Showing papers on "Landau quantization published in 1989"
TL;DR: A novel type of magnetoresistance oscillations is observed in high-mobility AlGaAs/GaAs heterojunctions with a holographically induced lateral periodic modulation in one direction, which results from an oscillatory dependence of the bandwidth of the modulation-broadened Landau levels of the two-dimensional electron system on the band index.
Abstract: A novel type of magnetoresistance oscillations is observed in high-mobility AlGaAs/GaAs heterojunctions with a holographically induced lateral periodic modulation in one direction. Theoretically, the effect is shown to result from an oscillatory dependence of the bandwidth of the modulation-broadened Landau levels of the two-dimensional electron system on the band index, which leads in high-mobility samples to a strongly anisotropic oscillating contribution to the conductivity tensor. The oscillations, periodic in ${\mathrm{B}}^{\mathrm{\ensuremath{-}}1}$, reflect the commensurability of cyclotron diameter at the Fermi energy and modulation period.
349 citations
TL;DR: In this article, the magnetoresistance of a quasi-two-dimensional electron system subject to a one-dimensional superlattice potential created by field effect in gated AlGaAs/GaAs heterojunctions was investigated.
Abstract: We investigate the magnetoresistance of a quasi-two-dimensional electron system subject to a one-dimensional superlattice potential created by field effect in gated AlGaAs/GaAs heterojunctions. At low temperatures this potential gives rise to a new type of magneto-resistance oscillations with a period governed by the ratio of the classical cyclotron diameter 2${\mathrm{R}}_{\mathrm{c}}$ to the superlattice period a. The oscillations are quantitatively explained in period, phase, and magnitude by the formation of Landau bands in the two-dimensional electron system under the influence of the periodic potential.
315 citations
TL;DR: The influence of nonparabolicity on the subband structure in a quantum well is analyzed and the confinement energy for the ground state usually is increased relative to a similar calculation in the parabolic approximation.
Abstract: The influence of nonparabolicity on the subband structure in a quantum well is analyzed. Starting from an accurate expression for the bulk conduction-band structure expanded up to fourth order in k, we determine both the shift of the confinement energies and the energy dispersion parallel to the layers E${(\mathrm{k}}_{?}$). The resulting eigenvalue equations are of the same form as in the parabolic case, but somewhat more complicated. The anisotropy of the bulk conduction band is included, and it is found to have a larger effect in quantum wells than in the bulk. The results can be expressed in terms of the perpendicular mass, which is relevant for the determination of confinement energies, and the parallel mass, which gives the curvature of E${(\mathrm{k}}_{?}$) at the bottom of a subband. We derive approximate expressions for these masses in the form of explicit functions of the confinement energy, which is experimentally accessible. The enhancement of the parallel mass relative to the bulk mass is found to be 2--3 times stronger than that of the perpendicular mass. It is shown that the boundary conditions need to be modified in the nonparabolic case. The nonintuitive result is that the confinement energy for the ground state usually is increased relative to a similar calculation in the parabolic approximation. We include the effect of a perpendicular magnetic field and derive an analytic expression for the Landau levels. The cyclotron mass is found to increase with magnetic field and approach the parallel mass in the limit of small magnetic fields. The parallel mass is also relevant for transport parallel to the layers, density of states, and exciton properties. The agreement with experiment is encouraging. Previous theoretical approaches are critically reviewed and the differences and similarities with this work are pointed out.
237 citations
TL;DR: The Hall conductance of a wide two-dimensional electron gas has been measured in a geometry in which two quantum point contacts form controllable current and voltage probes, separated by less than the transport mean free path.
Abstract: The Hall conductance of a wide two-dimensional electron gas has been measured in a geometry in which two quantum point contacts form controllable current and voltage probes, separated by less than the transport mean free path. Adjustable barriers in the point contacts allow selective population and detection of Landau levels. The quantization of the Hall conductance is determined by the number of quantum channels in the point contacts and is independent of the number of occupied bulk Landau levels. A theoretical description based on the Landauer-B\"uttiker formalism is given.
