Splitting Of Landau Levels Research Articles

Spin-splitting collapse in a 2D electron gas in AlGaAs/GaAs heterostructure

Shubnikov–de Haas (SdH) oscillations of a 2D electron gas in AlGaAs/GaAs heterostructure have been studied as a function of electron density n s in the region where spin splitting of Landau levels is observed. It is found that the Landau level number N c corresponding to the termination of spin splitting depends on the electron density as n 3/2 s while the ratio of N c to N SdH (the peak number related to the onset of SdH oscillations) is a constant within the accuracy of the experiment. The experimental results are compared with the theory which attributes the termination of spin splitting to the disorder-induced destruction of the exchange enhancement of the electron g factor.

Local Electronic Properties in the Presence of Internal and External Magnetic Fields Studied by Variable-Temperature Scanning Tunneling Spectroscopy

We have developed a new low-temperature ultrahigh vacuum scanning tunneling microscope (UHV-STM) setup combined with a solenoid and a split-pair magnet. The STM can be operated in the 10-11 mbar range, down to 7 K and in a rotatable magnetic field of up to 7 T perpendicular and 2 T parallel to the sample surface. This LT-UHV-STM setup was applied to study the Landau level quantization in n-type InAs(110). In addition to the observation of the Landau level splitting of the conduction band we were able to determine the energy dependence of the effective electron mass due to the nonparabolicity of the conduction band. Furthermore, we have studied the scattering of electron waves at dopant atoms located several nanometers (1–20 nm) below the surface. In a second study we have applied variable-temperature UHV-STM to investigate the temperature-dependent exchange splitting of a dz2 -like surface state of Gd(0001) thin films. The experimental results indicate that the high spatial localization of the surface state helps to maintain a local exchange splitting even above the Curie temperature but does not result in an enhanced surface Curie temperature. Finally, we have demonstrated spin-polarized vacuum tunneling from a ferromagnetically-coated tip into the exchange-split surface state of Gd(0001).

Studies of two-subband occupied electron gas in modulation-doped In0.52Al0.48As/In0.53Ga0.47As single quantum well by far-infrared modulated photoluminescence

We report an investigation of electronic and optical properties of two-subband occupied electron gas confined in Al0.48In0.52As/Ga0.47In0.53As quantum well by far-infrared (FIR) modulated photoluminescence (PL) measurements. We show that, in addition to the characterization of the effective mass and Fermi energy, this technique is a useful tool for the understanding of the luminescence processes. Well-resolved Landau-level splittings were observed in the FIR modulated PL spectrum at a fixed magnetic field. It is found that the PL spectrum involves the transitions between localized holes and electrons at all occupied k states. For the FIR modulated spectrum monitored at the peak position as a function of magnetic field, a strong double cyclotron-resonance signal was observed. The double structure of cyclotron resonance is attributed to the cyclotron transitions in the first and second subbands. The obtained effective masses are found to be considerably heavier than the bulk value by 22% and 46% for the first and second subband, respectively. The heavier effective mass of the second subband is opposite to the behavior measured in the triangular quantum well. We point out that, in order to explain the enhanced masses, both the effects of band nonparabolicity and wavefunction penetration into the barrier material have to be taken into account.

Exact density of states of the lowest Landau level in a spin- system with uncorrelated disorders

Using the path-integral approach developed by Br\'ezin et al. [ Nucl.Phys.B235, 24 (1984) ], we obtain an analytical expression for the density of states of a spin-1/2 disordered two-dimensional electron gas in a strong, perpendicular magnetic field. The density of states of this system illustrates the interplay between the Zeeman splitting of Landau levels and the disorder-induced broadening. We find that the broadening and the band splitting of the Landau bands are enhanced due to the level repulsion from the mixing of two spin orientations caused by the random scatterings. The comparison between the spin-1/2 model and the double-layer system is also discussed.

Exact Shape of the Lowest Landau Level in a Double-Layer System and a Superlattice with Uncorrelated Disorder.

