论文标题
圆柱纳米线中强的“自旋”轨道耦合的一维孔气的两波段描述
Two-band description of the strong `spin'-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire
论文作者
论文摘要
在数值和分析上研究了强磁场的存在，在圆柱形GE纳米线中，在圆柱形GE纳米线中耦合的一维孔气体的低能量有效哈密顿量。基于球形近似中的Luttinger-Kohn Hamiltonian，我们显示了有效的两波段汉密尔顿$ H^{\ rm可以准确地描述这种强的“自旋”轨道耦合的一维孔气体，可以准确地描述ef} = \ hbar^{2} k^{2} _ {z}/（2m^{*} _ {h}）+ασ^{x} k {x} k_ {z}+g^{*} _ {*} _ {h} _ {横向。 $α\equivα（b）$和有效的$ g $ -factor $ g^{*} _ {当沿任意方向应用磁场时，两波段的哈密顿描述仍然是一个良好的近似值。
The low-energy effective Hamiltonian of the strong `spin'-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire in the presence of a strong magnetic field is studied both numerically and analytically. Basing on the Luttinger-Kohn Hamiltonian in the spherical approximation, we show this strong `spin'-orbit coupled one-dimensional hole gas can be accurately described by an effective two-band Hamiltonian $H^{\rm ef}=\hbar^{2}k^{2}_{z}/(2m^{*}_{h})+ασ^{x}k_{z}+g^{*}_{h}μ_{B}Bσ^{z}/2$, as long as the magnetic field is purely longitudinal or purely transverse. The explicit magnetic field dependent expressions of the `spin'-orbit coupling $α\equivα(B)$ and the effective $g$-factor $g^{*}_{h}\equiv\,g^{*}_{h}(B)$ are given. When the magnetic field is applied in an arbitrary direction, the two-band Hamiltonian description is still a good approximation.