146 citations
TL;DR: Effects of symmetry on localization on two-dimensional square lattices are studied numerically and the critical randomness and exponent for a metal-insulator transition are determined in the presence of strong spin-orbit interactions.
Abstract: Effects of symmetry on localization on two-dimensional square lattices are studied numerically. The inverse localization length is determined by the system-size dependence of the Thouless number in magnetic fields or in the presence of strong spin-orbit interactions. A finite-size-scaling method is also applied to the case of spin-orbit interactions. Extended states, present in each Landau level in strong magnetic fields or in the case of small randomness, are found to merge together with increasing randomness and disappear beyond a certain critical randomness. In weak magnetic fields, the field tends to reduce the localization near the band center, while the localization is enhanced in the band-tail region. Spin-orbit interactions cause effects similar to, but much stronger than, that due to a weak magnetic field. The critical randomness and exponent for a metal-insulator transition are determined in the presence of strong spin-orbit interactions.
145 citations
IBM1
TL;DR: The magnetic-field-induced bifurcation of quantum levels into surface states and bulk-like Landau States was observed in this paper, where a single-particle energy spectrum was calculated.
Abstract: We observe the magnetic-field-induced bifurcation of quantum levels into surface states and bulklike Landau States. The disruption of the electric field quantization by a magnetic field is most dramatic for electrons bound in two dimensions perpendicular to the magnetic field. The interplay between competing spatial and magnetic quantization mechanisms results in a pronounced and complex level splitting. The observed splitting of zero-dimensional energy levels depends critically on the size of the quantum dots, and can be explained with a calculated single-particle energy spectrum.
140 citations
132 citations
TL;DR: In this article, a plasmon-pole approximation for dielectric function was used to find the magnetic oscillation of the self-energy of a photo-excited hole in the lowest Landau level.
75 citations
TL;DR: It is shown that quantum ballistic transport in high magnetic fields can occur on length scales larger than 200 µm and when a quantum point contact is used as a voltage probe which does not detect the upper Landau level.
Abstract: The Shubnikov–de Haas resistance oscillations of a wide two-dimensional electron gas are suppressed dramatically when current is injected with a quantum point contact which does not populate the upper Landau level. A similar suppression is observed when a quantum point contact is used as a voltage probe which does not detect the upper Landau level. The results are explained with a model in which the Shubnikov–de Haas oscillations arise from backscattering of electrons in the upper Landau level. It is shown that quantum ballistic transport in high magnetic fields can occur on length scales larger than 200 µm.
73 citations
TL;DR: On observe des minimums profonds dans la resistivite diagonale p xx d'un systeme electronique a deux dimensions dans GaAs, a un facteur de remplissage du niveau de Landau V=1/2 et 3/2.
Abstract: On observe des minimums profonds dans la resistivite diagonale p xx d'un systeme electronique a deux dimensions dans GaAs, a un facteur de remplissage du niveau de Landau V=1/2 et 3/2 Ces structures semblent avoir leur origine dans un nouvel etat a plusieurs particules, different de l'effet Hall quantique fractionnaire
63 citations
TL;DR: In this article, the low-temperature properties of a 2D orbital anti-ferromagnet (OAF) were investigated, which is one of the possible states of the weakly interacting electron system with a half-filled band on a square lattice.
Abstract: We consider the low-temperature properties of a two-dimensional orbital anti-ferromagnet (OAF), which is one of the possible states of the weakly interacting electron system with a half-filled band on a square lattice. Such a state can result from anisotropic electron-hole pairing due to the nesting property of the Fermi surface, and is characterized by nonzero local currents violating translational symmetry of the underlying lattice. Within a simple mean-field model, we show that, in the low-energy limit, the 2D OAF is described by (2+1)-dimensional quantum field theory of gapless fermion excitations associated with zeros of the gap function. The “relativistic” Landau quantization of the spectrum in external magnetic field shows up in unusual behavior of the magnetic susceptibility. Strong diamagnetism of the OAF is found in the perpendicular field, changing to paramagnetism upon the decreasing of the angle between the field and the plane. When the angle approaches zero, the susceptibility shows an oscillatory angle dependence.
TL;DR: The properties of electrical transport as well as the properties of energy transmission and dissipation in multiprobe samples are quantitatively discussed.
