Spin orientation of holes in quantum wells

Winkler, Roland; Culcer, Dimitrie; Papadakis, S. J.; Habib, B.; Shayegan, M.

doi:10.1088/0268-1242/23/11/114017

Cited by 75 publications

(103 citation statements)

References 75 publications

(209 reference statements)

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“…4,6,7,27,32,[36][37][38][39][40][41] However, we demonstrate that the validity of the SW-transformed model is limited to a relatively narrow range of parameters, indicating that in general the HH spin splitting contains higher-order terms in the wave vector, which are frequently sizeable. The limited applicability of the simple dispersion relation to realistic heterostructures is relevant to the current understanding of the spin-Hall conductivity, 32,37,39,52 hole spin helix, 40 and Zitterbewegung, 38,41 all of which have been derived based on the assumption that the HH spin splitting is proportional to k 3 .…”

Section: 26mentioning

confidence: 78%

Spin-orbit interactions in inversion-asymmetric two-dimensional hole systems: A variational analysis

Marcellina¹,

Hamilton²,

Winkler³

et al. 2017

Phys. Rev. B

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We present an in-depth study of the spin-orbit (SO) interactions occurring in inversion-asymmetric two-dimensional hole gases at semiconductor heterointerfaces. We focus on common semiconductors such as GaAs, InAs, InSb, Ge, and Si. We develop a semi-analytical variational method to quantify SO interactions, accounting for both structure inversion asymmetry (SIA) and bulk inversion asymmetry (BIA). Under certain circumstances, using the Schrieffer-Wolff (SW) transformation, the dispersion of the ground state heavy hole subbands can be written aswhere A, B, and C are material-and structure-dependent coefficients. We provide a simple method of calculating the parameters A, B, and C, yet demonstrate that the simple SW approximation leading to a SIA (Rashba) spin splitting ∝ k 3 frequently breaks down. We determine the parameter regimes at which this happens for the materials above and discuss a convenient semi-analytical method to obtain the correct spin splitting, effective masses, Fermi level, and subband occupancy, together with their dependence on the charge density, and dopant type, for both inversion and accumulation layers. Our results are in good agreement with fully numerical calculations as well as with experimental findings. They suggest that a naive application of the simple cubic Rashba model is of limited use in either common heterostructures or quantum dots. Finally, we find that for the single heterojunctions studied here the magnitudes of BIA terms are always much smaller than those of SIA terms.

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Section: 26mentioning

confidence: 78%

Spin-orbit interactions in inversion-asymmetric two-dimensional hole systems: A variational analysis

Marcellina¹,

Hamilton²,

Winkler³

et al. 2017

Phys. Rev. B

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“…Recently, a higher-order contribution of the Rashba SOI, the so-called k 3 (k-cubic) Rashba SOI, has received more attention [14,15]. The Hamiltonian for the k-cubic Rashba SOI is expressed as…”

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confidence: 99%

Cubic Rashba Spin-Orbit Interaction of a Two-Dimensional Hole Gas in a Strained-Ge/SiGeQuantum Well

et al. 2014

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The spin-orbit interaction (SOI) of a two-dimensional hole gas in the inversion symmetric semiconductor Ge is studied in a strained-Ge=SiGe quantum well structure. We observe weak antilocalization (WAL) in the magnetoconductivity measurement, revealing that the WAL feature can be fully described by the k-cubic Rashba SOI theory. Furthermore, we demonstrate electric field control of the Rashba SOI. Our findings reveal that the heavy hole (HH) in strained Ge is a purely cubic Rashba system, which is consistent with the spin angular momentum m j ¼ AE3=2 nature of the HH wave function. DOI: 10.1103/PhysRevLett.113.086601 PACS numbers: 72.25.Dc, 73.20.Fz, 73.21.-b The spin-orbit interaction (SOI) in a two-dimensional system is a subject of considerable interest because the SOI induces spin splitting at a zero magnetic field, which is important in both fundamental research and electronic device applications [1]. Recent developments of SOI-induced phenomena in the solid state demonstrate many possibilities utilizing spin current and the emergence of new physics such as the spin interferometer [2,3], persistent spin helix [4,5], spin Hall effect [6][7][8], and quantum spin Hall effect [9,10]. Up to now, there have been two well-known SOIs existing in solids: the Dresselhaus SOI [11] due to bulk inversion asymmetry (BIA) in the crystal structure and the Rashba SOI [12,13] due to spatial inversion asymmetry (SIA).In low-dimensional systems, the Rashba SOI becomes more important because it is stronger at the heterointerface and can be controlled by an external electric field. Many of the pioneering studies on the SOI-induced phenomena mentioned above were performed in two-dimensional electron systems, where the Rashba SOI is described by the k-linear Rashba term. In the Hamiltonian, the k-linear Rashba term can be written aswhere σ AE ¼ 1=2ðσ x AE iσ y Þ denote combinations of Pauli spin matrices, k AE ¼ k x AE ik y , and k x , k y are the components of the in-plane wave vector k ∥ . The effective magnetic field Ω 1 ðk ∥ Þ acting on the transport carrier due to the k-linear Rashba term is illustrated in Fig. 1(a).Recently, a higher-order contribution of the Rashba SOI, the so-called k 3 (k-cubic) Rashba SOI, has received more attention [14,15]. The Hamiltonian for the k-cubic Rashba SOI is expressed asand the effective magnetic field Ω 3 ðk ∥ Þ in k space is illustrated in Fig. 1(b) [15]. There is a significant difference in the effective field symmetry between the k-linear and the k-cubic Rashba SOI with one and three rotations in k space, respectively. The k 3 symmetry of the SOI is an interesting subject because it influences all of the SOI-induced phenomena as opposed to the k-linear Rashba term. For example, in case of the spin Hall effect, the k-cubic Rashba term is predicted to give rise to a larger spin Hall conductivity [17][18][19].

