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The central idea of metamaterials and metaoptics is that, besides their base materials, the geometry of structures offers a broad extra dimension to explore for exotic functionalities. Here, we discover that the topology of structures…
Second harmonic generation is a powerful tool directly connected to the symmetry of materials. Phase transitions, lattice rotations or electromagnetic coupling in multiferroic compounds can be revealed by using second harmonic…
The connection between topology and nonreciprocity in photonic systems is reviewed. Topological properties such as Chern number, and momentum-space properties such as Berry phase and Berry connection, are used to explain back-scattering…
Weyl semimetals are crystals in which electron bands cross at isolated points in momentum space. Associated with each crossing point (or Weyl node) is an integer topological invariant known as the Berry monopole charge. The discovery of new…
Circularly polarized photons have the Berry curvature in the semiclassical regime. Based on the kinetic equation for such chiral photons, we derive the (non)equilibrium expression of the photon current in the direction of the vorticity. We…
We study topological properties of families of Hamiltonians which may contain degenerate energy levels aka. band crossings. The primary tool are Chern classes, Berry phases and slicing by surfaces. To analyse the degenerate locus, we study…
This thesis focuses on two research areas: non-relativistic field theories and complexity. In the first part we review the general classification of the trace anomaly for 2+1 dimensional field theories coupled to a Newton-Cartan background…
We study theoretically the optical response of the surface states of a topological insulator, especially the generation of helicity-dependent direct current by circularly polarized light. Interestingly, the dominant current, due to an…
Non-Hermitian photonics provides a fertile platform for exploring phenomena with no Hermitian counterparts, including the non-Hermitian skin effect and exceptional points, with direct relevance for integrated photonic technologies. In this…
Electron energy bands of crystalline solids generically exhibit degeneracies called band-structure nodes. Here, we introduce non-Abelian topological charges that characterize line nodes inside the momentum space of crystalline metals with…
Exceptional points (EPs) with their intriguing spectral topology have attracted considerable attention in a broad range of physical systems, with potential sensing applications driving much of the present research in this field. Here we…
We theoretically establish that non-Hermitian perturbations induce a topological transformation of point-like Dirac monopoles into extended monopole distributions, characterized by distinct charge configurations emergent from three distinct…
Under symmetry breaking, a three-dimensional nodal-line semimetal can turn into a topological insulator or Weyl semimetal, accompanied by the generation of momentum-space Berry curvature. We develop a theory that unifies their circular…
We study theoretically the polarization state of light in multiple scattering media in the limit of weak gradients in refractive index. Linearly polarized photons are randomly rotated due to the Berry phase associated with the scattering…
The subject of the present paper is a detailed theoretical investigation of the energy spectrum and bandgaps, as well as topological and collective properties and linear response, in $d$-wave altermagnets in the presence of an off-resonance…
For a long period of time, we have been seeking how Berry curvature influnces the transport properties in materials breaking time-reversal symmetry. In time-reversal symmetric material, there will be no thermoelectric current induced by…
Exciton-polaritons are hybrid light-matter quasiparticles formed by strongly interacting photons and excitons (electron-hole pairs) in semiconductor microcavities. They have emerged as a robust solid-state platform for next-generation…
In non-relativistic physics, the concepts of geometry and topology are usually applied to characterize spatial structures or structures in momentum space. We introduce the concept of temporal geometry, which encompasses the geometric and…
Non-Hermitian quantum systems can exhibit unique observables characterizing topologically protected transport in the presence of decay. The topological protection arises from winding numbers associated with non-decaying dark states, which…
Geometric or Berry phases are fundamental manifestations that appear in many areas of physics. They arise from the geometry of the space describing the properties of multi-component wave fields. An important example for electromagnetic…