Zeeman Spin Splitting Research Articles

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.

Effects of photoluminescence polarization in semiconductor quantum wells subjected to an in-plane magnetic field

The strong effects of optical polarization anisotropy observed previously in quantum wells subjected to an in-plane magnetic field receive a complete description within the microscopic approach. The theory we develop involves two sources of optical polarization. The first source is due to correlations between electron and heavy-hole (HH) phases of $\ensuremath{\psi}$ functions arising due to electron Zeeman spin splitting and joint manifestation of low-symmetry and Zeeman interactions of HH's in an in-plane magnetic field. In this case, four possible phase-controlled electron-HH transitions constitute the polarization effect, which can reach its maximal amount $(\ifmmode\pm\else\textpm\fi{}1)$ at low temperatures when only one transition survives. The other polarization source stems from an admixture of excited light-hole states to HH's by low-symmetry interactions. The contribution of this mechanism to the total polarization is relatively small but can be independent of temperature and magnetic field. An analysis of the different mechanisms of HH splitting exhibits their strong polarization anisotropy. The joint action of these mechanisms can result in new peculiarities, which should be taken into account for an explanation of different experimental situations.

Competition between Rashba Effect and Exchange Interaction in a Hg 0:98 Mn 0:02 Te Magnetic 2DEG

Magnetotransport measurements are used to study the peculiar properties of a modulation doped n-type Hg0.98Mn0.02Te magnetic 2DEG. The Rashba effect and giant Zeeman spin splitting are observed simultaneously and can be separated by temperature and gate voltage dependent Shubnikov-de Haas oscillations. The Rashba effect is found to be the dominant term up to 5 T.

Kondo ground state in a quantum dot with an even number of electrons in a magnetic field

Kondo conduction has been observed in a quantum dot with an even number of electrons at the triplet-singlet degeneracy point produced by applying a small magnetic field B orthogonal to the dot plane. At a much larger field $B\ensuremath{\sim}{B}_{*},$ orbital effects induce the reversed transition from the singlet to the triplet state. We study the newly proposed Kondo behavior at this point. Here the Zeeman spin splitting cannot be neglected, which changes the nature of the Kondo coupling. On the grounds of exact diagonalization results in a dot with cylindrical symmetry, we show that, at odds with what happens at the other crossing point, close to ${B}_{*},$ orbital and spin degrees of freedom are ``locked together,'' so that the Kondo coupling involves a fictitious spin $\frac{1}{2}$ only, which is fully compensated for by conduction electrons under suitable conditions. In this sense, spin at the dot is fractionalized. We derive the scaling equation of the system by means of a nonperturbative variational approach. The approach is extended to the $B\ensuremath{\ne}{B}_{*}$ case and the residual magnetization on the dot is discussed.

Near-field magneto-optical spectroscopy of single self-assembled InAs quantum dots

We report observations of Zeeman spin splitting in photoluminescence from single InAs/GaAs self-assembled quantum dots (SAQDs) fabricated by Stranski–Krastanow growth. A low-temperature near-field optical microscope incorporating a superconducting magnet enabled us to resolve the luminescence from individual SAQDs. We have measured Zeeman split components from single SAQDs in magnetic fields up to 10 T. Circularly-polarized photoluminescence resolved carriers of different spin polarity. Dependence of the splitting on the QD structures was also investigated.

Observation of spin splitting in single InAs self-assembled quantum dots in AlAs

Using magneto-tunneling spectroscopy, we observe the Zeeman spin splitting of the ground state of a single InAs quantum dot grown within AlAs. We obtain values for the g factor of different quantum dots between +0.52±0.08 and +1.6±0.2, with magnetic field applied in the plane of the dot. This value for the g factor is considerably different from that of bulk InAs (g=−14.8), and we explain this using a simple three band k⋅p calculation. Using the spin split states of the dot as a probe, we observe the complete spin polarization of the emitter accumulation layer.