Abstract: General properties of a contact in a two-dimensional electron gas (2D EG), where more than one Landau level is occupied at high magnetic fields, and is quantitatively analyzed on the basis of a Landauer-B\"uttiker formalism. When acting as a current source (drain), a contact generally populates different Landau levels to different degrees. When acting as a voltage probe, a contact does not generally indicate a mean value of the chemical potentials of different Landau levels. A voltage-probe contact works also to partially equalize populations of different Landau levels. These properties, first pointed out qualitatively by B\"uttiker, are quantitatively analyzed in terms of ${n}^{2}$ parameters when n Landau levels are occupied in the 2D EG. The analysis is applied to the n=2 case to calculate characteristic resistances of multiprobe samples. Results of recent experiments are explained on the basis of the analysis. The properties of electrical transport as well as the properties of energy transmission and dissipation in multiprobe samples are quantitatively discussed.
TL;DR: In this paper, the energy levels and allowed optical transitions with energies ΔE of a quasi-zero-dimensional (Q0D) electron gas in a magnetic field B were investigated theoretically and experimentally.
Abstract: We have investigated theoretically and experimentally the energy levels and allowed optical transitions with energies ΔE of a quasi‐zero‐dimensional (Q0D) electron gas in a magnetic field B. Using a two‐dimensional harmonic confining potential with oscillator frequency ω0, the theory predicts two values for ΔE. The resonance position in the magnetotransmission spectra from the Q0D system realized on a grid‐gate GaAs/AlGaAs heterostructure, depends strongly on the 2D confining potential induced by the gate voltage Vg and, when Vg=−0.5 and −1.5 V, agrees with ΔE calculated with ℏω0=1.5 and 2.8 meV, respectively.
TL;DR: The geometrical approach to phase-space quantization introduced by Klauder [KQ] is interpreted in terms of a universal magnetic field acting on a free particle moving in a higher dimensional configuration space; quantization corresponds to freezing the particle to its first Landau level as discussed by the authors.
Abstract: The geometrical approach to phase-space quantization introduced by Klauder [KQ] is interpreted in terms of a universal magnetic field acting on a free particle moving in a higher dimensional configuration space; quantization corresponds to freezing the particle to its first Landau level. The Geometric Quantization [GQ] scheme appears as the natural technique to define the interaction with the magnetic field for a particle on a general Riemannian manifold. The freedom of redefining the operators' ordering makes it possible to select that particular definition of the Hamiltonian which is adapted to a specific polarization; in this way the first Landau level acquires the expected degeneracy. This unification with GQ makes it clear how algebraic relations between classical observables are or are not preserved under quantization. From this point of view all quantum systems appear as the low energy sector of a generalized theory in which all classical observables have a uniquely assigned quantum counterpart such that Poisson bracket relations are isomorphic to the commutation relations.
TL;DR: In this paper, the experimental line shape of dσ x y /d N s for (0↓-) and (1↑-) Landau subbands in Si-MOS inversion layers in the range of 0.35 K≦ T ≦1.5 K and in a magnetic field of 15 T.
Abstract: Temperature ( T ) dependence of the mobility edge is examined by a model calculation which reproduces the experimental line shape of dσ x y /d N s (σ x y : Hall conductivity, N s : electron concentration) for (0↓-) and (1↑-) Landau subbands in Si-MOS inversion layers in the range of 0.35 K≦ T ≦1.5 K and in a magnetic field of 15 T. The result show that the critical behaviour of localization depends on the Landau quantum number.
TL;DR: The microwave-induced change of the magnetoresistivity of As-InP heterostructures reveals resonant structure which is attributed to electron-spin resonance of the two-dimensional conduction electrons.
