Rashba Spin-orbit Splitting Research Articles

Zero-field spin splitting in modulation-doped AlxGa1−xN∕GaN two-dimensional electron systems

Low-temperature magnetotransport measurements were performed on AlxGa1−xN∕GaN two-dimensional electron systems. By studying the beating pattern in the Shubnikov–de Haas oscillations in a perpendicular magnetic field, we are able to measure the zero-field spin-splitting energies in our systems. Our experimental results demonstrate that the Rashba term due to structural inversion asymmetry is the dominant mechanism which gives rise to the measured zero-field spin splitting in our wurzite AlGaN∕GaN structures. By utilizing the persistent photoconductivity (PPC) effect, we are able to increase the carrier density n in our AlGaN∕GaN two-dimensional electron system. It is found that the Rashba spin-orbit splitting parameter α decreases with increasing n. We suggest that the formation of long-lived electron-hole pairs induced by the PPC effect decreases the large electric field near the AlGaN∕GaN interface, causing α to decrease with increasing n.

Effectivegfactor ofn-typeHgTe/Hg1−xCdxTesingle quantum wells

The effective g factor of modulation doped n-type HgTe single quantum wells, SQW's, has been determined by the coincidence method in tilted magnetic fields to lie between 15 and 35. For symmetrically doped samples the effective g factor has been found to be constant for different filling factors; however, for asymmetric SQW's, a large increase with increasing filling factor has been observed. This can be ascribed to a combination of Zeeman spin splitting and Rashba spin-orbit splitting. Reasonable agreement has been achieved between theoretical calculations based on the $8\ifmmode\times\else\texttimes\fi{}8\mathit{k}\ensuremath{\cdot}\mathit{p}$ method and experimental results.

Giant Rashba spin splitting in HgTe/HgCdTe quantum wells

Giant Rashba spin splitting has been found in n-HgTe/HgCdTe quantum wells with an inverted band structure by studying the beating patterns in Shubnikov-de Haas oscillations. Fast Fourier transformation, node positions, as well as numerical simulations, are used to deduce the Rashba spin-orbit splitting and result in an excellent agreement in Rashba spin splitting energy (28-36 meV).

MBE growth and characterization of HgTe based quantum wells and superlattices

The MBE growth of type III HgTe/Hg1−xCdxTe heterostructures will be discussed. Spin–orbit (s–o) coupling is particularily large in HgTe based quantum wells; the observed value of 17meV is at least two to three times larger than values reported in the literature for III–V heterostructures or any other system. Rashba spin–orbit splitting in n type modulation doped quantum wells (QWs) has been investigated as a function of the 2DEG density and compared with self-consistent Hartree calculations based on an 8×8k·p model. Furthermore the presence of two periodic SdH oscillations in p type QWs with an inverted band structure has been observed and is the first direct evidence that these heterostructures are indirect semiconductors.

Electron spin splitting in polarization-doped group-III nitrides

The Rashba spin-orbit splitting parameter has been calculated in wurtzite GaN/AlGaN heterostructures. Despite the fact that wide-bandgap semiconductors are expected to have a smaller spin-orbit coupling parameter than that in InGaAs-based III-V materials, the electron spin-split energy in GaN/AlGaN heterostructure is predicted to have the same order of magnitude, due to the strong polarization field at the interface and polarization-induced doping. This, taken together with the existence of room-temperature ferromagnetism in GaN(Mn), could make the GaN-based material system competitive in spintronic applications.

Determination of the g-factor of n-type HgTe/Hg 1− xCd xTe single quantum wells

The effective g-factor of modulation doped n-type HgTe single quantum wells, SQWs, has been determined by the coincidence method in tilted magnetic fields to lie between 15 and 35. For symmetrically doped samples the effective g-factor has been found to be constant for different filling factors; however, for asymmetric SQWs, a large increase with increasing filling factor has been observed. This can be ascribed to a combination of Zeeman spin splitting and Rashba spin–orbit splitting. Reasonable agreement has been achieved between theoretical calculations based on the 8×8 k · p method and experimental results.