Spatial spin distribution of a skyrmion in a two-dimensional electron gas at a small g-factor

The effect of a weak Zeeman spin splitting on the spatial distribution and the energy of an isolated skyrmion in a 2D electron gas under a strong magnetic field at filling factor is studied within the framework of the Hartree-Fock approximation. Finite Zeeman splitting introduces two different characteristic lengths into the problem, corresponding to the tail and the core of the spin distribution. The non-linear differential equation for the macroscopic spin density associated with the skyrmion is solved in the limit of very small g-factor, for which the tail of the skyrmion is much longer than its core radius. In this limit the Coulomb repulsion energy of the skyrmion, which determines the core radius, does not affect the shape of the spin distribution.

Magnetooptical studies of a single quantum dot:ffExcited states and spin flip of excitons

We report on microphotoluminescence experiments in magnetic fields on single quantum dots formed by width fluctuations in a narrow GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As quantum well. The ground state as well as two excited states are discussed. We find a different diamagnetic shift and Zeeman spin splitting for these states. Resonantly exciting zero-dimensional excitons, we observe a strong magnetic-field dependence of the spin flip rates.

Discrete energy levels and superconductivity in nanometer-scale Al particles

We have fabricated single-electron tunneling transistors in which the central island is an aluminum grain with radius in the range 2–10 nm. The corresponding spacing between electron-in-a-box levels is in the range ∼0.01 to ∼1 meV. Using tunneling spectroscopy at 50 mK, we have, for the first time, resolved these discrete levels in a metallic grain. By observing the Zeeman spin splitting in a magnetic field, we can distinguish grains with even vs. odd numbers of electrons. A superconducting energy gap can be seen if the grain is large enough so that the level spacing is smaller than the energy gap. This gap is reduced continuously to zero by a magnetic field of 3–4 Tesla. While the superconducting gap adds to the Coulomb gap in determining the threshold voltage for tunneling into a grain with an initially even number of electrons, it subtracts from the Coulomb gap for a grain with an initially odd number of electrons because the tunneling electron can pair with the odd electron, forming a lower-energy fully-paired state.

Modifications of weak localization contributions to magnetoresistance due to magnetic impurities in amorphous DyxY1−xNi alloys (invited)

High-field magnetoresistance experiments performed on thick amorphous alloys offer a simple way to study three-dimensional (3D) weak localization of conduction electrons. After the precursor work of Fert et al. on nonmagnetic amorphous alloys, we found it interesting to study how these effects would disappear under substitutions of magnetic impurities (1% to 10% of Dy) in a nonmagnetic amorphous alloy (YNi). The experiments, performed between 1.5 to 50 K and in magnetic fields up to 20 T, showed (i) in YNi, characteristic features of the magnetoresistance due to weak localization under strong spin-orbit scattering and (ii) in DyxY1−xNi, a coexistence of weak localization effects with the classical contribution of spin alignment by the applied magnetic field, saturating at negative values. This last contribution dominates the behavior of Dy-richer samples whereas weak localization is clearly observed for x≤3%. In all the samples a dramatic increase of the initial magnetoresistance slope Δρ/ρH2 (where ρ=resistivity and H=applied field) is observed when magnetic impurity concentrations increase. We explain this increase of weak localization effects, in the framework of the available weak localization theory, by an enhancement of the Zeeman spin splitting due to interactions between localized (4f ) and delocalized (d, s) electronic states.

Effect of Spin-Orbit Interaction on Magnetoresistance in the Weakly Localized Regime of Three-Dimensional Disordered Systems

Effects of Zeeman spin splitting and spin-orbit interaction on magnetoresistance in three-dimensional disordered systems are investigated in the weakly localized regime and the results are compared with recent experiments on InSb by Morita et al.

Theory of Impurity Bands in Magnetic Fields. II. Transport Properties

The Hall coefficient and the magnetoresistance in a weak magnetic field are investigated for the impurity conduction processes based on a simplified model where the impurity potential is short-ranged. The formation of the impurity band and the modification of the intrinsic band are treated on the same footing by the Green function method. It is shown that the sign of the Hall coefficient is always electronic for n -type semiconductors irrespective of the degree of compensation. Two origins of the magneto-resistance, the Zeeman spin splitting and the Landau orbital motion, are separately calculated and both longitudinal and transverse magnetoresistances are shown to be of the same order of magnitude in the impurity band region. Numerical calculations of these transport coefficients are carried out as functions of the impurity concentration and of the degree of compensation. Intuitive discussion is made on the intrinsic nature of the impurity conduction processes. Further, the relation between the Hall coef...