Low-energy subband wave-functions and effective $g$-factor of one-dimensional hole gas

Abstract

One-dimensional (1D) hole gas confined in a cylindrical Ge nanowire has potential applications in quantum information technologies. Here, we analytically study the low-energy properties of this 1D hole gas. The subbands of the hole gas are two-fold degenerate. The low-energy subband wave-functions are obtained exactly, and the degenerate pairs are related to each other via a combination of the time-reversal and the spin-rotation transformations. In evaluating the effective $g$-factor of these low-energy subbands, the orbital effects of the magnetic field are shown to contribute as strongly as the Zeeman term. Also, near the center of the $k_z$ space, there is a sharp dip or a sharp peak in the effective $g$-factor. At the site $k_z=0$, the longitudinal $g$-factor $g_l$ is much less than the transverse $g$-factor $g_t$ for the lowest subband, while away from the site $k_z=0$, $g_l$ can be comparable to $g_t$.

11 pages, 9 figures

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Cited by in corpus (9)

• Hole Spin Qubits in Ge Nanowire Quantum Dots: Interplay of Orbital Magnetic Field, Strain, and Growth Direction
• Enhanced orbital magnetic field effects in Ge hole nanowires
• Microscopic analysis of proximity-induced superconductivity and metallization effects in superconductor-germanium hole nanowires
• Low-energy hole subband dispersions in a cylindrical Ge nanowire: the effects of the nanowire growth direction
• Two-band description of the strong `spin'-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire
• Electrical manipulation of a hole `spin'-orbit qubit in nanowire quantum dot: the nontrivial magnetic field effects
• 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
• Searching strong `spin'-orbit coupled one-dimensional hole gas in strong magnetic fields