Anisotropic $g$-tensors in hole quantum dots: The role of the transverse confinement direction

Abstract

Qubits encoded in the spin state of heavy holes confined in Si- and Ge-based semiconductor quantum dots are currently leading the efforts toward spin-based quantum information processing. The virtual absence of spinful nuclei in purified samples yields long qubit coherence times and the intricate coupling between spin and momentum in the valence band can provide very fast spin-orbit-based qubit control, e.g., via electrically induced modulations of the heavy-hole $g$-tensor. A thorough understanding of all aspects of the interplay between spin-orbit coupling, the confining potentials, and applied magnetic fields is thus quintessential for the development of the optimal hole-spin-based qubit platform. Here we theoretically investigate the manifestation of the effective $g$-tensor and effective mass of heavy holes in two-dimensional hole gases as well as in lateral quantum dots. We include the effects of the anisotropy of the effective Luttinger Hamiltonian (particularly relevant for Si-based systems) and we focus on the detailed role of the orientation of the transverse confining potential. We derive most general analytic expressions for the anisotropic $g$-tensor and we present a general and straightforward way to calculate corrections to this $g$-tensor for localized holes due to various types of spin-orbit interaction, exemplifying the approach by including a simple linear Rashba-like term. Our results thus contribute to the understanding needed to find optimal points in parameter space for hole-spin qubits, where confinement is effective and spin-orbit-mediated electric control over the spin states is efficient.

12 pages, 5 figures

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Cited by in corpus (10)

• Electrical operation of planar Ge hole spin qubits in an in-plane magnetic field
• Hole spin qubits in thin curved quantum wells
• Enhanced orbital magnetic field effects in Ge hole nanowires
• Electrical operation of hole spin qubits in planar MOS silicon quantum dots
• Dephasing of planar Ge hole spin qubits due to 1/$\text{f}$ charge noise
• Effects of spin-orbit coupling and in-plane Zeeman fields on the critical current in two-dimensional hole gas SNS junctions
• Probing details of spin--orbit coupling through Pauli spin blockade
• Quantification of the heavy-hole--light-hole mixing in two-dimensional hole gases
• Effect of disorder and strain on the operation of planar Ge hole spin qubits
• Anomalous zero-field splitting for hole spin qubits in Si and Ge quantum dots