Dimensional reduction of the Luttinger Hamiltonian and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>g</mml:mi></mml:math>-factors of holes in symmetric two-dimensional semiconductor heterostructures

We analyze orbital effects of an in-plane magnetic field on the spin structure of states of a gated quantum dot based in a two-dimensional electron gas. Starting with a k·p Hamiltonian, we perturbatively calculate these effects for the conduction band of GaAs, up to the third power of the magnetic field. We quantify several corrections to the g-tensor and reveal their relative importance. We find that for typical parameters, the Rashba spin-orbit term and the isotropic term, H43 ∝ P 2 B · σ, give the largest contributions in magnitude. The in-plane anisotropy of the g-factor is, on the other hand, dominated by the Dresselhaus spin-orbit term. At zero magnetic field, the total correction to the g-factor is typically 5-10% of its bulk value. In strong in-plane magnetic fields, the corrections are modified appreciably. arXiv:1808.03963v2 [cond-mat.mes-hall] 4 Dec 2018 3 We stick here to the triangular heterostructure confinement in Eq. (4) and do not discuss in the main text, for the sake of brevity, other confinement types considered in Ref. 22. We give results for a symmetric confinement in App. D. 4 The corrections resulting from such terms are expected to be much smaller than the terms denoted gz (see below), which are of similar origin and which are subdominant.

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“…35 having partial overlap with what we do here, 1 and Ref. 36 focusing on holes and being similar in spirit.…”

Section: Introductionsupporting

confidence: 57%

g -factor of electrons in gate-defined quantum dots in a strong in-plane magnetic field

et al. 2018

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“…The functions g 1 (k) and g 2 (k) have been calculated recently for symmetric heterostructures [20]. Here we calculate them for asymmetric ones.…”

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confidence: 99%

“…The contribution of this mechanism is small and is calculated in Section B of the supplementary material, see also Refs. [20][21][22].…”

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confidence: 99%

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Mechanisms for Strong Anisotropy of In-Plane g -Factors in Hole Based Quantum Point Contacts

et al. 2017

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In-plane hole g-factors measured in quantum point contacts based on p-type heterostructures strongly depend on the orientation of the magnetic field with respect to the electric current. This effect, first reported a decade ago and confirmed in a number of publications, has remained an open problem. In this work, we present systematic experimental studies to disentangle different mechanisms contributing to the effect and develop the theory which describes it successfully. We show that there is a new mechanism for the anisotropy related to the existence of an additional B+k 4 − σ+ effective Zeeman interaction for holes, which is kinematically different from the standard single Zeeman term B−k 2 − σ+ considered until now.PACS numbers: 71.70. Ej, 73.22.Dj, 71.18.+y A quantum point contact (QPC) is a narrow quasione-dimensional (1D) constriction linking two twodimensional (2D) electron or hole reservoirs. Experimental studies of QPCs started with the discovery of the conductance quantization in steps of. The steps are due to the quantization of transverse channels [3]. Effects of many-body correlations in QPCs were identified by a "0.7-anomaly" in the conductance, an enhancement of the g-factor in the 1D limit [4], and by a zero bias anomaly [5]. G-factors in n-type QPCs have been measured in numerous experiments; a relatively recent one is reported in Ref. [6].The in-plane electron g-factor in a QPC takes the same value for any direction of the in-plane magnetic field. Even in InGaAs, which has appreciable spin-orbit coupling, no in-plane g-factor anisotropy has been observed [7]. Contrary to this, measurements for holes in QPCs based on GaAs p-type heterostructures indicate a huge anisotropy. All previously reported values of the g-factor for magnetic fields applied perpendicular to the QPC are consistent with g ⊥ = 0 within experimental error, while the g-factor g || for the parallel direction is nonzero [8][9][10].Regardless of numerous studies, the g-factor anisotropy effect in QPCs remains unclear.One mechanism to explain the g-factor anisotropy was suggested in Ref. [9]. This mechanism is based on the crystal anisotropy of the cubic lattice. While it is not negligible, the contribution of this mechanism is too small to explain the observed anisotropy.In this work, we identify a new mechanism for the g-factor anisotropy unrelated to the crystal lattice. It is instructive to use classification in powers of crystal anisotropy η defined below. The new mechanism is leading in η and the mechanism [9] is subleading. The new mechanism is negligible at very low hole densities. However, at real physical densities it is the major anisotropy mechanism. Previous measurements were performed in 2D hole systems formed at a single heterojunction [8, 9], which can be modeled as a triangular potential well. There is also a measurement with an asymmetric quantum well [10] which can be modeled as a square potential with an electric field along the z-axis. The z-axis is perpendicular to the plane of the 2D hole system. The z-as...

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“…The Zeeman splitting can differ by an order of magnitude for the in-plane and out-of-plane directions of B. 14,[41][42][43][44][45][46] (See also Refs. 47-52 for related work on quantum wires.)…”

Section: Introductionmentioning

confidence: 99%

Asymmetric g Tensor in Low-Symmetry Two-Dimensional Hole Systems

Gradl¹,

Winkler²,

Kempf³

et al. 2018

Phys. Rev. X

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The complex structure of the valence band in many semiconductors leads to multifaceted and unusual properties for spin-3/2 hole systems compared to common spin-1/2 electron systems. In particular, two-dimensional hole systems show a highly anisotropic Zeeman interaction. We have investigated this anisotropy in GaAs/AlAs quantum well structures both experimentally and theoretically. By performing time-resolved Kerr rotation measurements, we found a non-diagonal tensor g that manifests itself in unusual precessional motion as well as distinct dependencies of hole spin dynamics on the direction of the magnetic field B. We quantify the individual components of the tensor g for [113]-, [111]-and [110]-grown samples. We complement the experiments by a comprehensive theoretical study of Zeeman coupling in in-plane and out-of-plane fields B. To this end, we develop a detailed multiband theory for the tensor g. Using perturbation theory, we derive transparent analytical expressions for the components of the tensor g that we complement with accurate numerical calculations based on our theoretical framework. We obtain very good agreement between experiment and theory. Our study demonstrates that the tensor g is neither symmetric nor antisymmetric. Opposite off-diagonal components can differ in size by up to an order of magnitude. The tensor g encodes not only the Zeeman energy splitting but also the direction of the axis about which the spins precess in the external field B. In general, this axis is not aligned with B. Hence our study extends the general concept of optical orientation to the regime of nontrivial Zeeman coupling.

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Dimensional reduction of the Luttinger Hamiltonian andg-factors of holes in symmetric two-dimensional semiconductor heterostructures

Cited by 28 publications

References 34 publications

g -factor of electrons in gate-defined quantum dots in a strong in-plane magnetic field

g -factor of electrons in gate-defined quantum dots in a strong in-plane magnetic field

Mechanisms for Strong Anisotropy of In-Plane g -Factors in Hole Based Quantum Point Contacts

Asymmetric g Tensor in Low-Symmetry Two-Dimensional Hole Systems

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