Horaires des Exposes :
10:00-11:00 Hermann Schulz-Baldes (University of Erlangen-Nürnberg)
Invariants of disordered semimetals via the spectral localizer
The spectral localizer consists of placing the Hamiltonian in a Dirac trap. For topological insulators its spectral asymmetry is equal to the topological invariants, providing a highly efficient tool for numerical computation. Here this technique is extended to disordered semimetals and allows to access the number of Dirac or Weyl points as well as weak invariants. These latter invariants imply the existence of surface states. Joint work with Tom Stoiber.
11:30-12:30 Jean-Noel Fuchs (Paris, Sorbonne)
Does the Su-Schrieffer-Heeger model describe a topological insulator?
The SSH model is commonly taken as the simplest example of a one-dimensional band insulator featuring a phase transition between two phases: a trivial phase with zero winding number and a topological phase with unit winding number. We will argue that, due to several subtleties, this model actually has a single gapped phase with vanishing bulk polarization, which makes it a trivial inversion-symmetric insulator. We will also compare it to other one-dimensional models with simpler behavior such as the Shockley model. Most of the talk will turn around the concept of bulk electric polarization for a periodic crystal and the key concept of the "polarization quantum". Ref: J.-N. Fuchs and F. Piéchon, "Electric polarization of one-dimensional inversion-symmetric two-band insulators", arXiv:2106.03595 .
14:30-15:30 Oded Zilberberg (ETH Zurich)
From high-dimensional quantum Hall physics to High-order topology through topological pumps. Oded Zilberberg (ETH Zurich)
Chern numbers appear naturally in even dimensional systems as integrals over local geometrical curvatures. They manifest in physics in even-dimensional quantum Hall effects, as well as in odd-dimensional topological pumps that additionally depend parametrically on time. Interestingly, quantum Hall systems and topological pumps can be related to one another through dimensional reduction, leading (alongside added symmetries) to a natural relationship between TIs of different dimensions - all stemming from the physics of even-dimensional Hall systems. Specifically, I will show that TIs and high-order TIs can also be obtained using dimensional reduction from quantum Hall systems, and that their bulk-boundary correspondence naturally maps to the bulk responses of their ancestor Hall systems. Similarly, in interacting systems that excitations spectrum of the many-body physics exhibits similar bulk and boundary effects. Alongside this discussion, I will present recent realizations of topological pumps using two completely different bosonic systems, namely, using coupled photonic waveguide arrays and with trapped atoms in optical superlattices.
16:00-17:00 Pavel Kalugin (Paris Saclay)
Matching rules for real aperiodic solids
We discuss how the mathematical notion of matching rules should be adapted to the problem of propagation of aperiodic order in real materials. A universal geometric framework for working with such rules, based on flat-branched semi-simplicial (FBS) complexes, is proposed. For the case of quasicrystals, we suggest an especially robust order propagation mechanism, based on the homology theory, which can be explored directly in the phased diffraction data. We argue that the structure of a quasicrystal should be modeled in terms of decorated FBS complexes. Such a model entirely determines the density of atomic species, and yields experimentally verifiable constraints on their contribution to the structure factors, even in presence of residual disorder. Ref.: Kalugin, P. and Katz, A. (2019) Robust minimal matching rules for quasicrystals Acta Cryst. A 75(5), 669–693. Kalugin, P. and Katz, A. (2021) Constraints on pure point diffraction on aperiodic point patterns of finite local complexity arXiv:2107.05671