Department of Physics • University of Cologne

A unified theory for space-time and matter might be based on finite projective geometries instead of differentiable manifolds and fields. Each point of the world is equipped with a quadratic form over a finite Galois field which define neighbors in the finite set of points. Due to the projective equivalence of all quadratic forms this world is necessarily a 4-dimensional, locally Lorentz-covariant space-time with a gauge symmetry G(3)xG(2)xG(1) for internal points which represent elementary particle degrees of freedom. Thus, matter appears as a geometric distortion of an inhomogeneous field of quadrics and all physical properties (spins, charges) of the standard model seem to follow from its finite geometric structure in a continuum limit. The finiteness inevitably induces a fermionic quantization of all matter fields and a bosonic for gauge fields. The main difference to Einstein's general theory of relativity is the use of finite fields instead of real numbers to parametrize points of events.

The continuum of excitations in RuCl3 have been studied to high temperature—less-well studied are the effects of high magnetic fields. We measured the magnetotropic coefficient—second derivative of the free energy with respect to field-angle—up to 65 tesla. We find a scale-invariant response with applied temperature and magnetic field, contrasting with the large exchange energy apparent in the angle-dependence. This paradox hints at a strongly-correlated magnetic state in the high-field limit of RuCl3.

Large Li2FeSiO4 single crystals featuring the high temperature Pmnb-phase (γ-Li2FeSiO4) were grown for the first time by the optical floating zone method under high Ar-pressure and the single crystal structure was solved. The system exhibits tetrahedrally coordinated Fe2+ ions in a high-spin (i.e.,

Nonlinear optics is limited by the weak nonlinear response of available materials, a problem that is generally circumvented by relying on macroscopic structures in which light propagates over many optical cycles, thus giving rise to accumulated unity-order nonlinear effects. While this strategy cannot be extended to subwavelength optics, one can alternatively use localized optical resonances with high quality factors to increase light-matter interaction times at the expense of inelastic losses associated with the nonlinear response. In this context, highly-doped graphene has been identified as a promising material platform for nonlinear optics that combines long-lived, electrically-tunable plasmons with an intensely anharmonic response to light originating from its unique electronic band structure. I will discuss recent progress in the exploration of nonlinear graphene plasmonics, starting with a description of the appealing properties of plasmons in graphene nanostructures down to molecular sizes, followed by a discussion of the unprecedented level of intrinsic optical nonlinearity in graphene and its enhancement by resonant coupling to its supported plasmons of high harmonic and Kerr nonlinearities, strong interactions of nonlinear plasmons with quantum emitters or amongst themselves, and the extraordinary thermo-optical capabilities of this material enabling nonlinear optical switching on the single-photon level.

Recent experiments in quantum Hall bilayer systems have revealed a new strongly correlated state: the semi-quantuzed quantum Hall state. This state arises in a bilayer quantum Hall system with strong interlayer-interactions, has a quantized Hall resistance and vanishing longitudinal resistance, while at the same time featuring a gapless sector that allows this state to exist for a continuum of filling factors. In this talk, I will explain what a semi-quantized quantum Hall state is, and use a coupled-wire construction to predict possible future experiments in the already existing experimental platforms.