We extend Wegner's exact solution for the 2D density of states at the lowest Landau level with a short-range disorder to the cases of a double-layer system and a superlattice. For the double-layer system, an analytical expression for the density of states, illustrating the interplay between the tunnel splitting of Landau levels and the disorder-induced broadening, is obtained. For the superlattice, we derive an integral equation, the eigenvalue of which determines the exact density of states. By solving this equation numerically, we trace the disappearance of the miniband with increasing disorder.

Even-odd filling-factor switching in one-dimensional lateral superlattices.

The magnetoresistance of a two-dimensional electron system, subjected to a one-dimensional lateral potential modulation is studied for various potential amplitudes. The interplay between Landau level splitting and modulation broadening is shown to generate a transition from even to odd filling factors for the Shubnikov--de Haas resistance minima. The effect provides a tool to determine the potential amplitude. Calculations within a one-particle model agree with this evidence of the van Hove--like structure of the Landau bands. \textcopyright{} 1996 The American Physical Society.

Structural and physical properties of mercury-iron selenide layers and quantum wells.

Epitaxial layers and single quantum wells (SQW's) of Fermi-level pinned mercury--iron selenide (HgSe:Fe) have been grown by molecular-beam epitaxy on ZnTe buffer layers and characterized by in situ reflection high-energy electron-diffraction (RHEED) and high-field magnetospectroscopy investigations. The onset of strain relaxation at the critical thickness has been determined by time-dependent intensity-profile analysis of different reflexes in the RHEED pattern. In spite of the small mismatch and the very low growth temperature, a growth-mode transition from a two-dimensional--to--three-dimensional (2D-to-3D) Stranski-Krastanov growth mode has been identified, which coincides exactly with the critical thickness equilibrium value of about 61 nm predicted by the Matthews-Blakeslee theory. Due to this mechanism, the surface roughness transition region is extended and the onset of plastic relaxation is delayed up to a thickness of about 280 nm. Hall-effect measurements have been performed to determine the iron concentration in the HgSe layers below and above the Fermi-level pinning threshold concentration. With increasing iron concentration both a pronounced increase of the mobility and decrease of the Dingle temperature have been found in the layers. This agrees well with the present available data from HgSe:Fe bulk crystals and also with the values predicted by the short-range correlation model.However, the maximum carrier mobility of about 2.7\ifmmode\times\else\texttimes\fi{}${10}^{5}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ measured in a 1.5-\ensuremath{\mu}m-thick HgSe:Fe layer indicates that long-range correlations also have to be considered in the transport mechanism of mercury--iron selenide. HgSe:Fe SQW's grown in the strained-layer region below the equilibrium critical thickness have been analyzed by Shubnikov--de Haas (SdH) measurements and Hall-effect measurements in magnetic fields up to 50 T. The existence of a two-dimensional electron system (Q2D) in the SQW has been confirmed by the cosine dependence of the SdH oscillation period. The subband splitting in the SQW in dependence of the quantum-well width has been investigated by Hall-resistance measurements. One subband has been identified experimentally in a 12-nm HgSe:Fe quantum well, whereas for high magnetic fields at least two subbands are measured in the 25-nm structures. The Landau-level splitting has been simulated using the Pidgeon-Brown model. In this way the subband splitting and the spin splitting observed experimentally can be explained. The broadening of the localized iron level has been determined from simulation curves.

Stimulated Brillouin scattering in magnetized direct-gap semiconductors.

