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

We show that a strong 'spin'-orbit coupled one-dimensional 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 = (h) over bar (2)k(z)(2)/ (2m(h)*) + alpha sigma K-z(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 subband dispersions by the strong magnetic field. Also, for a moderate nanowirc radius R = 10 nm, the induced effective hole mass m(h)*(0.065 similar to 0.08m(e)) and the `spin'-orbit coupling alpha (0.35 similar to 0.8 eV angstrom) 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.