Conduction Band Landau Levels Research Articles

Tunability of the fractional quantum Hall states in buckled Dirac materials

We report on the fractional quantum Hall states of germanene and silicene where one expects a strong spin-orbit interaction. This interaction causes an enhancement of the electron-electron interaction strength in one of the Landau levels corresponding to the valence band of the system. This enhancement manifests itself as an increase of the fractional quantum Hall effect gaps compared to that in graphene and is due to the spin-orbit induced coupling of the Landau levels of the conduction and valence bands, which modifies the corresponding wave functions and the interaction within a single level. Due to the buckled structure, a perpendicular electric field lifts the valley degeneracy and strongly modifies the interaction effects within a single Landau level: in one valley the perpendicular electric field enhances the interaction strength in the conduction band Landau level, while in another valley, the electric field strongly suppresses the interaction effects.

Optically pumped NMR: Revealing spin-dependent Landau level transitions in GaAs

We show that high-resolution optically pumped NMR (OPNMR) studies can reveal spin-dependent optical transitions between valence- and conduction-band Landau levels in bulk semiconductors such as GaAs. The OPNMR signal intensity exhibits oscillations as a function of pump photon energy that evolve with magnetic field. In contrast to standard polarized magnetoabsorption measurements, OPNMR is sensitive to the polarization of the photoexcited electron spins (i.e., the difference between spin-up and spin-down electron populations rather than the sum). This allows one to clearly resolve the spin dependence of optical transitions that might normally be obscured in conventional magnetoabsorption studies. The data are in good agreement with theoretical calculations of the transitions from the spin-split light-hole Landau levels in the valence band to the conduction-band Landau levels of GaAs.

TERAHERTZ MAGNETOSPECTROSCOPY OF HEAVILY-DOPED Si(P)

We demonstrate that lightly-doped Si ( P ) displays extremely sharp absorption lines – the narrowest yet reported for any impurity in natural Si . The Zeeman splitting of many of these lines in magnetic fields <10 T has been studied previously by a number of groups. In this paper we focus on the behavior of metastable states associated with conduction-band Landau levels. The use of a rather heavily doped sample and strong magnetic fields, up to 18 T, assists in the observation of these.

Magnetic freezeout of electrons into muonium atoms inGaAs

High-field muon-spin-resonance techniques have been used to study muonium atom formation via electron capture by a positive muon implanted into $\mathrm{GaAs}$ with $\mathrm{Cr}$ impurities in magnetic fields up to $7\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. The distribution of muon polarization between neutral atoms and charged states is found to depend strongly on magnetic field when the energy of the electron's lowest-order conduction band Landau level becomes comparable to the characteristic binding energy of the electron in a weakly bound muonium atom. This effect is discussed in terms of magnetic freezeout of free electrons into weakly bound muonium states.

Electronic states and cyclotron resonance inn-type InMnAs

We present a theory for electronic and magneto-optical properties of n-type ${\mathrm{In}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$ magnetic alloy semiconductors in a high magnetic field $B\ensuremath{\Vert}\mathrm{z\ifmmode \hat{}\else \^{}\fi{}}.$ We use an eight-band Pidgeon-Brown model generalized to include the wave vector ${(k}_{z})$ dependence of the electronic states as well as $s\ensuremath{-}d$ and $p\ensuremath{-}d$ exchange interactions with localized Mn d electrons. Calculated conduction-band Landau levels exhibit effective masses and g factors that are strongly dependent on temperature, magnetic field, Mn concentration $(x),$ and ${k}_{z}.$ Cyclotron resonance (CR) spectra are computed using Fermi's golden rule and compared with ultrahigh-magnetic-field $(>50$ T) CR experiments, which show that the electron CR peak position is sensitive to x. Detailed comparison between theory and experiment allowed us to extract the $s\ensuremath{-}d$ and $p\ensuremath{-}d$ exchange parameters $\ensuremath{\alpha}$ and $\ensuremath{\beta}.$ We find that not only $\ensuremath{\alpha}$ but also $\ensuremath{\beta}$ affects the electron mass because of the strong interband coupling in this narrow-gap semiconductor. In addition, we derive analytical expressions for effective masses and g factors within the eight-band model. Results indicates that $(\ensuremath{\alpha}\ensuremath{-}\ensuremath{\beta})$ is the crucial parameter that determines the exchange interaction correction to the cyclotron masses. These findings should be useful for designing novel devices based on ferromagnetic semiconductors.

