Chiralité | EPFL Graph Search

La chiralité (du grec χείρ, kheir : main) est une importante propriété reliant les notions de symétrie et d'orientation, intervenant dans diverses branches de la science. Un objet ou un système est appelé chiral s’il n'est pas superposable à son image dans un miroir. Cet objet et son image miroir constituent alors deux formes différentes qualifiées d'énantiomorphes (du grec formes opposées) ou, en se référant à des molécules, des conformations spatiales « gauches » et « droites » appelées énantiomères dotés d'une asymétrie moléculaire tridimensionnelle. Le groupe des isométries laissant globalement invariant l'objet initial ne possède que des rotations. Un objet (ou une molécule) non chiral est dit achiral (ou parfois amphichiral). Il est superposable à son image miroir. Autrement dit, le groupe des isométries laissant globalement invariant l'objet possède au moins une isométrie indirecte. La chirogenèse est la formation de molécules chirales. Chiralité en mathématiques

Topological defects and gravity in theories with extra dimensions

Ewald Rössl

Recent proposals of large and infinite extra dimensions triggered a strong research activity in theories in which our universe is considered as a sub-manifold of some higher-dimensional space-time, a so-called 3-brane. In this context, it is generally assumed that some mechanism is at work which binds Standard Model particles to the 3-brane, an effect often referred to as the localization of matter on the brane. Gravity, however, is allowed to propagate in general also in the extra dimensions. As demonstrated by Randall and Sundrum in 1999, it is also possible to localize gravity itself on a 3-brane. In the setup they proposed. the 3-brane is realized as a singular domain wall separating two patches of 3-dimensional anti-de-Sitter (AdS5) space-time. The potential between two test masses on the brane at distances larger than the AdS5-radius was shown to be the usual 4-dimensional Newtonian 1/r potential with strongly suppressed corrections. The model of Randall and Sundrum, usually referred to as the Randall-Sundrum II setup, constitutes the center of interest for this thesis. The main goal of this work is to find possible generalizations to higher dimensions of the simple setup considered by Randall and Sundrum. One of the motivations for such a generalization is that a realistic theory should possibly be able to explain the chiral nature of 4-dimensional fermions on the brane. One way to explain chiral fermions from higher dimensions is to consider 3-braves identified with the cores of topological defects located in a higher-dimensional transverse space. Naturally a richer topological structure of the field configuration in transverse space provides the possibility of a more realistic spectrum of chiral fermions localized on the 3-brane. After two introductory chapters on extra dimensions and non-factorizable geometries which are relevant for the Randall-Sundrum II model, we briefly discuss basics of topological defects in the following third chapter. In the rest of the third chapter we consider various solutions to higher-dimensional Einstein equations coupled to a series of physically different sources and discuss their properties of localization of gravity. Due to their asymptotic nature, these solutions are only valid far from the cores of the defects in transverse space. Therefore, it seems reasonable to complement the consideration by presenting a particular numerical example of a solution to the Einstein equations coupled to a set of scalar and gauge fields: this solution describes a 3-brave realized as a 't Hooft-Polyakov monopole residing in the 3-dimensional transverse space of a 7-dimensional space-time. The last chapter of this work is dedicated to the study of a modification of the original Randall-Sundrum II model of another kind. The motivation is given by the geodesic incompleteness of the latter scenario with respect to time-like and light-like geodesics. We will describe a model which resembles the Randall-Sundrurn II model with respect to its properties of gravity localization but with the advantage that the underlying space-time manifold is geodesically complete. Parts of the calculations related to the properties of gravity at low energies in this model are rather technical in nature and we therefore preferred to assemble them in several appendices. We finally add some concluding remarks and discuss possible further developments.

EPFL2004

Exploiting the chirality of intermetallic PdGa

Samuel Thomas Stolz

The intermetallic compound PdGa has recently attracted considerable interest for combining high catalytic activity with high reaction selectivity in symmetric heterogeneous catalysis, in particular semi-hydrogenation of acetylene and methanol steam reforming. However, its potential for asymmetric heterogeneous catalysis, for which its chiral bulk crystal structure predestines it, remained largely unexplored. The possibility to prepare clean, atomically well-defined, and bulk-truncated low Miller-index surfaces of chiral PdGa (Pd1Ga1) under ultra-high vacuum conditions paves the way to tackle several fundamental research questions in chemistry and physics under idealized conditions. In particular, the PdGa{111} surfaces and their unique properties are ideally suited to serve as model system to study ensemble (geometry) and ligand (electronic) effects and show the enormous potential of PdGa towards asymmetric heterogeneous catalysis. In this work, the focus is on obtaining fundamental insights into chirality transfer of intrinsically chiral surfaces on the electronic structure and on each of the principal steps of a catalytic reaction pathway by experimental surface analytical tools. With regard to the relation of the chiral crystal structure of PdGa and its electronic structure, crystals of the space group P213, such as PdGa, are predicted to exhibit peculiar symmetry-protected fermionic quasiparticles. Using ARPES, we were able to evidence such symmetry-protected fermionic quasiparticles in PdGa, to exhibit multifold band-crossings at the high-symmetry points G and R in the Brillouin zone are fermionic quasiparticles with topological charge of magnitude 4 The non-centrosymmetry of PdGa is not only manifested in the emergence of chiral Fermi-arcs, but its chirality governs also the interaction with molecules and its surfaces, which is expressed, for instance in unidirectional motion or enantioselective on-surface reactions. In particular, we have evidenced and induced directed rotation with a directionality of 98% of isolated small, achiral acetylene (C2H2) molecules on Pd3-terminated PdGa{111} surfaces by using LT-STM. The rotor of this exceptionally small motor consists of 4 atoms only and thus operates not only in the classical, electrically driven regime, but also in an unexpected quantum tunneling regime with persisting high directionality. This strong chirality transfer from the substrate to the molecule is also encountered in enantiospecific interactions with prochiral molecules which is a prerequisite for enantioselective control in on-surface reactions, i.e., asymmetric heterogeneous catalysis. With this focus, we have studied three different reactions on the two structurally different Pd1- and Pd3-terminated PdGa{111} surfaces with regard to enantiomeric excess and the relevance of ensemble effect (geometry) over the ligand effect (electronic structure): Enantioselective debromination of 5-Bromo-7Methylbenz(a)Anthracene (BMA) Nearly enantiopure homocoupling of 9-Ethynylphenanthrene (9-EP) Regio- and enantioselective azide-alkyne Huisgen cycloaddition between 3-(4-Azidophenyl)propionic azid (APA) and 9-EP Our results highlight the outstanding potential of intermetallic PdGa in numerous fields of research, specifically as a chiral topo-logical material with non-trivial bandstructure, as stator for molecular motors, or as template for asymmetric heterogeneous catalysis.

EPFL2020

Topological defects and gravity in theories with extra dimensions

Ewald Rössl

EPFL2004

Exploiting the chirality of intermetallic PdGa

Samuel Thomas Stolz

EPFL2020