In the presence of external magnetic field Fermi-liquid state supports oscillatory spin modes known as Silin modes. We predict existence generalized in a multivalley system, monolayer graphene. A gauge- and Berry-gauge- invariant kinetic equation for Fermi liquid is developed applied to case graphene with extrinsic spin-orbit coupling (SOC). The interplay SOC Berry curvature allows excitation v...

We present an experimental and theoretical study of the anomalous Hall effect (AHE) in MnAs epilayers grown over GaAs, with aim to identify intrinsic contribution AHE, which can be accurately evaluated using ab initio electronic structure calculations. Our magnetotransport measurements show a quadratic behavior resistivity longitudinal resistivity, characteristic scattering-independent processe...

The existing paradigm for topological insulators asserts that an energy gap separates conduction and valence bands with opposite invariants. Here, we propose \textit{equal}-energy Chern invariants can be \textit{spatially} separated -- onto facets of a finite crystalline Hopf insulator. On single facet, the number curvature quanta is in one-to-one correspondence bulk homotopy invariant insulato...