The deformed Galilean generators are constructed on a space where both position and momentum coordinates are noncommutating operators. A dynamical model invariant under deformed phase space transformations is constructed. The Dirac brackets of this model reproduce the original non-commutative algebra. Also, the deformed generators are abstracted from this model in a consistent manner. Finally, ...

The anomalous velocity term in the semiclassical model of a Bloch electron deviates the trajectory from the conventional one. When the Berry curvature (alias noncommutative parameter) is a monopole in momentum space, as found recently in some ferromagnetic crystals while observing the anomalous Hall effect, we get a transverse shift, similar to that in the optical Hall effect. cond-mat/0606472,...

We will extend the concept of electron band Berry curvatures to superconducting materials. We show that this can be defined for the Bogoliubov-de Gennes equation describing the superconducting state in a periodic crystal. In addition, the concept is exploited to understand the driving mechanism for the optical Kerr effect in time reversal symmetry breaking superconductors. Finally, we establish...

The semiclassical motion of electrons in phase space x = (R,k) is influenced by Berry phases described by a six-component vector potential A = (AR,Ak). In chiral magnets, Dzyaloshinskii-Moriya (DM) interactions induce slowly varying magnetic textures (helices and skyrmion lattices) for which all components of A are important, inducing effectively a curvature in mixed position and momentum space...

The geometric structure of a single-particle energy band in a solid is fundamental for a wide range of many-body phenomena and is uniquely characterized by the distribution of Berry curvature over the Brillouin zone. We realize an atomic interferometer to measure Berry flux in momentum space, in analogy to an Aharonov-Bohm interferometer that measures magnetic flux in real space. We demonstrate...