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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 = ℏ 2 k z 2 / ( 2 m h * ) + α σ z k z + g h * μ B B σ 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 ∼ 0.08 m e ) and the ‘spin’-orbit coupling α (0.35 ∼ 0.8 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.
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 = ℏ 2 k z 2 / ( 2 m h * ) + α σ z k z + g h * μ B B σ 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 ∼ 0.08 m e ) and the ‘spin’-orbit coupling α (0.35 ∼ 0.8 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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Using the Numerical Renormalization Group method, we study the properties of a quantum impurity coupled to a zigzag silicene nanoribbon (ZSNR) that is subjected to the action of a magnetic field applied in a generic direction. We propose a simulation of what a scanning tunneling microscope will see when investigating the Kondo peak of a magnetic impurity coupled to the metallic edge of this topologically non-trivial nanoribbon. This system is subjected to an external magnetic field that polarizes the host much more strongly than the impurity. Thus, we are indirectly analyzing the ZSNR polarization through the STM analysis of the fate of the Kondo state subjected to the influence of the polarized conduction electron band. Our numerical simulations demonstrate that the spin-orbit-coupling-generated band polarization anisotropy is strong enough to have a qualitative effect on the Kondo peak for magnetic fields applied along different directions, suggesting that this contrast could be experimentally detected.
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