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We show that a strong `spin'-orbit coupled one-dimensional (1D) hole gas isachievable via applying a strong magnetic field to the original two-folddegenerate (spin degeneracy) hole gas confined in a cylindrical Ge nanowire.Both strong longitudinal and strong transverse magnetic fields are feasible toachieve this goal. Based on quasi-degenerate perturbation calculations, we showthe induced low-energy subband dispersion of the hole gas can be written as$E=\hbar^{2}k^{2}_{z}/(2m^{*}_{h})+\alpha\sigma^{z}k_{z}+g^{*}_{h}\mu_{B}B\sigma^{x}/2$,a form exactly the same as that of the electron gas in the conduction band.Here the Pauli matrices $\sigma^{z,x}$ represent a pseudo spin (or `spin' ),because the real spin degree of freedom has been split off from the subbanddispersions 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 $\alpha$ ($0.35\sim0.8$ eV~\AA) have a smallmagnetic 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 smallmagnetic field dependence in the large field region.

Searching strong `spin'-orbit coupled one-dimensional hole gas in strong magnetic fields