of mathematics, which classifies geometrical objects according to global properties labelled by an integer (genus number). Interestingly topology has appeared as a power tool in physics, providing profound new insights into physical phenomena such as the quantum Hall effect of the valley Hall effect. The geometrical objects to which these mathematical concepts apply in the context of condensed matter physics are the Bloch eigenmodes and the topological properties of the system intimately depend on how these eigenmodes vary in k-space. Thus to get access to the topological properties of a periodic system, it is highly desirable to measure the eigenmodes of its Hamiltonian.

In the present talk, I will present a novel technics we have developed which enables full tomography of the Bloch eigenmodes in a lattice of coupled microcavity. From this tomography, we get experimental access to all the components of the geometric tensor as well as to the Hamiltonian and its topological invariants. Interesting this technics can probe eigenmodes close to band touching points with sublinewidth resolution. While we benchmark the technics using a two band lattice, the technics can be generalised straightforwardly to lattices with a large number of bands, thus opening the door to the exploration of multiband topology.

Professor Jacqueline Bloch

French National Centre for Scientific Research, France

Professor Jacqueline Bloch

French National Centre for Scientific Research, France

Jacqueline Bloch is Director of Research at the CNRS, Associate Professor at the Ecole and member of the French Academy of Sciences. She is an experimental physicist, expert in semiconductor physics, light matter interaction, quantum and nonlinear optics and develops her research at the Centre for Nanosciences and Nanotechnologies in Palaiseau. Making use of quantum fluids of polaritons in lattices of coupled microcavities, she is currently exploring topological photonics and the physics of open Bose Einstein condensates.

I will present my group's recently experimental work on the fractional pumping of solitons in nonlinear Thouless pumps, using waveguide arrays. Specifically, I will show that the displacement (in unit cells) of solitons in Thouless pumps is strictly quantized to the Chern number of the band from which the soliton bifurcates in the low power regime; whereas in the intermediate power regime, nonlinear bifurcations lead to fractional quantization of soliton motion. This fractional quantization can be predicted from the multi-band Wannier functions associated with the states of the pump.

Professor Mikael Rechtsman

Pennsylvania State University, USA

Professor Mikael Rechtsman

Pennsylvania State University, USA

Mikael Rechtsman is a Professor of Physics at Pennsylvania State University in the USA, and currently the visiting QuantAlps professor of physics at the Néel Institute of the CNRS in Grenoble, France. His research group carries out both experimental and theoretical research in nonlinear, quantum and topological photonics. He is perhaps best known for the first demonstration of a topological insulators for light.

Topology, a well-established concept in mathematics, has nowadays become essential to described condensed matter. At its core are chiral electron states on the bulk, surfaced and edges of the condensed matter systems, in which spin and momentum of the electrons are locked parallel or anti-parallel to each other. Magnetic and non-magnetic Weyl semimetals for example, exhibit chiral bulk states that have enabled the realisation of predictions from high energy and astrophysics involving the chiral quantum number, such as the chiral anomaly, the mixed axial-gravitational anomaly and axions. The potential for connecting chirality as a quantum number to other chiral phenomena across different areas of science, including the asymmetry of matter and antimatter and homochirality of life, brings topological materials to the fore.

Professor Claudia Felser

Max Planck Institute for Chemical Physics of Solids, Germany

Professor Claudia Felser

Max Planck Institute for Chemical Physics of Solids, Germany

Claudia Felser studied chemistry and physics at the University of Cologne, completing her diploma in solid state chemistry (1989) and her doctorate in physical chemistry. After postdoctoral fellowships at the Max Planck Institute in Stuttgart (Germany) and the CNRS in Nantes (France), she joined the University of Mainz in 1996 as an assistant professor. In 2003, she became a full professor at the University of Mainz and is currently the Director of the Max Planck Institute for Chemical Physics of Solids in Dresden.

Claudia Felser in a fellow of the IEEE Magnetic Society, American Physical Society, and Institute of Physics. She is a member of the Leopoldina, the Germany National Academy of Sciences, and acatech, the German National Academy of Science and Engineering. Her research focuses on the design and synthesis, and physical characterisation of new quantum materials, particularly Heusler compounds and topological materials for energy conversion and spintronics. She was inducted into the Hall of Fame of German Research in 2023, and has received several prestigious awards, including the Liebig Medal of the German Chemical Society, the Max Born Prize of DPG and IOP, and the APS James C McGroddy Prize, and the Von Hippel Award.