Following the time-dependent perturbation technique for the density matrix, the phenomenon of stimulated Brillouin scattering (SBS) has been analytically studied in weakly noncentrosymmetric (NCS) crystals like InSb immersed in a moderately strong magnetostatic field. The twofold role of the magnetostatic field B in terms of the sharpening of the density of states and Landau-level splitting have been examined quantum mechanically. The extremely large value of the spectroscopic splitting factor (${\mathit{g}}_{\mathit{c}}$-${\mathit{g}}_{\mathit{v}}$) and the very low electron and hole effective masses play the key roles in the significant enhancement in Brillouin susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathbf{B}}$, even when B is reasonably low. The origin of the NCS effect has been assumed to be in the parity indefiniteness of the energy states in the crystals exhibiting lack of inversion symmetry. We have considered near-resonant band-to-band electron transition in the direct-gap crystals to reduce to a simple one-dimensional problem in the presence of the magnetostatic field. Numerical estimates have been made for the InSb crystal at 77 K, duly irradiated by a pulsed 5.3 \ensuremath{\mu}m CO laser. The SBS threshold is found to be well below the crystal damage threshold and ${\mathrm{\ensuremath{\chi}}}_{\mathbf{B}}$ is found to be appreciably large. The results support strongly the candidacy of InSb for establishing itself as a promising crystal for strong SBS and optical-phase conjugation while immersed in a moderate magnetostatic field.

Cyclotron resonance of electrons in a semiconductor quantum well

The cyclotron resonance of electrons confined in a quantum well was investigated by means of the Wigner-Brillouin perturbation theory. It is found that the splitting of Landau levels can occur near the frequency of the long-wavelength transverse-optical phonons of the well barriers owing to the interface phonons. Decreasing the width of the well increases the electron-phonon interaction. Electronic screening weakens the interaction.

Landau levels of bragg confined electrons and holes

We report on the observation of the electronic Landau level splitting in Bragg confining structures (BCS) under an applied magnetic field at T = 2 K. The BCS consists of finite GaAs/Al 0.32Ga 0.68As superlattice (SL) sections that clad Al 0.32Ga 0.68As spacer layers. The SL sections act as Bragg reflectors that give rise to confined electron and hole states in the spacer layers ( e B, hh B and lh B ). The Landau levels are observed in the photoluminescence excitation spectra in the Faraday configuration. The electron and hole cyclotron frequencies correspond to a two-dimensional motion in the Bragg confining barrier. We use the magnetic field dependence in order to determine the e B- hh B and e B- lh B band gaps and from these we find the Bragg confined exciton binding energy.

Electron and hole effective masses from magnetoluminescence studies of modulation-doped InP/In0.53Ga0.47As heterostructures.

Two-dimensional (2D) carrier-recombination processes in modulation-doped unstrained InP/${\mathrm{In}}_{0.53}$${\mathrm{Ga}}_{0.47}$As heterostructures with 500-\AA{}-wide ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As active layers have been investigated with magneto-optical spectroscopy. Photoluminescence bands related to the 2D confined carriers have been observed in both n- and p-type modulation-doped structures. For the n-type structures it is found that the emissions observed are transitions between 2D electrons at the interface potentials and holes in the ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As valence band. Excitonic effects are not observed, even for the emission related to the third confined electronic state. For the p-type structures the transitions occur across the ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As layer between 2D holes and 2D electrons at the opposite interface notch potentials. Both the n- and the p-type modulation-doped structures show well-resolved Landau-level splitting when a magnetic field is applied parallel to the growth direction. The effective masses of both 2D electrons and 2D holes confined in the ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As layer are simultaneously obtained by analysis of the same magneto-optical data. Effective-mass values of ${\mathit{m}}_{\mathit{e}}$=(0.054\ifmmode\pm\else\textpm\fi{}0.005)${\mathit{m}}_{0}$ for the first subband electrons and ${\mathit{m}}_{\mathrm{hh}}$=(0.463\ifmmode\pm\else\textpm\fi{}0.005)${\mathit{m}}_{0}$ for the first subband heavy holes, respectively, are derived from our spectra. The effective mass of n=2 subband electrons was found to be about 9% larger than the effective mass of n=1 electrons.