Effective mass of conduction electrons inCd1−xMnxTe

Electron cyclotron resonance in ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Te}$ $(x=0,$ 0.064, 0.097, 0.11) has been studied in high magnetic fields up to 150 T at photon energies in the range 44--117 meV. We found that the band-edge effective mass of the conduction electrons increases significantly with the Mn concentration. For comparison with the experimental results, the conduction-band Landau levels were calculated by means of the eight-band Pidgeon-Brown model taking into account the $s(p)\ensuremath{-}d$ exchange interaction. The increase of the band gap due to the Mn ions alone is not sufficient to explain the observed enhancement of the mass. A possible reason for the mass enhancement is an effect of the $\mathrm{sp}\ensuremath{-}d$ hybridization. We also found that the electron mass decreases significantly with decreasing temperature. A large spin splitting of the Landau levels due to the exchange field qualitatively explains the relative temperature dependence of the mass.

Heterostructure interface effects on the far-infrared magneto-optical spectra of InAs/Gasb quantum wells

The electronic and optical properties of InAs/GaSb heterostructures depend on the type of bonding at the interfaces, InSb bonds or GaAs bonds. We have studied cyclotron resonance (CR) in the far-infrared on two samples, each consisting of a single 30 nm InAs quantum well surrounded by thick GaSb barriers. The only intended difference between the samples is the interface bonding type, Ga–As bonds and In–Sb bonds. The CR for the sample with Ga–As interface bonds shows two lines whose positions are determined by nonparabolicity effects, whereas the sample with In–Sb bonds shows multiple lines due to strong cross-interface coupling between the InAs conduction band Landau levels (LLs) and the valence band LLs in GaSb. We find that the CR is a sensitive probe of interface bonding type for such structures.

Magneto-Optical Absorption Studies of Modulation-Doped CdTe and dMnTe Quantum Wells

We present interband magneto-absorption spectra up to 20 T taken at 2 K for 100 Å CdTe and CdMnTe single and multiple quantum wells containing a two-dimensional electron gas with concentrations ne up to 4 × 1011 cm—2. Without magnetic field B the absorption spectrum is characterized by two strong peaks, whose energy difference increases linearly with the electron concentration ne. This is interpreted in the framework of the many-body theory proposed by Hawrylak. In a magnetic field B, the spectra of high ne (4 × 1011 cm—2) quantum wells show circularly polarized absorption lines. We find that: (i) asBis increased there is a dominant, strongly enhanced absorption transition whose position is related to the zigzags of the Fermi level on the conduction band Landau levels; (ii) at integer values of the filling factorν, in absorption spectra, there is a sudden redshift of this line equal to the cyclotron energy of the electron ħωeh ; (iii) between the discontinuities, in emission spectra, the values of the transition slope are nħωeh (i.e. not the expected values (n + 1/2) ħωeh) where n is the Landau level index and ħωeh represents the sum of the cyclotron energy of the electron and the hole.

Influence of Auger and LO-phonon scattering on bulk and ‘quasi’-quantum wire mid-IR laser diodes

Measurements of the light-current characteristics of bulk InSb on InSb and InAlSb on InSb lasers, emitting at 5.1 μm at 77K, have been made in the temperature range from 4.2 to 110K. For the alloy device the authors find values of the characteristic temperature T 0 of around 22K above 90K, which indicates that Auger recombination is dominant, but T 0 increasing to around 45K at lower temperatures. This increase is consistent with a decrease in Auger recombination with decreasing temperature. Using the all InSb device, the authors have applied magnetic fields along the cavity direction at 4.2K, in order to change the density of states (DOS) to a peaked distribution at the Landau level energies. This enabled them to study the effects of a 'quasi'-quantum wire structure with an easily variable degree of confinement. A reduction in the threshold current I th with B-field of up to 30% was seen. The most striking results were obtained when the current was kept constant and the magnetic field was swept. Peaks in the light output were observed at exactly the field positions where the conduction band Landau level separation is resonant with the LO-phonon energy, giving enhanced electron cooling. Between the resonances the light output was suppressed due to the effect of the 'phonon bottleneck'. Finally, the size of a a real wire, corresponding to the Landau confinement which gives the greatest improvement, has been estimated to be 800 A.

K⋅p finite-difference method: Band structures and cyclotron resonances ofAlxGa1−xSb/InAsquantum wells

A simple theoretical six-band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ finite difference method is developed and applied to calculate the electronic band structures and electronic Landau-level structures of the symmetric and asymmetric ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{S}\mathrm{b}/\mathrm{I}\mathrm{n}\mathrm{A}\mathrm{s}$ quantum wells (QW's). The QW may exhibit a semiconductor-semimetal transition by changing the Al composition in the ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{Sb}$ layer. The cyclotron-resonance splitting in the semiconducting structures is due to the large InAs conduction-band nonparabolicity and Zeeman effect. Broken-gap type-II semimetallic QW, in which the conduction-valence Landau-level mixing can yield a significant spin splitting for the InAs conduction-band Landau levels, produces a prominent electron double-line structure in the cyclotron-resonance spectra, whether the QW is symmetric or asymmetric. Strong oscillations in the electron cyclotron-resonance mass, amplitude, and linewidth are evident. The abnormal cyclotron-resonance mass jumps, amplitude minima, and linewidth maxima occurring near the even filling factors are due to the conduction-valence Landau-level mixing effect. These results are in good agreement with the experimental results.

