多带哈密顿量的柱坐标表示
Cylindrical coordinate representation for multiband Hamiltonians
摘要：
利用布里渊区心布洛赫函数的旋转不变组合作为基函数，在柱坐标系中表示纤锌矿和锌铁氧体半导体异质结构的价带和凯恩函数哈密顿量.对于圆柱对称系统，该基础允许将包络函数视为对称轴上的总角动量投影算子的本征态，算子的本征值通常作为参数进入哈密顿量。补充的对称轴上的包络函数的边界条件的哈密顿量，我们提出了第一次一个完整的形式主义，有效的建模和描述的多带电子态的低维半导体结构与圆柱对称。为了证明圆柱对称近似的效力，并建立其适用于实际结构的标准，我们映射的地面和几个激发的价带状态在一个孤立的纤锌矿GAN量子线的六边形横截面的圆形横截面的等效量子线的状态。
英文摘要：
Rotationally invariant combinations of the Brillouin zone-center Bloch functions are used as basis function to express in cylindrical coordinates the valence-band and Kane envelope-function Hamiltonians for wurtzite and zinc-blende semiconductor heterostructures. For cylindrically symmetric systems, this basis allows to treat the envelope functions as eigenstates of the operator of projection of total angular momentum on the symmetry axis, with the operator's eigenvalue conventionally entering the Hamiltonians as a parameter. Complementing the Hamiltonians with boundary conditions for the envelope functions on the symmetry axis, we present for the first time a complete formalism for efficient modeling and description of multiband electron states in low-dimensional semiconductor structures with cylindrical symmetry. To demonstrate the potency of the cylindrical symmetry approximation and establish a criterion of its applicability for actual structures, we map the ground and several excited valence-band states in an isolated wurtzite GaN quantum wire of a hexagonal cross-section to the states in an equivalent quantum wire of a circular cross-section.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