On the conductivity of lateral-surface superlattices in magnetic fields

The authors present results for the band conductivity and the density of states of electrons in realistic two-dimensional periodic potentials and magnetic fields. They show the effects of the number of flux quanta per unit cell in producing Hofstader's-butterfly-like splittings in the limit of small field, but outside the simple tight-binding limit, and for high fields where the dominant effect is the local splitting of Landau levels to form weakly coupled edge states round the minima and maxima of the potential. The broadening and splitting of these states to form Hofstader's butterfly then occurs on a much finer energy scale.

Magnetoluminescence study of many-body effects in a dense electron-hole plasma of strained InxGa1-xAs/GaAs quantum wells.

High-excitation luminescence spectra from a highly homogeneous electron-hole system have been investigated in strained undoped ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/GaAs quantum wells (QW's) with nearly parabolic conduction and valence bands in magnetic fields H\ensuremath{\le}12 T. The spectra show well pronounced Landau levels which are shifted to lower energy with respect to separately measured magnetoexciton photoexcitation maxima in the empty QW. The shift depends on the carrier density, subband, and Landau-level number. For the dense (${\mathit{n}}_{\mathit{e}\mathrm{\ensuremath{-}}\mathit{h}}$>${10}^{12}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$) magnetoplasma with electron temperature of the order of the cyclotron energy, a simple plasma approximation has been found to describe the Landau-level splitting. The band-gap shrinkage and reduced effective-mass ${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}1}$=${\mathit{m}}_{\mathit{e}}^{\mathrm{\ensuremath{-}}1}$+${\mathit{m}}_{\mathit{e}}^{\mathrm{\ensuremath{-}}1}$ renormalization have been carefully measured and compared with those in the unstrained ${\mathrm{In}}_{0.53}$${\mathrm{Ga}}_{0.47}$As/InP QW's. The difference has been revealed in the reduced effective-mass renormalization connected with renormalization of ${\mathit{m}}_{\mathit{h}}$ due to the change of the light-hole--heavy-hole subband splitting.

Influence of quantization of band states on the effective electron mass in quaternary alloys

An attempt is made to study the effective electron mass in quaternary alloys, taking a In1−xGaxAsyP1−y lattice matched to InP, by using the three-band Kane model under different physical conditions,e.g. bulk specimens, magnetic quantization, cross-field configuration, quantum well, electric-field-aided quantum well, magnetic-field-aided quantum well, quantum well under cross fields, quantum well wires, electric-field-aided quantum well wires, magnetic-field-aided quantum well wires and quantum well wires under cross fields by formulating the respective expressions. We have plotted the effective Fermi level mass with various physical variables under different conditions. In the presence of a quantizing magnetic field the effective mass depends on the spin splitting of Landau levels due to the spin-orbit splitting parameter of the valence bands. Under cross-field configuration and the various quantum confined low-dimensional systems, the effective masses depend on the respective quantum numbers in addition to the Fermi energies even for parabolic models because of the inherent features of such systems. In addition, the corresponding results for relatively wide-gap materials have also been obtained from our generalized formulations under certain limiting conditions.

Antiscreening and exchange-enhanced spin splitting in quantum wires.

Theoretical work is presented, suggesting that in regimes of experimental interest, the exchange enhancement of the spin splitting of Landau levels in quantum wires as evidenced in their two-terminal conductance is increased by the confinement. This is due to an effect in which electron-electron interactions are strengthened by interaction with polarizable edge-state charge. This antiscreening effect is confirmed by calculating exchange enhancement in a quasi-one-dimensional conductor in the ``screened'' Hartree-Fock approximation. Preliminary experimental evidence for the effect is also presented.

Magnetoresistance in a grid-type lateral superlattice: the role of disorder

The magnetoresistance of a two-dimensional electron gas (2DEG) subjected to a weak two-dimensional (2D) lateral superlattice potential is expected to reflect the peculiar self-similar energy spectrum of Bloch electrons in a magnetic field, i.e., the splitting of Landau levels (LL's) into sublevels. One experimentally established effect of a periodic potential is that the discrete LL's are transformed into Landau bands and cause magnetoresistance oscillations due to an extra band-conductivity contribution. Theoretically, this band-conductivity contribution is expected to be suppressed if the splitting of the Landau bands is resolved. We study the suppression of the band-conductivity as a function of the electron mobility at millikelvin temperatures. Microfabricated gates, defined on top of high mobility GaAs/AlGaAs heterojunctions. are used to electrostatically impose a 2D-periodic potential with 150 nm period upon the 2DEG. By applying a positive bias the electron mobility is increased and we find the band-conductivity effectively suppressed if the mobility is well above 1 × 10 6 cm 2/Vs.

