Strong spin-orbit interaction and 
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-factor renormalization of hole spins in Ge/Si nanowire quantum dots

Froning, Florian; Rančić, Marko J.; Hetényi, Bence; Bosco, Stefano; Rehmann, Mirko K.; Li, Ang; Bakkers, Erik P. A. M.; Zwanenburg, Floris A.; Loss, Daniel; Zumbühl, Dominik M.; Braakman, Floris

doi:10.1103/physrevresearch.3.013081

Cited by 79 publications

(72 citation statements)

References 62 publications

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“…Refs. [69][70][71]. We follow the procedure presented in [72], resulting in a Hamiltonian that can be written in terms of two independent harmonic oscillators,…”

Section: A Level Structurementioning

confidence: 99%

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

Qvist¹,

Danon²

2021

Preprint

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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 spinorbit-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.

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“…Refs. [69][70][71]. We follow the procedure presented in [72], resulting in a Hamiltonian that can be written in terms of two independent harmonic oscillators,…”

Section: A Level Structurementioning

confidence: 99%

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

Qvist¹,

Danon²

2021

Preprint

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“…Before trapping a hole in a gated semiconductor quantum dot, one should first achieve two-dimensional (2D) hole gas in a quantum well [6,19] or one-dimensional (1D) hole gas in a quantum wire [20][21][22][23]. The large intrinsic hole spin-orbit coupling is expected to give rise to sizable effects when strong quantum confinement is present.…”

Section: Introductionmentioning

confidence: 99%

“…Note that this strong spin-orbit coupled 1D dispersion has been extensively studied when electrons in the conduction band are concerned [29][30][31][32][33]. Inspired by recent experimental advances in manipulating electrically the hole spin in a Ge nanowire quantum dot [23,34], here we address the 'spin'-orbit coupling physics in the Ge nanowire.…”

Section: Introductionmentioning

confidence: 99%

Electrical manipulation of a hole `spin'-orbit qubit in nanowire quantum dot: the nontrivial magnetic field effects

Li,

Zhang

2021

Preprint

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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 spin-degeneracy in the hole subband dispersions, such that the remaining (spinless) low-energy subband dispersion exhibits strong 'spin'orbit coupling. Recent experimental study in a Ge nanowire hole quantum dot [Froning et al. Nat. Nanotechnol. 16, 308 (2021)] has demonstrated a strong electrical Rabi frequency (∼200 MHz) and a non-vanishing longitudinal g-factor g l so = 1.06. Here, we understand these interesting results in terms of the 'spin'-orbit coupling physics. 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 l so is naturally non-vanishing, and has the same order of magnitude as the transverse g t so . Also, both g l so and g t so are magnetic field dependent. Moreover, the 'spin'-orbit coupling has opposite dependence on the longitudinal field and the transverse field, such that the responses of the qubit level splitting and the Rabi frequency to these two fields are totally different.

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“…Spin blockade detection [21][22][23][24], control over the charge state down to a single hole [25,26], fabrication of arrays [27][28][29], and demonstration of single [30,31] and two-qubit operations [32] are among recent experimental achievements with planar dots. In contrast, the strong confinement-induced spin-orbital mixing in a nanowire geometry [33][34][35] gives large and tunable spinorbit interaction [36][37][38][39] and fast spin manipulation [40,41].…”

mentioning

confidence: 99%

“…Our work leaves space for interesting extensions. For example, the dependence on the device geometry prompts the question of how the additional spin-orbit interactions impact spin dephasing in other devices, such as nanowire-based hole-spin qubits [37] or FinFETs [16].…”

mentioning

confidence: 99%

Charge-noise induced dephasing in silicon hole-spin qubits

Malkoc,

Stano,

Loss

2022

Preprint

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We investigate theoretically charge-noise induced spin dephasing of a hole confined in a quasi-twodimensional silicon quantum dot. Central to our treatment is accounting for higher-order corrections to the Luttinger Hamiltonian. Using experimentally reported parameters, we find that the new terms give rise to sweet-spots for the hole-spin dephasing, which are sensitive to device details: dot size and asymmetry, growth direction, and applied magnetic and electric fields. Furthermore, we estimate that the dephasing time at the sweet-spots is boosted by several orders of magnitude, up to order of milliseconds.

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Strong spin-orbit interaction and g -factor renormalization of hole spins in Ge/Si nanowire quantum dots

Cited by 79 publications

References 62 publications

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

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

Electrical manipulation of a hole `spin'-orbit qubit in nanowire quantum dot: the nontrivial magnetic field effects

Charge-noise induced dephasing in silicon hole-spin qubits

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