Two-band description of the strong `spin'-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire

Abstract

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 $H^{\mathrm{ef}}={\hslash }^2{k}_z^2/(2m_h^{\ast })+\alpha {\sigma }^x{k}_z+g_h^{\ast }{\mu }_{B}B{\sigma }^z/2$, as long as the magnetic field is purely longitudinal or purely transverse. The explicit magnetic field dependent expressions of the `spin'-orbit coupling $\alpha \equiv \alpha (B)$ and the effective $g$-factor $g_h^{\ast }\equiv g_h^{\ast }(B)$ are given. When the magnetic field is applied in an arbitrary direction, the two-band Hamiltonian description is still a good approximation.

8 pages, 7 figures

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Cited by in corpus (4)

• Low-energy hole subband dispersions in a cylindrical Ge nanowire: the effects of the nanowire growth direction
• Hole subband dispersions in a cylindrical Ge nanowire: exact results based on the axial Luttinger-Kohn Hamiltonian
• Hole subband dispersions and strong `spin'-orbit coupling in a cylindrical Ge nanowire
• Spin-photon interaction in a nanowire quantum dot with asymmetrical confining potential