Magnetoluminescence study of n-type modulation-doped ZnSe/ZnxCd1−xSe quantum-well structures

We have studied the band-edge photoluminescence from two n-type modulation-doped ZnSe/${\mathrm{Zn}}_{\mathrm{x}}$${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$Se single quantum-well structures with electron areal densities of 1.1\ifmmode\times\else\texttimes\fi{}${10}^{12}$ and 1.9\ifmmode\times\else\texttimes\fi{}${10}^{12}$${\mathrm{fcm}}^{\mathrm{\ensuremath{-}}2}$ in magnetic fields up to 30 T. The sharp excitonic transitions observed in undoped samples are replaced by a broad luminescence band. In a magnetic field, the luminescence spectra consist of distinct features associated with interband transitions between electrons occupying the conduction-band Landau levels and photoexcited holes. The energies of these transitions exhibit anomalies for even filling factors due to many-body effects.

Conduction electrons bound to magneto-donors and magneto-acceptors in [formula omitted] quantum wells

Interband photoluminescence from asymmetric modulation-doped GaAsGaAlAs quantum wells in the presence of a magnetic field has been investigated. The free-carrier Landau level excitations as well as transitions between magneto-donor and free hole states have been observed. Experiments with tilted magnetic field provide strong evidence for the existence of conduction electrons bound to ionized magneto-acceptors, characterized by discrete energies above the conduction band Landau levels. The observations are compared with the theory.

Bound magneto-acceptor and magneto-donor states in the conduction band of GaAsGaAlAs heterostructures

Interband magneto-photoluminescence from asymmetric modulation-doped GaAsGaAlAs quantum wells has been investigated. In addition to the free-carrier Landau level excitations, transitions between magneto-donor and free hole states have been observed. Experiments with tilted magnetic field provide strong evidence for the existence of conduction electrons bound to ionized magneto-acceptors characterized by discrete energies above the conduction band Landau levels.

Far-infrared magnetoabsorption studies of zero-gap Hg1-xMnxSe crystals.

The results of magnetotransmission measurements performed on ${\mathrm{Hg}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Se crystals (0.021\ensuremath{\le}x\ensuremath{\le}0.05) at different temperatures are presented. The investigated materials have an inverted band structure (like HgSe). Most of the observed features are explained by transitions between conduction-band Landau levels, described by the Pidgeon-Brown model extended to include exchange interaction. The obtained values of the interaction gap ${\mathit{E}}_{0}$ and matrix element P complement results obtained from transport and interband magnetotransmission measurements, and show a nonlinear behavior of ${\mathit{E}}_{0}$ vs Mn composition x and a strong nonmonotonic dependence of P on x. The temperature dependence of Landau-level energies at low temperatures (between 2 and 8 K) is due to the changes of magnetization with temperature. In addition to spin and combined resonances, transitions allowed by warping and/or inversion asymmetry such as the second and third cyclotron harmonics are observed. The transitions, which could not be explained by transitions between Landau levels, are attributed to transitions from an impurity level (probably an ionized acceptor state) resonant with the conduction band. The zero-field energy of the level is estimated to be 3.8 meV above the top of the valence band.

Magneto-optical investigation of impurity and defect levels in HgCdTe alloys

We have observed and described magneto-optical transitions between impurity/defect levels and conduction band Landau levels for a variety of n-type HgCdTe samples with 0.2<x<0.3. The activation energies of these levels fall into two categories: (1) 10–12 meV above the valence band edge, independent of Eg and (2) two close spaced levels at ≂0.5 Eg. In addition, the spectra of several narrow gap (Eg≤100 meV) samples exhibit shallower and deeper acceptor-like levels.

Theory of optical spectra in a magnetic field in doped semiconductor quantum wells: Impurity-induced broadening and transitions.