We have found that superconductivity and superfluidity are connected to quantum geometry: the superfluid weight in a multiband system is proportional to the minimal quantum metric of the band. The quantum metric is connected to the Berry curvature, which relates to superconductivity to the topological properties of the band. Using this theory, we have shown that superconductivity is also possible in a flat band where individual electrons would not move. These results may be relevant for explaining the observation of superconductivity in twisted bilayer graphene. The quantum transport in a flat band shows unique behaviour: while supercurrent can flow, quasiparticle transport is highly suppressed even in non-equilibrium conditions. This may have important consequences for superconducting devices. We have predicted that flat band systems as part of Josephson junctions can lead to behaviour distinct from the dispersive case. We have also found that quantum geometry governs Bose-Einstein condensates in flat bands. While most of the mentioned work is for on-site interactions, in a recent study we found that nearest-neighbour pairing at flat band and van Hove singularities of the kagome and Lieb lattices is strongly influenced by the geometric properties of the eigenfunctions, and it is crucial to determine the superfluid weight of the superconducting and pair density wave orders as it may contradict the predictions by pairing susceptibility.

Professor Päivi Törmä

Aalto University, Finland

Professor Päivi Törmä

Aalto University, Finland

Päivi Törmä is a professor in the Department of Applied Physics, Aalto University, Finland, and has a MSc degree from the University of Oulu, Finland, a Master of Advanced Study degree from the University of Cambridge, UK, and a PhD in 1996 from the University of Helsinki. Her research ranges from theoretical quantum many-body physics to experiments in nanophotonics. Her work has revealed a new connection between quantum geometry and superconductivity that explains why flat bands can carry supercurrent, which is essential in the search for superconductors that work at high temperatures. In her experiments, Päivi has worked on the strong coupling of surface plasmon polariton modes and molecules and her group succeeded in realising the first plasmonic Bose-Einstein condensate.

Topological quantum chemistry (TQC) has provided a complete description of the universal properties of all possible atomic band insulators across all space groups by taking crystalline unitary symmetries into account. It links the chemical and symmetry structure of a given material with its topological properties. While this formalism has filled the gap between mathematical classification and the practical diagnosis of topological materials, an obvious limitation is that it only applies to weakly interacting systems. It remains an open question to what extent this formalism can be generalised to correlated systems that exhibit symmetry-protected topology, such as Kondo or Mott insulators.

In this talk, I will first introduce TQC and its application to correlated systems. We will then analyse the topology of SmB₆ Kondo insulators and compare our findings with many-body results. Building on this insight, we will present a new family of experimentally grown Kondo materials and discuss their topological properties.

For Mott insulators, we have developed a general framework to address this outstanding question, and we illustrate its power by applying it to these systems. In our approach, the concept of Green's function Berry curvature - which is frequency-dependent - is introduced. We apply this concept to a system that features symmetry-protected nodes in its noninteracting band structure. Here, strong correlations driver the system into a Mott insulating state, creating contours in frequency-momentum space where the Green's function vanishes. The Green's function Berry flux associated with these zeroes is found to be quantised, serving as a direct probe of the system's topology. Our framework enables a comprehensive search for strongly correlated topological materials characterised by Green's function topology. Finally, we will discuss a recent experiment on the correlated Mott insulator NiS₂.

Professor Maia Vergniory

Université de Sherbrooke, Canada

Professor Maia Vergniory

Université de Sherbrooke, Canada

Maia Vergniory is a Basque computational physicist and senior researcher at the Donostia International Physics Centre (DIPC) in San Sebastián, Spain, as well as a Professor at the Université de Sherbooke in Canada. Her research pioneers the theory and discovery of topological materials - crystals whose surface states conduct electricity robustly while the bulk remains insulating - using high-throughput ab initio calculation and the Topological Quantum Chemistry framework to classify and predict new compounds. Her work has earned her the 2017 L'Oréal-UNESCO For Women in Science Award, in 2019 the Ikerbasques Foundation award and was elected as a Fellow of the American Physical Society in 2022. In 2023 she received the Canadian Excellence Research Chair.