在强磁场中寻找强自旋-轨道耦合的一维空穴气
Searching strong `spin'-orbit coupled one-dimensional hole gas in strong magnetic fields
摘要：
我们表明，一个强大的“自旋”-轨道耦合一维（1D）空穴气是通过施加强磁场，原来的两个倍简并（自旋简并）空穴气限制在一个圆柱形的Ge纳米线。强纵向磁场和强横向磁场都可以实现这一目标。基于准简并微扰计算，我们发现空穴气的诱导低能子带色散可以写成$E=\hbar^{2}k^{2}_{z}/(2m^{*}_{h})+ασ^{z}k_{z}+g^{*}_{h}μ_{B}Bσ^{x}/2$，与导带中电子气的形式完全相同。这里的泡利矩阵$σ^{z,x}$代表一个伪自旋（或“自旋”），因为真实的自旋自由度已经被强磁场从子带色散中分离出来。此外，对于中等纳米线半径$R=10$ nm，诱导的有效空穴质量$m^{*}_{h}$（$0.065\sim0.08~m_{e}$）和“自旋”-轨道耦合$α$（$0.35\sim0.8$ eV~ eV）在所研究的磁场间隔$1<B<15$ T中具有小的磁场依赖性，而空穴“自旋”的有效$g$ -因子$g^{*}_{h}$仅在大的场区域中具有小的磁场依赖性。
英文摘要：
We show that a strong `spin'-orbit coupled one-dimensional (1D) hole gas is achievable via applying a strong magnetic field to the original two-fold degenerate (spin degeneracy) hole gas confined in a cylindrical Ge nanowire. Both strong longitudinal and strong transverse magnetic fields are feasible to achieve this goal. Based on quasi-degenerate perturbation calculations, we show the induced low-energy subband dispersion of the hole gas can be written as $E=\hbar^{2}k^{2}_{z}/(2m^{*}_{h})+ασ^{z}k_{z}+g^{*}_{h}μ_{B}Bσ^{x}/2$, a form exactly the same as that of the electron gas in the conduction band. Here the Pauli matrices $σ^{z,x}$ represent a pseudo spin (or `spin' ), because the real spin degree of freedom has been split off from the subband dispersions by the strong magnetic field. Also, for a moderate nanowire radius $R=10$ nm, the induced effective hole mass $m^{*}_{h}$ ($0.065\sim0.08~m_{e}$) and the `spin'-orbit coupling $α$ ($0.35\sim0.8$ eV~Å) have a small magnetic field dependence in the studied magnetic field interval $1<B<15$ T, while the effective $g$-factor $g^{*}_{h}$ of the hole `spin' only has a small magnetic field dependence in the large field region.
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