The effect of carrier-impurity interactions on luminescence- and excitation-spectroscopy line shapes and the Landau-level spectral density in a strong quantizing magnetic field is examined in modulation-doped semiconductor quantum wells. The line-shape function is obtained by summing the ladder diagrams,'' extending our previous one-rung'' approximation. Apart from yielding a line broadening, the carrier-impurity interaction is found to induce off-diagonal transitions (ODT) ({ital n}{r arrow}{ital n}{prime}; {ital n}{prime}{ne}{ital n}) between the Landau levels in the conduction and valence bands, breaking the usual {ital n}{r arrow}{ital n} selection rule. Here the first and second integers indicate the Landau quantum numbers in the conduction (valence) and valence (conduction) bands, respectively, for luminescence (excitation), for example, in an {ital n}-type system. The Landau-level spectral density (essential for obtaining the line-shape functions) is investigated by a self-consistent Born approximation which includes inter-Landau-level impurity scattering. The theory is applied to an {ital n}-type strained In{sub {ital x}}Ga{sub 1{minus}{ital x}}As/GaAs quantum well, where optical transitions arise between the conduction band and the strain-split in-plane light-hole'' band. For excitation spectra, the theory predicts that ODT introduce lines below the usual {ital n}{sub {ital F}}{r arrow}n{sub F} threshold transition as well as satellite lines between the usual main {ital n}{rmore » arrow}{ital n} lines above the threshold (i.e., {ital n}{ge}{ital n}{sub {ital F}}). Here {ital n}{sub {ital F}} is the quantum number of the lowest-lying empty or partially filled conduction-band Landau level. The luminescence line shape is dominated by ODT 1, 2,...{r arrow}0 (in addition to the main 0{r arrow}0 transition) at low temperatures and by the usual {ital n}{r arrow}{ital n} transitions at high temperatures.« less

Resonant Raman scattering and piezomodulated reflectivity of InP in high magnetic fields.

In a magnetic field the efficiency for Raman scattering by LO phonons in InP(001) exhibits resonant structure which can be associated with interband magneto-optical transitions between Landau levels. The Raman processes are found to occur in outgoing resonance and theoretical transitions, determined by an 8\ifmmode\times\else\texttimes\fi{}8 k\ensuremath{\cdot}p calculation, are assigned to the experimental fan lines. A model for the Raman processes is deduced which explains the resonances in different scattering configurations with circularly polarized light using deformation-potential and Fr\"ohlich electron-phonon interaction in a heavily mixed valence band. To substantiate the theoretical description of the Raman processes by obtaining directly the interband transitions, piezoreflectance measurements are performed. For conduction-band Landau levels ${E}_{n}$ around ${E}_{0}$+\ensuremath{\Elzxh}\ensuremath{\Omega}(LO), pronounced anticrossings are found which can be attributed to resonant magnetopolaron effects. No anticrossings other than with the \ensuremath{\Vert}n=0, 1-LO〉 state are observed in the reflectivity measurements which were performed up to 18.5 T. In the Raman data, however, anticrossings with higher Landau levels up to \ensuremath{\Vert}n=2, 1-LO〉 are found.

Nonlinear magneto-optical spectroscopy of Hg1−xCdxTe by two-photon absorption techniques

In this paper we present new and important results on Hg1−xCdxTe alloys using CO2 laser-based magneto-optical methods that include (i) the observation and analysis of two-photon magnetoabsorption spectra in a variety of samples from x≂0.24 to 0.30, and (ii) the observation of magneto-optical transitions of electrons from both midgap levels and shallow acceptor levels to the conduction-band Landau levels. These measurements allow the most accurate determination of the energy gap and binding energies associated with impurities and defects. In addition, analysis of the temperature dependence of two-photon spectra obtained on all samples investigated reveals a nonlinear variation of the energy gap versus temperature not previously reported. The temperature dependence of the energy gap below 100 K cannot be explained by any of the currently used empirical relationships. The laser-based magneto-optical techniques we present here for Hg1−xCdxTe are generic and can easily be applied to other semiconductor or superlattice systems by using an appropriate combination of laser sources and magnetic fields.

Magnetoreflectance and luminescense study of beryllium acceptors in selectively doped GaAs/Al xGa 1−xAs multiple quantum wells

We present a magneto-optical study of p-type GaAs/Al xGa 1−xAs quantum wells doped with Be acceptors over the central one-third of the GaAs layers. Using magneto-reflectance and magneto-luminescence spectroscopies, we have investigated (a) interband Landau transitions and (b) transitions from the conduction band Landau levels to the Be acceptors. Binding energies of the acceptors were determined and the dependence of the impurity ground state energy on magnetic field has been studied.

Magneto-photoluminescence studies of manganese acceptors in GaAs/AlGaAs multiple quantum wells

We have investigated the photoluminescence associated with residual manganese acceptors in n-type, modulation doped, GaAs/AlGaAs multiple quantum wells. In a magnetic field the luminescence breaks into discrete lines attributed to transitions between conduction band Landau levels and manganese acceptor states. The polarization of the luminescence was studied as function of magnetic field. A simple model based on the spin exchange interaction between the holes and the manganese ions successfully describes the polarization data.