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Research 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: |
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Some recent 2024 highlights Quantised Integrated Shift Effect in Multigap Topological Phases. Writing in Physical Review Letters, we show that novel multigap phases exhibit a quantized shift response. This culminates in a quantised sum rule for sets of bands in general systems with certain symmetries. See departmental highlight Dualities of Paired Quantum Hall Bilayer States. Writing in Physical Review Letters, we highlight that dualities shed new light on bilayer quantum Hall systems. See departmental highlight Interferometry of non-abelian band singularities and euler class topology. Writing in Physical Review Letters, we show how to experimentally probe non-Abelian braiding processes and charges in ultracold atomic systems. See departmental highlight Anomalous non-Abelian multi-gap topology. Writing in Nature Communications, we show that periodic (Floquet) driving can induce anomalous multi-gap topological properties that have no static counterpart. See departmental highlight Some 2023 highlights Topological polarization in twisted bilayers. We show in a recent Nature Communications (Editors'highlights) publication that certain bi-layer systems can have non-trivial in-plane polarization features. When there is a relative twist angle or lattice mismatch between the layers, forming a supercell known as a moiré superlattice, there is a local polarization for each different stacking, resulting in a network of moiré polar domains (MPDs). We discovered that the in-pane component can be non-trivial, completing half a winding in each domain and thereby realizing a topological object known as a meron (half-skyrmion). These polarization features also correspond to ferroelectric properties and are anticipated to be manipulable. See departmental highlight Some 2022 highlights Unconventional Fermi surface generation. Fermi surfaces play an important role in controlling the electronic, transport and thermodynamic properties of materials. As the Fermi surface consists of closed contours in the momentum space for well-defined energy bands, disconnected sections known as Fermi arcs can be signatures of unusual electronic states, such as a pseudogap. Another way to obtain Fermi arcs is to break either the time-reversal symmetry or the inversion symmetry of a three-dimensional Dirac semimetal, which results in formation of pairs of Weyl nodes that have opposite chirality, and their projections are connected by Fermi arcs at the bulk boundary. We find in a recent Nature publication that NdBi generates a pair of Fermi surfaces with opposite curvature upon crossing the phase transition into the anti-ferromagnetic regime. The opposite curvature that follows the order parameter is unusual, thereby differing from previous theoretically considered and experimentally reported cases of magnetic splitting, such as traditional Zeeman and Rashba, in which the curvature of the bands is preserved. See departmental highlight Bicircular Light Floquet Engineering of Magnetic Symmetry. In a recent Phys. Rev. Lett publication we show that bicircular light (BCL) is a versatile way to control magnetic symmetries and topology in materials. The electric field of BCL, which is a superposition of two circularly polarized waves with frequencies that are integer multiples of each other, traces out a rose pattern in the polarization plane that can be chosen to break selective symmetries, including spatial inversion. We also apply our paradigm to the specific case of the Dirac semimetal Cd3As2. See departmental highlight Multi-Gap topology in phonons. We show in a recent Nature Communications publication that multi-gap topologies as proposed by our group as well as the accompanying phase transitions driven by braiding processes can be readily observed in the bosonic spectra of phonons and in monolayer silicates in particular. The associated braiding process can be controlled by means of an electric field and epitaxial strain. See departmental highlight Some 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 2020 highlights A dynamical view on uncovering enigmatic topology In a recent Phys. Rev. Letter 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 Phys. Rev. Letter 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 Phys. Rev. Letter 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 retrieved the same counting 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 a relatively 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. 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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