有效磁场下磁性原子与非磁原子涡旋态的研究以及调制磁场下紧束缚电子系统的输运性质研究
摘要
本文共分成三个部分,第一部分为对磁性超冷原子涡旋态的研究。在这一部分中我们研究了一个谐振子势约束下的扁圆形玻色爱因斯坦凝聚态,这个凝聚态包含了有磁偶极矩(磁矩)和没有磁矩的两种原子。当磁矩沿着约束势对称轴方向极化时,磁性原子分布在约束势中心附近,并形成一个平台。当约束势开始绕着对称轴旋转时,如果磁偶极相互作用强于原子接触相互作用,第一个涡旋出现在磁性原子中。反之亦然。在旋转速度较快时,大量的涡旋形成了互补的三角形,四方形,和条纹形涡旋点阵。当磁矩垂直于对称轴极化,两种原子会相分离成一种核壳结构。这是由于磁偶极相互作用的不对称性引起的。在慢速旋转下,磁性原子形成了一个大洞形涡旋态。在快速旋转下,涡旋点阵形成互补的条纹。值得一提的是,有劈裂的条纹会与完整的条纹结构相互竞争。这些现象有望在铬两种不同自旋态原子的混合物中观测到。
本文的第二部分为交错磁场调制下的晶体中光吸收性质的研究。在这一部分中我们基于交错磁场调制下的紧束缚格点-电子模型,仔细研究了四方和三角形晶格中的场致光吸收的问题。在两种晶格中交错磁场都导致了晶格可分为两子格,伴随着两支能带。带间光输运在整个吸收谱中占了主要部分。我们仔细讨论了主吸收峰频率和吸收谱权重与交错磁通及化学势的关系。
本文的第三部分为二维电子系统中磁输运性质的研究。在这一部分中我们研究了一个在有Rashba自旋轨道耦合的紧束缚电子系统的磁输运性质。我们发现当我们固定外磁场并调节Rashba耦合常数时,系统的自旋霍尔电导和电荷霍尔电导都有一个四步演化的行为。其中自旋霍尔电导表现出尺度相关的共振跃变并改变了正负号,而电荷霍尔电导展现了三次量子跃变。有趣的是这样的四步演化行为与柱状系统边界态的拓扑性质可以对应起来,并且不受弱无序的影响。
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 parameterd 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.
本文的第二部分为交错磁场调制下的晶体中光吸收性质的研究。在这一部分中我们基于交错磁场调制下的紧束缚格点-电子模型,仔细研究了四方和三角形晶格中的场致光吸收的问题。在两种晶格中交错磁场都导致了晶格可分为两子格,伴随着两支能带。带间光输运在整个吸收谱中占了主要部分。我们仔细讨论了主吸收峰频率和吸收谱权重与交错磁通及化学势的关系。
本文的第三部分为二维电子系统中磁输运性质的研究。在这一部分中我们研究了一个在有Rashba自旋轨道耦合的紧束缚电子系统的磁输运性质。我们发现当我们固定外磁场并调节Rashba耦合常数时,系统的自旋霍尔电导和电荷霍尔电导都有一个四步演化的行为。其中自旋霍尔电导表现出尺度相关的共振跃变并改变了正负号,而电荷霍尔电导展现了三次量子跃变。有趣的是这样的四步演化行为与柱状系统边界态的拓扑性质可以对应起来,并且不受弱无序的影响。
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 parameterd 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.
引文
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