MBE growth and characterization of Hg based compounds and heterostructures

The MBE growth of Hg 1− x Cd x Te alloys and type III HgTe/Hg 1− x Cd x Te heterostructures has been discussed, including similarities and differences between the (0 0 1) and (1 1 2)B orientations. Furthermore the MBE growth of HgTe based quantum wells (QWs) with the incorporation of Mn are additional topics. An investigation of the optical properties of type III superlattices with a normal band structure has lead to information about band structure of these heterostructures as well as information about the interface and the semimetallic QW. For example, by means of the full 8×8 Kane Hamiltonian in the envelope function approximation, it has been demonstrated that the energy separation between the H1–E1 and L1–E1 intersubband transition energies is primarily determined by the valence band offset, Λ, between HgTe and CdTe. This has led to unambiguous values for the offset and its temperature dependence, i.e. Λ( T)=570±60 meV and dΛ/d T=−0.40±0.04T meV/K. Furthermore the energy gap of HgTe at room temperature has also been determined. Magneto-transport measurements of n-type QWs show very pronounced Shubnikov-de Haas (SdH) oscillations and well developed quantum Hall plateaus for temperatures up to approximately 60 K. A large Rashba spin–orbit splitting of the first conduction subband, H1, has been observed in HgTe/Hg 1− x Cd x Te QWs with an inverted band structure. Self-consistent Hartree calculations of the band structure based on the above model allows us to quantitatively describe the experimental results and demonstrates that the heavy hole nature of the H1 subband greatly influences the spatial distribution of electrons in the QW and thus enhances the Rashba spin splitting, i.e. Δ E H1= βk ∥ 3. Furthermore, the presence of two periodic SdH oscillations in p-type QWs with an inverted band structure has been observed and is the first direct evidence that these heterostructures are indirect semiconductors. The influence of Mn in the upper barrier on the 2D electrons in the well has been investigated as a function of their separation. With spacer thicknesses of 10 and 15 nm, no appreciable change is observed, however, a reduction of the spacer thickness to 5 nm results in an increase in the maximum population difference between the two Rashba spin split H1 subbands by a factor of approximately two.

Growth and Magneto-Transport of Gate Controlled n-Type HgTe/Hg0.3Cd0.7Te Quantum Wells with the Inclusion of Mn

A series of gate controlled n-type asymmetrically modulation doped HgTe quantum wells (QWs) with Mn in one of the barriers have been investigated. From a Fourier analysis of the Shubnikovde Haas (SdH) oscillations, the population difference of the two spin split H1 subbands has been determined for three QWs with different spacer thicknesses between the quantum well and the Mn ions. This population difference shows a significant enhancement in the QW with a 5 nm spacer compared to the QWs with 10 and 15 nm thick spacers. The latter results agree with the predictions for Rashba spin-orbit splitting, however, we must assume that Mn in the QW with the thin spacer increases the asymmetry of the QW.

Large Rashba spin–orbit splitting in gate controlled n-type modulation doped HgTe/Hg 0.3Cd 0.7− xMn xTe quantum wells

We report on Rashba spin–orbit splitting in a series of gated n-type HgTe/Hg 0.3Cd 0.7− x Mn x Te quantum wells with an inverted band structure. By analyzing the gate-voltage-dependent beating pattern observed in the Shubnikov–de Haas oscillations, we determine the gate voltage dependence of the spin–orbit coupling parameter β, which can be tuned by a factor of about 5 in the narrow spacer sample. Our experimental data and its analysis show that the Hg 0.3Cd 0.7− x Mn x Te layer strongly enhances the spin–orbit splitting, when close enough to the two-dimensional electron gas.

Spin-orbit splitting of electronic states in semiconductor asymmetric quantum wells

The spin-orbit splitting in the dispersion relation for electrons in III-V semiconductor asymmetric quantum wells is studied within the standard envelope-function formalism starting from the eight-band Kane model for the bulk. The Rashba spin-orbit splitting in the different subbands is obtained for both triangular and square asymmetric quantum wells. It is shown, for example, that the Rashba splitting in AlAs/GaAs/${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As square quantum wells is of the order of 1 meV and presents a maximum as a function of the well width. The splitting of the excited subband in square and triangular quantum wells is shown to be bigger and smaller than the splitting in the first subband, respectively. A simple single-band approach, employing spin-dependent boundary conditions and approximate coupling parameters, is also introduced and its range of validity assessed. The discussion presented clarifies the treatment of abrupt interfaces, the Ando argument against the splitting, and the use of common approximations such as neglecting the barrier penetration or the energy-dependent corrections to the parameters. Good agreement is found with available experimental data.