Hole Spin Qubits in Ge Nanowire Quantum Dots: Interplay of Orbital Magnetic Field, Strain, and Growth Direction

Abstract

Hole spin qubits in quasi one-dimensional structures are a promising platform for quantum information processing because of the strong spin-orbit interaction (SOI). We present analytical results and discuss device designs that optimize the SOI in Ge semiconductors. We show that at the magnetic field values at which qubits are operated, orbital effects of magnetic fields can strongly affect the response of the spin qubit. We study one-dimensional hole systems in Ge under the influence of electric and magnetic fields applied perpendicularly to the device. In our theoretical description, we include these effects exactly. The orbital effects lead to a strong renormalization of the g-factor. We find a sweet-spot of the nanowire (NW) g-factor where charge noise is strongly suppressed and present an effective low-energy model that captures the dependence of the SOI on the electromagnetic fields. Moreover, we compare properties of NWs with square and circular cross-sections with ones of gate-defined one-dimensional channels in two-dimensional Ge heterostructures. Interestingly, the effective model predicts a flat band ground state for fine-tuned electric and magnetic fields. By considering a quantum dot (QD) harmonically confined by gates, we demonstrate that the NW g-factor sweet spot is retained in the QD. Our calculations reveal that this sweet spot can be designed to coincide with the maximum of the SOI, yielding highly coherent qubits with large Rabi frequencies. We also study the effective g-factor of NWs grown along different high symmetry axes and find that our model derived for isotropic semiconductors is valid for the most relevant growth directions of non-isotropic Ge NWs. Moreover, a NW grown along one of the three main crystallographic axes shows the largest SOI. Our results show that the isotropic approximation is not justified in Ge in all cases.

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• Majorana zero modes in gate-defined germanium hole nanowires
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• Modelling of spin decoherence in a Si hole qubit perturbed by a single charge fluctuator
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• Electrical manipulation of a hole `spin'-orbit qubit in nanowire quantum dot: the nontrivial magnetic field effects
• Two-band description of the strong `spin'-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire
• Quantification of the heavy-hole--light-hole mixing in two-dimensional hole gases
• Hole subband dispersions in a cylindrical Ge nanowire: exact results based on the axial Luttinger-Kohn Hamiltonian
• Spin-photon interaction in a nanowire quantum dot with asymmetrical confining potential
• Hole subband dispersions and strong `spin'-orbit coupling in a cylindrical Ge nanowire
• Effect of disorder and strain on the operation of planar Ge hole spin qubits
• Cancelling second order frequency shifts in Ge hole spin qubits via bichromatic control
• Heavy-hole spin relaxation in quantum dots: Isotropic versus anisotropic effects
• Giant Rabi frequencies between qubit and excited hole states in silicon quantum dots
• Anomalous zero-field splitting for hole spin qubits in Si and Ge quantum dots