The renormalization of the electron g factor by the confining potential in semiconductor nanostructures is considered. A new effective k • p Hamiltonian for the electronic states in III-V semiconductor nanostructures in the presence of an external magnetic field is introduced. The mesoscopic spin-orbit (Rashba type) and Zeeman interactions are taken into account on an equal footing. It is then solved analytically for the electron effective g factor in symmetric quantum wells (g * QW). Comparison with different spin quantum beat measurements in GaAs and InGaAs structures demonstrates the accuracy and utility of the theory. The quantum size effects in g * QW are easily understood and its anisotropy g * QW (i.e., the difference between the in-plane and perpendicular configurations) is shown to be given by a mesoscopic spin-orbit effect having the same origin as the Rashba one.
Mainstream among topological insulators, GaSb/InAs quantum wells present a broken gap alignment for the energy bands which supports the quantum spin Hall insulator phase and forms an important building block in the search of exotic states of matter. Such structures allow the band-gap inversion with electrons and holes confined in adjacent layers, providing a fertile ground to tune the corresponding topological properties. Using a full 3D 8-band k · p method we investigate the inverted band structure of GaSb/InAs/GaSb and InAs/GaSb/InAs multilayers and the behavior of the helical edge states, under the influence of an electric field applied along the growth direction. By tuning the electric field modulus, we induce the change of the energy levels of both conduction and valence bands, resulting in a quantum spin Hall insulator phase where the helical edge states are predominantly confined in the GaSb layer. In particular, we found that InAs/GaSb/InAs has a large hybridization gap of about 12 meV and, therefore, are promising to observe massless Dirac fermions with a large Fermi velocity. Our comprehensive characterization of GaSb/InAs multilayers creates a basis platform upon which further optimization of III-V heterostructures can be contrasted. arXiv:1903.02687v3 [cond-mat.mes-hall]
A spin-dependent variational theory is used to analyze the Rashba spin-orbit splitting in two-dimensional electron gases formed in III-V semiconductor inversion layers. The spin split conduction subbands in CdTe/InSb, insulator/InAs, InP/InGaAs, InAlAs/InGaAs, and AlGaAs/GaAs heterojunctions are calculated. The theory, presented here in detail, is based on the 8 × 8 k · p Kane model and on the introduction of simple and convenient spin-dependent Fang-Howard trial functions, and leads to analytical expressions for the split subbands, as well as allows for a detailed knowledge of the Rashba spin-orbit coupling, including its explicit dependence on structure parameters and its decomposition into separate contributions. The Rashba coupling parameter and the population difference in the spin-split subbands, as experimentally determined from the beating pattern of the Shubnikov-de Haas (SdH) oscillations, are obtained as a function of the electron density (n s ). The separate contributions to the particularly large Rashba splitting in CdTe/InSb heterojunctions are also computed and discussed. It is shown, for example, that due to the spin-dependent boundary conditions, the direct Rashba spin-orbit coupling term in the effective Hamiltonian dominates the splitting only for n s > 10 10 cm −2 while it is the barrier penetration kinetic energy term that gives the largest contribution to the Rashba effect at lower densities.
The electron effective g factor tensor in asymmetric III-V semiconductor quantum wells (AQWs) and its tuning with the structure parameters and composition are investigated with envelope-function theory and the ´k p 8 8 • Kane model. The spin-dependent terms in the electron effective Hamiltonian in the presence of an external magnetic field are treated as a perturbation and the g factors * ĝ and * g , for the magnetic field in the QW plane and along the growth direction, are obtained analytically as a function of the well width L. The effects of the structure inversion asymmetry (SIA) on the electron g factor are analyzed. For the g-factor main anisotropy * * D = -^ AQWs are presented and discussed with the available experimental data; in particular InAs QWs are shown to not only present much larger g factors but also a larger g-factor anisotropy, and with the opposite sign with respect to GaAs QWs.
Control of the Rashba spin-orbit coupling in semiconductor two-dimensional electron gases ͑2DEGs͒ is of fundamental interest to the rapidly evolving semiconductor spintronics and depends on the detailed knowledge of the controversial interface and barrier penetration effects. Based on the 8 ϫ 8 k · p Kane model for the bulk, we propose a spin-dependent variational solution for the conduction subbands of III-V heterojuctions, which reveals analytically the different contributions to the Rashba splitting and its dependency on heterostructure and band parameters as the band offset and effective masses. Perturbation expansions are used to derive renormalized parameters for an effective, simple, and yet accurate one band model. Spin-dependent modified Fang-Howard trial functions, which satisfy the spin-dependent boundary conditions, are then introduced. The subband splitting is given as a function of the variational parameter which is obtained minimizing the total energy of the 2DEG. Our calculations applied to InAlAs/InGaAs heterojunctions, where a near 20% increase in the splitting is observed due to the barrier penetration, are in good agreement with both experiment and exact numerical calculations. Well-known expressions in the limit of a perfect insulating barrier are exactly reproduced. The desired control of the spin-orbit splitting for twodimensional ͑2D͒ electron gases ͑2DEGs͒ in III-V semiconductor heterojunctions, as in the Datta and Das spin transistor, has not been achieved yet. The quantitative agreement between theory and experiment is far from complete. Among different studies, there are in particular long-standing controversies concerning the barrier and boundary effects, 1,2 as well as regarding the splitting dependence on the electron density and the consistency among the different experimental methods. [3][4][5] In view of the spintronics, semiconductor heterojunctions form a special class of Rashba split 2DEGs. The electrons are confined by a triangular potential and the strength of the Rashba coupling as well as the electron density ͑n s ͒ can be varied with the gate voltage. Different experiments have been quantitatively interpreted with a simple model for the 2DEGs, 6 i.e., H c = ប 2 ͑k x 2 + k y 2 ͒ / 2m ء + ␣ ء · k ϫ e z , where the Rashba coupling parameter derived from Kane model in the infinite barrier approximation 7 is given byHere the band parameters are those of the well material and E is the confining electric field seen by the 2DEG near the interface. The spin splitting at the Fermi level is then given by ␦ =2␣ ء k F . However, this model has some limitations because it does not include nonparabolicity, barrier penetration, and spin-dependent boundary conditions known to lead to sizable corrections. 2,[8][9][10][11][12][13] There is, however, no simple or consensus way to include or calculate these effects which are usually included through numerical integration of multiband models. 2,[8][9][10][11][12] The problems with such numerical calculations are the spurious solutions, ...
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