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.
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