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“…of the (311) hole g-tensor: Uniquely to (311) oriented GaAs 2D systems, theory [22] and experiment [23] have shown that when a field is applied along the in-plane [233] direction, in addition to an in-plane polarisation with g-factor g xx , there exists an anomalous out-of-plane polarisation due to an off-diagonal term g xz in the gtensor. The Hamiltonian describing the Zeeman term for 2D heavy holes in (311) GaAs is then: …”

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confidence: 99%

Electrical control of the sign of thegfactor in a GaAs hole quantum point contact

et al. 2016

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Zeeman splitting of 1D hole subbands is investigated in quantum point contacts (QPCs) fabricated on a (311) oriented GaAs-AlGaAs heterostructure. Transport measurements can determine the magnitude of the g-factor, but cannot usually determine the sign. Here we use a combination of tilted fields and a unique off-diagonal element in the hole g-tensor to directly detect the sign of g * . We are able to tune not only the magnitude, but also the sign of the g-factor by electrical means, which is of interest for spintronics applications. Furthermore, we show theoretically that the resulting behaviour of g * can be explained by the momentum dependence of the spin-orbit interaction.Electrical manipulation of spin is the underlying principal of many proposed spintronic and quantum computing device architectures [1][2][3][4]. In particular, electrical control of the effective Landé g-factor in semiconductor nanostructures has been a major focus of recent research, with theoretical investigations predicting strong g * tunability in both magnitude and sign [5][6][7]. The ability to invert the sign of the g-factor and tune the system through a state of zero spin polarisation (g * = 0) could be a valuable asset in engineering solid-state spin devices [8][9][10].In this regard, quantum confined hole systems in GaAs are prime candidates due to the strong coupling between spin and orbital motion in the valence band [11]. The spin 3/2 nature of valence band holes in GaAs leads to several unique properties such as a tensor structure of g * with large anisotropy between all three spatial directions [12,13], and tunability of the g-factor across orders of magnitude [14][15][16].Previous studies of the g-factor of quantum confined holes revealed a non-monotonic dependance of |g * | on the gate bias, suggestive of a change in sign of g * [6,17]. However, these studies could not directly detect the sign of g * , only its magnitude. In this work, we utilise a novel approach to directly detect the sign of g * by exploiting a unique property of the (311) GaAs hole g-tensor, and demonstrate a gate-controlled sign change of g * in a hole quantum point contact (QPC) on (311) GaAs.We also introduce a theoretical model showing that the observed sign reversal of g * arises from the in-plane momentum dependence of the spin-orbit interaction in the valence band. Typically it is not possible to experimentally probe the directional k-dependence of the 2D hole g-tensor, since transport measurements represent an average over all k-states at the Fermi surface. However, by using an electrostatically controlled QPC fabricated along particular in-plane directions of a 2D hole system, * Alex.Hamilton@unsw.edu.au we can perform a direct spectroscopic measurement of g * , and investigate its dependence on the magnitude and direction of the in-plane momentum [14,17,18].The device used in this work was fabricated from a (311)A-oriented heterostructure, in which a 2D hole system is induced at an AlGaAs/GaAs interface by applying a negative voltage (-0.7V) to a...

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Spin orientation of holes in quantum wells

Cited by 75 publications

References 75 publications

Spin-orbit interactions in inversion-asymmetric two-dimensional hole systems: A variational analysis

Spin-orbit interactions in inversion-asymmetric two-dimensional hole systems: A variational analysis

Cubic Rashba Spin-Orbit Interaction of a Two-Dimensional Hole Gas in a Strained-Ge/SiGeQuantum Well

Electrical control of the sign of thegfactor in a GaAs hole quantum point contact

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