We try to make progress on both timely as well as original problems, see also underneath Wordle. For a contemporary view on our activities, as well as a full account, please check the Arxiv or Google Scholar data:
Some recent 2021 highlights

Prediction and observation of non-Abelian semimetals in Kagome lattices In a recent Nature Physics publication we verified non-Abelian semimetals studied in our group the past year. Topological phases of matter lie at the heart of physics, connecting elegant mathematical principles to real materials that are believed to shape future electronic and quantum computing technologies. To date, studies in this discipline have almost exclusively been restricted to single-gap band topology because of the Fermi-Dirac f illing effect. Here, we theoretically analyze and experimentally confirm a novel class of multi-gap topological phases, the non-Abelian topological semimetals. These unprecedented forms of matter depend on the notion of Euler class and frame charges which arise due to non-Abelian charge conversion processes when band nodes of different gaps are braided along each other in momentum space. We identify such exotic phenomena in acoustic metamaterials on a kagome geometry which exhibit a rich topological phase diagram induced by the creation, braiding and recombination of band nodes. Using acoustic pump-probe measurements, we verify the non-Abelian charge conversion processes where topological charges of nodes are transferred from one gap to another. Moreover, in such processes, we discover symmetry-enforced intermediate phases featuring triply-degenerate band nodes with unique dispersions that are directly linked to the multi-gap topological invariants. Furthermore, we confirm that edge states can faithfully characterize the multi-gap topological phase diagram. Our study unveils a new regime of topological phases where multi-gap topology and non-Abelian charges of band nodes play a crucial role in understanding semimetals with inter-connected multiple bands. See departmental highlight

Topological correspondence between magnetic space group representations and subdimensions In a recent Editor's suggestion, we identify a general class of electronic configurations that in a magnetic background necessarily induce topological structure. The phases additionally feature a correspondence relating antiferromagnetic and ferro/ferrimagnetic realizations. More importantly, we find novel types of magnetic topology upon considering this mechanism in all space groups. These phases are exclusively mapped out in this analysis that takes into account planes and lines in the Brillouin zone, prompting a new notion of subdimensional topology that nonetheless has full 3D physical signatures, such as Fermi arcs. See departmental highlight

Discovery of a weak ti with van Hove surface states In a recent Nature communications publication we teamed up with experimentalists to analyse RhBi2. We predicted and observed that this material entails a weak TI with optimal space group. Due to a lack of constraints, all topology can be explicitly revealed and surface states are shown to have saddle points that are located in the vicinity of a Dirac point resulting in a van Hove singularity. See departmental highlight

Some recent 2020 highlights

A dynamical view on uncovering enigmatic topology In a recent Physical Review Letters publication we show that a new phase of matter characterised by Euler class, an invariant that goes beyond any conventional characterization scheme, can be experimentally discerned in a dynamical context. Namely, upon quenching, the system's collective wave function starts tying specific knots that can be measured. See departmental highlight

Novel braiding properties in momentum space and topology in a general class of metals. In a recent Nature Physics publication we show that certain metals can have band nodes that have novel topological charges. These charges can be converted by braiding nodes of diffrent gaps along each other in momentum space. In fact the, underlying topology is determined by these processes, see departmental highlight

Artificial intelligence learns to distinguish between different topological band structures. In a recent Physical Review Letters publication we propose a machine-learning approach that can distinguish, without any form of previous knowledge, topologically distinct bandstructures. See departmental highlight

Exhaustive framework for describing boundary modes in open quantum systems. In a recent Physical Review Letters publication we find a generic famework to enumerate boundary modes in open quantum systems. See departmental highlight

Some selected highlights

Topological Classification of Crystalline Insulators through Band Structure Combinatorics. In this Phys. Rev X. publication we proposed a simple algorithm to calculate all K-theoretic invariants for crystalline systems that have no other tenfold way symmetry. These ideas closely relate to the concepts of topological quantum chemistry and symmetry indicators, which use our counting rules in momentum space in order to compare which of these classes have real space atomic limits.

The space group classification of topological band insulators. In this Nature Physics publication we found at an early stage that crystalline symmetries can protect new topological phases beyond the standard variants protected by time-reversal, particle-hole and chiral symmetry. The connection with defects and the evaluation of information at high symmetry points guided follow-up pursuits, in particular the above publication. These pursuits of studying interplay between topology and crystalline symmetries has become an impressive field by now.

Generalized Liquid Crystals: Giant Fluctuations and the Vestigial Chiral Order of I, O, and T Matter. In this Phys. Rev X. publication we used a lattice gauge formulation to describe nematic phases from a general point of view. In particular, we find that that a vestigial phase carrying no more than chiral order becomes ubiquitous departing from high point-group symmetry chiral building blocks, such as I, O, and T symmetric matter.

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