We theoretically consider g factor and spin lifetimes of holes in a longitudinal Ge/Si core/shell nanowire quantum dot that is exposed to external magnetic and electric fields. For the ground states, we find a large anisotropy of the g factor which is highly tunable by applying electric fields. This tunability depends strongly on the direction of the electric field with respect to the magnetic field. We calculate the single-phonon hole spin relaxation times T1 for zero and small electric fields and propose an optimal setup in which very large T1 of the order of tens of milliseconds can be reached. Increasing the relative shell thickness or the longitudinal confinement length further prolongs T1. In the absence of electric fields, the dephasing vanishes and the decoherence time T2 is determined by T2 = 2T1.PACS numbers: 71.70. Ej, 81.07.Vb, 81.07.Ta Semiconducting nanowires (NWs) allow to create nanoscale systems defined precisely regarding composition, geometry, and electronic properties and hence are subject to great experimental efforts. Furthermore, they offer new ways for implementing spin-based quantum computation.1 Both III-V compounds and group-IV materials are considered and operated in the conduction band (CB, electrons) 2-9 and in the valence band (VB, holes)10-22 regime. A particularly favored material is InAs, where single-electron quantum dots (QDs) 3 and electrically controlled spin rotations 5,6,8 have been implemented. Recently, qubits have also been implemented in InSb NW QDs, 7,9,22 a system for which extremely large electron g factors have been found. 4,7 However, the strong hyperfine interaction in InAs and InSb is considered the dominant source for the short coherence times observed.5,9 The latter may therefore be substantially prolonged in group-IV NWs that can be grown nuclearspin-free. In this context, Ge and Si have emerged as promising materials for nanoscale systems such as lateral QDs, 23-26 self-assembled QDs, 27-29 cylindrical core/shell NWs, 10-20 and ultrathin, triangular NWs.
21For applications in spintronics and quantum information processing, it can be advantageous to consider holes instead of electrons. Due to the p-wave symmetry of the Bloch states, holes experience a strong spin-orbit interaction (SOI) on the atomic level leading to an effective spin J = 3/2 behavior. Hence spin and momentum are coupled strongly which allows efficient control of the hole spin by electrical means. Furthermore, hole spin lifetimes are prolonged in the presence of confinement.
30-35In Ge/Si core/shell NWs, the large VB offset leads to an accumulation of holes in the core.11,36 They form a one dimensional (1D) hole gas with an unusually large, tunable Rashba-type SOI, referred to as direct Rashba SOI (DRSOI).37 This DRSOI makes Ge/Si core/shell NWs attractive candidates for quantum information processing via electric-dipole induced spin resonance, 38 and we mention that signatures of a tunable Rashba SOI were already deduced from magnetotransport experiments.
17Experiments on gate defined QDs...