Nuclear-spin relaxation and spin-wave collective modes in a disordered two-dimensional electron gas.

The spin-polarization of nuclei near a two-dimensional electron gas (2D EG) may be relaxed by spin-flip excitations of the electron system. The spectrum of low-energy electronic spin-flip excitations depends on the disorder broadening of Landau levels and on the interaction enhancement of the Landau-level spin splitting. Disorder vertex corrections to the spin-flip response function capture the fact that the nuclear relaxation rate depends on local rather than thermodynamic Landau-level broadening, while interaction vertex corrections can strongly enhance the relaxation rate. We illustrate these effects by summing the disorder and interaction ladder diagrams for the spin-flip response function in the strong-magnetic-field limit. Our approach is also able to describe the effect of disorder on the spin-wave collective modes of a spin-polarized 2D EG.

Magnetoresistance oscillations in a grid potential: Indication of a Hofstadter-type energy spectrum.

We present experimental and theoretical results on magnetoresistivity oscillations of high-mobility two-dimensional electron systems in a weak superlattice potential. Experimentally, the band conductivity of a sample with a holographically produced grid potential is shown to be considerably smaller than that of the same sample with a similar linear grating potential of the same lattice constant. This is explained by a magnetotransport theory with due consideration of collision broadening effects and the peculiar subband splitting of Landau levels resulting in a Hofstadter-type energy spectrum.

Magnetoresistance Oscillations in a Two-Dimensional Electron Gas Subject to a Weak Lateral Superlattice Potential

Recent progress of our understanding of the novel magnetoresistance oscillations observed on two-dimensional electron gases with a weak lateral superlattice is reviewed. The discussion is based on a quantum mechanical single-electron picture, taking consistently into account the effect of the superlattice on the energy spectrum and the effect of randomly distributed impurities on collision broadening and transport scattering rate. This, first, allows to explain the original results of Weiss et al. on high-mobility AlxGa1-xAsGaAs heterostructures with an unidirectional modulation potential produced by holographic illumination: the large-amplitude oscillations of ρxx, measured when the current flows in the direction of the modulation, are atributed to a bandconductivity σyy, and the weaker antiphase oscillations of ρyy (∝ σxx, Current parallel to equipotentials) are shown to result from quantum oscillations of the scattering rate. Second, for the case of a modulation with square symmetry, where the energy spectrum is given by Hofstadter's famous "butterfly", it explains the dramatic suppression of the bandconductivity, which has recently been observed on high-mobility samples, as a consequence of the splitting of Landau levels into the Hofstadter-type subbands.

Magneto-Transport Measurements on Si/Si1−xGex Resonant Tunneling Structures

ABSTRACTWe have investigated magneto-transport properties of differently strained Si/ Si1−xGex resonant tunneling devices. The built-in strain was either put in the Si layers, by means of a thick., relaxed Si1−xGex buffer layer, or in the Si1−xGex layers, in which case all Si1−xGex layers were grown below the critical thickness, and a Si1−xGex spacer layer with graded Ge content was used. Magnetic fields parallel to the interface have been employed to probe the in-plane dispersion in the quantum well. This is used to study the effect of band-mixing in the two strain configurations. A field perpendicular to the interface resolves some Landau level splitting. Most strikingly, however, is the similarity in the spectra with the case when the magnetic field is applied parallel to the interfaces. This indicates broadening of the levels, possibly due to scattering, and the importance of 3-dimensional band structure effects.