Abstract: The microwave-induced change of the magnetoresistivity of ${\mathrm{Ga}}_{0.47}$${\mathrm{In}}_{0.53}$As-InP heterostructures reveals resonant structure which is attributed to electron-spin resonance of the two-dimensional conduction electrons. With microwave frequencies up to 480 GHz and in magnetic fields up to 12 T, we studied the spin splitting of the two lowest Landau levels in different samples. The spin splitting of these Landau levels is a quadratic function of the magnetic field and its extrapolation to zero magnetic field leads to vanishing spin splitting. The g factors depend on the magnetic field B and the Landau level N as follows: g(B,N)=${g}_{0}$-c(N+1/2)B, where ${g}_{0}$ and c are sample-dependent parameters, which are of the order of ${g}_{0}$\ensuremath{\approxeq}4.1 and c\ensuremath{\approxeq}0.08 ${\mathrm{T}}^{\mathrm{\ensuremath{-}}1}$, in the studied heterostructures.
TL;DR: In this paper, single and multiple quantum wells of GaSb/GaInSb were grown by metalorganic vapor phase epitaxy and X-ray diffraction on an 80 A single well confirmed the Ga1−xInxSb composition to be x=0.15, for which the lattice mismatch is ≊ 1.0%.
Abstract: Single and multiple quantum wells of GaSb/GaInSb were grown by metalorganic vapor phase epitaxy. X‐ray diffraction on an 80 A single well confirmed the Ga1−xInxSb composition to be x=0.15, for which the lattice mismatch is ≊1.0%. Photoluminescence and photoconductivity from this sample both showed a signal due to carriers in the well, the position of which was in good agreement with the calculated band diagram. Shubnikov–de Haas oscillations in the transverse magnetoresistance (ρxx) of a four‐period multiquantum well, and the associated quantum Hall effect, indicated that a two‐dimensional hole gas was present in one of the wells. Unusually, the strongest oscillations were seen for occupancy of an odd number of (spin split) Landau levels (ν=1,3,5,...,etc.) This sample also showed luminescence peaks at 738 and 755 meV which were attributed to recombination in the wells.
TL;DR: In this article, a model Hamiltonian for the calculation of disordered two-dimensional systems in a strong perpendicular magnetic field is proposed based on the statistical properties of the random Landau model, and especially tailored for numerical applications.
TL;DR: In this paper, the authors determine the electric-field-induced spin splitting of the electron subbands on the surface of narrow gap HgCdTe from measurements of the oscillatory magnetoconductivity and cyclotron resonance.
Abstract: The authors determine the electric-field-induced spin splitting of the electron subbands on the surface of narrow gap HgCdTe from measurements of the oscillatory magnetoconductivity and cyclotron resonance. The coalescence and crossing of the Landau levels in the Shubnikov-de Haas oscillations is analysed in terms of the model developed by Bychkov and Rashba (extended to include nonparabolicity). Together with the resonance data it allows them to obtain the dispersion E0+or-(k/sub ///) of the electrically spin-split ground state subband. The experiments provide for the first time a number to be compared with sophisticated subband calculations.
TL;DR: A straightforward derivation of Landau's collision term within linear response theory using the memory function approach to correlation function is presented in this article, where the relation with recent works in nuclear physics on the subject of the damping of collective modes is discussed by means of the equations of motion method.
TL;DR: Mise en evidence de l'effet d'un champ magnetique sur l'augmentation de the diffusion Raman dans GaAs observe des pics d'intensite 7 fois superieure a celle obtenue en champ nul.
Abstract: Mise en evidence de l'effet d'un champ magnetique sur l'augmentation de la diffusion Raman dans GaAs. On observe des pics d'intensite 7 fois superieure a celle obtenue en champ nul ainsi qu'un comportement resonnant de l'efficacite Raman des pics de phonons multiples selon la valeur de H. Possibilite d'identifier le niveau de Landau participant aux resonances. Des interactions electron-phonon intra-bandes et intra-niveaux de Frohlich conduisent a la diffusion Raman a haut ordre
TL;DR: In this paper, a spin assignment of fractional QHE states in the N=0 Landau level is determined from finite-size calculations of the Coulomb energy. But the experimental consequences are briefly discussed.
Abstract: Spin assignments of fractional QHE states in the N=0 Landau level are determined from finite-size calculations of the Coulomb energy. There is a spin-unpolarised ground state at 2/3 filling, with partial polarisation at 3/5 filling and full polarisation at 1/q filling with q odd. This explained in terms of competition between Coulomb repulsion, exchange and interaction of unlike spins. The experimental consequences are briefly discussed.
