Electrical manipulation of a hole ‘spin’–orbit qubit in nanowire quantum dot: The nontrivial magnetic field effects

Abstract

Strong ‘spin’–orbit coupled one-dimensional hole gas is achievable in a Ge nanowire in the presence of a strong magnetic field. The strong magnetic field lifts the two-fold degeneracy in the hole subband dispersions, so that the effective low-energy subband dispersion exhibits strong spin–orbit coupling. Here, we study the electrical spin manipulation in a Ge nanowire quantum dot for both the lowest and second lowest hole subband dispersions. Using a finite square well to model the quantum dot confining potential, we calculate exactly the level splitting of the spin–orbit qubit and the Rabi frequency in the electric-dipole spin resonance. The spin–orbit coupling modulated longitudinal g-factor g so is not only non-vanishing but also magnetic field dependent. Moreover, the spin–orbit couplings of the lowest and second lowest subband dispersions have opposite magnetic dependences, so that the results for these two subband dispersions are totally different. It should be noticed that we focus only on the properties of the hole ‘spin’ instead of the real hole spin.