Brillouin zone | EPFL Graph Search

In mathematics and solid state physics, the first Brillouin zone (named after Léon Brillouin) is a uniquely defined primitive cell in reciprocal space. In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice is broken up into Brillouin zones. The boundaries of this cell are given by planes related to points on the reciprocal lattice. The importance of the Brillouin zone stems from the description of waves in a periodic medium given by Bloch's theorem, in which it is found that the solutions can be completely characterized by their behavior in a single Brillouin zone. The first Brillouin zone is the locus of points in reciprocal space that are closer to the origin of the reciprocal lattice than they are to any other reciprocal lattice points (see the derivation of the Wigner–Seitz cell). Another definition is as the set of points in k-space that can be reached from the origin without crossing any Bragg plane. Equivalent

Interaction of Confined Polaritons in Microcavity Structures

Morteza Navadeh Toupchi

A polariton is a quasiparticle formed from the coupling of a confined photon in a cavity to electronic excitation, like exciton in a semiconductor. This dissertation reports on series of experiments in confined polariton interaction by design, fabrication, and characterization of semiconductor microcavity structures operating in strong or weak coupling regime. In the first part of the thesis, we mainly concentrate on the optical study of the 2D microcavity sample, including spin-dependent lower-upper polariton cross interactions by pump-probe spectroscopy technique, supported by theoretical analyses and numerical simulations based on Gross-Pitaevskii equations. In particular, we present a scattering resonance behavior via an exciton molecule (biexciton) when polaritons from both the upper and lower branches with anti-parallel spins are involved through a polaritonic cross Feshbach resonance. This demonstration will permit the control of the polariton interbranch scattering. The second part of the thesis is dedicated to the design and fabrication of the potentials where the photonic part of polaritons is confined laterally by adjusting the thickness of the cavity layer locally in so-called mesa structures. By engineering a periodic lattice of mesas on a two-dimensional microcavity, it is possible to couple confined polariton modes of nearby mesas to establish an optical lattice analogous to the crystalline semiconductorsâ electronic band structures. We especially demonstrate the localization of light with a lasing mode at the edge of the Brillouin zone in a two-dimensional triangular lattice. We produce a self-trapping of light by optically inducing a local breaking of the strong-coupling regime of excitons to photons. In the weak coupling regime, we control the confined modes by the shape of the generated defect. We also reveal a controllable localization degree and experimental signature of the Anderson localization in microcavity polaritons by inducing positional disorder in the triangular lattice. The last part is devoted to the fabrication of sub-micron size mesas to enhance polariton interaction by confining them tightly and discuss the quantum correlation of polaritons by a Hanbury Brown and Twiss (HBT) setting toward polariton blockade.

EPFL2021

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

Soft-phonon driven hexagonal-orthorhombic phase transition in BaVS3

Helmuth Berger

The lattice dynamics of low-dimensional BaVS3 is reported across the hexagonal-orthorhombic phase transition occurring at T-S = 250 K using a combination of the thermal diffuse scattering of x rays, inelastic x-ray scattering, and density functional theory calculations. We observed the occurrence of strongly temperature-dependent diffuse scattering upon approaching the transition, centered at the F points associated with weak Bragg reflections with odd L. Inelastic scattering experiments related this observation to the condensation of a low-lying overdamped optical phonon at the Brillouin zone center, evidenced by significant variations of quasielastic scattering. These results unravel the dynamical origin of the zigzag distortion of the V chains at T-S, which is probably a prerequisite of the Peierls anomaly driving the metal-insulator transition at T-MI = 70 K.

2019