TL;DR: The tunneling processes between two systems of independently contacted quantized states were investigated, and transitions between different subbands on both sides of the barrier were observed as a series of peaks in the derivative of the tunneling current dI/dV.
Abstract: We have investigated the tunneling processes between two systems of independently contacted quantized states. Shifting the two systems energetically with respect to each other, we were able to observe transitions between different subbands on both sides of the barrier as a series of peaks in the derivative of the tunneling current dI/dV. If a magnetic field is applied perpendicular to the sample, additional peaks are resolved in dI/dV. These peaks are unambiguously identified as tunneling processes between different Landau levels on both sides of the barrier.
TL;DR: Mesure des caracteristiques courant-Tension d'un support asymetrique a effet tunnel resonnant et a double barriere, GaAs/Al x Ga 1-x, en presence de champ magnetique parallele a la direction de l'effet tunnel.
Abstract: We report measurements of the current-voltage characteristics of an asymmetric GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As double-barrier resonant-tunneling device in a magnetic field B parallel to the tunneling direction. In the resonant-tunneling regime the magnetic field induces weak steplike features in the I(V) curve and sawtooth oscillations in the I(B) curve that are periodic in inverse field. We explain these magnetotunneling features by Landau quantization of the three-dimensional states in the emitter and the two-dimensional states in the well, which induces steplike structure in the tunneling supply function. The experimental I(V,B) line shape is in good agreement with self-consistent numerical calculations.
TL;DR: On presente l'observation des discontinuites dans les caracteristiques de dV/dI des systemes electroniques bi-dimensionnels a haute mobilite dans des heterostructures de GaAs/Al x Ga 1-x As pour des facteurs de remplissage du niveau de Landau tres bas.
Abstract: On presente l'observation des discontinuites dans les caracteristiques de dV/dI des systemes electroniques bi-dimensionnels a haute mobilite dans des heterostructures de GaAs/Al x Ga 1-x As pour des facteurs de remplissage du niveau de Landau tres bas. On discute d'un modele de transport du courant inhomogene qui soit capable de prendre en compte les observations independantes de l'etat electronique bi-dimensionnel
TL;DR: In this article, a model for the Raman processes is deduced which explains the resonances in different scattering configurations with circularly polarized light using deformationpotential and Fr\"ohlich electron-phonon interaction in a heavily mixed valence band.
Abstract: 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.
TL;DR: In this article, the magneto-optical spectrum of the shallow donors in n-GaAs is studied using a far-infrared laser at photon energies greater than the binding energy of the donors.
Abstract: The magneto-optical spectrum of the shallow donors in n-GaAs is studied using a far-infrared laser at photon energies greater than the binding energy of the donors. The transitions from the (1s) ground state into the Landau levels are not observed but, instead, series of transitions from the ground state into donor states associated with the individual Landau levels. The strongest series corresponds to the (000)-(0N0) transitions and the second strongest series to (000-0N2) transitions where N is the index of the Landau level involved (and where the high-field notation is employed). The corresponding low-field notation is 1s-2p+, 1s-3d+2, 1s-4f+3, 1s-5g+4 etc. for the strongest series which can be followed up to the N=17 Landau level. Central cell structure due to the presence of several different donors can be observed on many of the lines associated with the N=1 and N=2 Landau levels. The 1s-3p+ transition can be used to determine chemical shifts accurately for the donor species present, as this line avoids the overabsorption effects which can distort the stronger 1s-2p+ line. A few weak lines remain unidentified.
TL;DR: On observe de nombreuses phases differentes qui apparaissent quand on fait varier la densite en couche and the separation de couche.
Abstract: We have constructed the phase diagram for a multiple-quantum-well system of two-dimensional electron layers in a strong perpendicular magnetic field. There are a number of different phases which appear as in-layer density and layer separation are varied. At densities corresponding to low filling factors of the lowest Landau level there are solid phases, while at higher densities a sequence of Laughlin-liquid-like states occurs at small layer separation. The excitations of the liquid states can exhibit irrational charge.