Effective Magnetic Field Of Magnetic Atoms With The Magnetic Vortex State Research As Well As The Modulation Magnetic Field Tight-binding Transport Properties Of Electronic Systems Research

This article includes three parts. The first part is the investigation of vor-tex properties of ultracold magnetic atoms. We study a harmonically trapped highly oblate two-component Bose-Einstein condensate, which consists of both dipolar and scalar bosonic atoms. When the dipoles are polarized along the sym-metry axis of the trap, the dipolar atoms’density exhibits a flat-disk regime at the trap center. It is found that the dipolar component is easier to in-duce the first vortex when the trap is rotating about the symmetry axis, if the long-range dipolar interactions dominate over the contact interactions, and vice versa.Vortex lattices with the compensating triangular, square, and stripe struc-tures can be formed respectively under rapid rotation. When the dipoles are polarized perpendicular to the rotation axis, the two components are generically phase separated into a kernel-shell structure due to the anisotropic dipole-dipole interactions. While the giant-hole states are induced under slow rotation, the compensating stripe vortex structures are stabilized under fast rotation. In particular, a stripe-splitting structure is found to be competing with the stripe ones. These features are expected to be observed in the mixture of52Cr atoms in the two different spin states.The second part is the investigation of optical absorption properties in a crystal under a staggered magnetic field. We present a detailed analysis of the field-induced optical absorption (FIOA) in square and triangular lattices based on the tight-binding lattice-electron model with hopping integrals modulated by the staggered magnetic flux (SMF). The SMF generates a two-sublattice system with two branches of energy band in both cases, and the inter-band optical transition dominates the absorption spectrum. The dependence of the main absorption peak (MAP) frequency and the absorption spectra weight on the flux parameterd chemical potential uare discussed in detail.The third part is the investigation of the magnetotransport properties in two-dimensional electron system. We report the investigation of magne-totransport properties of tight-binding electrons with Rashba spin-orbit cou-pling (SOC). Four-step evolutions of the spin Hall and charge-Hall conductances (SHC and CHC) have been found when fixing the magnetic field and tuning the Rashba SOC:the SHC shows size-dependent resonant jumps and even changes its sign; the CHC exhibits three successive quantum jumps. More arrestingly, such four-step evolutions are reflected in topological characters of edge states of a cylindrical system and are robust against weak disorder.