标题： 圆柱形Ge纳米线中的空穴能带色散和强自旋-轨道耦合 显示英文标题

标题： Hole subband dispersions and strong `spin'-orbit coupling in a cylindrical Ge nanowire

摘要： 准一维空穴气在半导体Ge纳米线中是可实现的。 空穴气的最低两个子带色散仅仅是两个带有反交叉的平移抛物曲线，位于$k_{z}=0$。 这种特殊的低能子带结构表明存在强的“自旋”（伪自旋）-轨道耦合。 基于轴向近似下的Luttinger-Kohn哈密顿量，我们展示了两组组合色散，这些色散不仅彼此隔离，而且在强磁场存在下具有强的“自旋”-轨道耦合。 对三个有代表性的纳米线生长方向[001]、[111]和[110]进行了实际计算。 这些结果通过构建空穴气的低能有效哈密顿量进一步得到确认。 我们还计算了外加电场引起的自旋分裂，以与磁场引起的自旋分裂进行比较。 显示英文摘要

摘要： Quasi-one-dimensional hole gas is achievable in a semiconductor Ge nanowire. The lowest two subband dispersions of the hole gas are just two shifted parabolic curves with an anticrossing at $k_{z}=0$. This peculiar low-energy subband structure manifests the existence of a strong `spin' (pseudo spin)-orbit coupling. Based on the Luttinger-Kohn Hamiltonian in the axial approximation, we show two sets of combined dispersions that not only isolated from each other but also with strong `spin'-orbit coupling are obtainable in the presence of strong magnetic field. Realistic calculations are performed for three representative nanowire growth directions [001], [111], and [110]. These results are further confirmed via constructing the low-energy effective Hamiltonian of the hole gas. We also calculate the external electric field induced spin splitting for comparison with the magnetic field induced spin splitting.