Fractional quantum Hall effect at a suppressed energy gap

In the fractional quantum Hall effect regime, the diagonal (ρ_xx) and Hall (ρ_xy) magnetoresistivity tensor components of the two-dimensional electron system (2DES) in gated GaAs/Al_xGa_1−x As heterojunctions are measured together with the capacitance between 2DES and the gate. The 1/3-and 2/3-fractional quantum Hall effects are observed at rather low magnetic fields where the corresponding fractional minima in the thermodynamic density of the states have already disappeared, thus, implying the suppression of the quasiparticle energy gaps. The text was submitted by the authors in English.     

A direct connection between quantum Hall plateaus and exact pair states in a 2D electron gas

It is previously found that the two-dimensional (2D) electron-pair in a homogeneous magnetic field has a set of exact solutions for a denumerably infinite set of magnetic fields. Here we demonstrate that as a function of magnetic field a band-like structure of energy associated with the exact pair states exists. A direct and simple connection between the pair states and the quantum Hall effect is revealed by the band-like structure of the hydrogen “pseudo-atom”. From such a connection one can predict the sites and widths of the integral and fractional quantum Hall plateaus for an electron gas in a GaAs-Al _x Ga_1−x As heterojunction. The results are in good agreement with the existing experimental data.     

Frequency and density dependent radiative recombination processes in III–V semiconductor quantum wells and superlattices

In this paper we review the radiative recombination processes occurring in semiconductor quantum wells and superlattices under different excitation conditions. We consider processes whose radiative efficiency depends on the photogenerated density of elementary excitations and on the frequency of the exciting field, including luminescence induced by multiphoton absorption, exciton and biexciton radiative decay, luminescence arising from inelastic excitonic scattering, and electron-hole plasma recombination.

Semiconductor quantum wells are ideal systems for the investigation of radiative recombination processes at different carrier densities owing to the peculiar wavefunction confinement which enhances the optical non-linearities and the bistable behaviour of the crystal. Radiative recombination processes induced by multi-photon absorption processes can be studied by exciting the crystal in the transparency region under an intense photon flux. The application of this non-linear spectroscopy gives direct access to the excited excitonic states in the quantum wells owing to the symmetry properties and the selection rules for artificially layered semiconductor heterostructures.

Different radiative recombination processes can be selectively tuned at exciting photon energies resonant with real states or in the continuum of the conduction band depending on the actual density of photogenerated carriers. We define three density regimes in which different quasi-particles are responsible for the dominant radiative recombination mechanisms of the crystal: (i) The dilute boson gas regime, in which exciton density is lower than 10¹⁰ cm^-2. Under this condition the decay of free and bound excitons is the main radiative recombination channel in the crystal. (ii) The intermediate density range (n < 10¹¹ cm^-2) at which excitonic molecules (biexcitons) and inelastic excitonic scattering processes contribute with additional decay mechanisms to the characteristic luminescence spectra. (iii) The high density range (n ?10¹² cm^-2) where screening of the Coulomb interaction leads to exciton ionization. The optical transitions hence originate from the radiative decay of free-carriers in a dense electron-hole plasma.

The fundamental theoretical and experimental aspects of the radiative recombination processes are discussed with special attention to the GaAs/Al _x Ga_1-x As and Ga _x In_1-x As/Al _y In_1-y As materials systems. The experimental investigations of these effects are performed in the limit of intense exciting fields by tuning the density of photogenerated quasi-particles and the frequency of the exciting photons. Under these conditions the optical response of the quantum well strongly deviates from the well-known linear excitonic behaviour. The optical properties of the crystal are then no longer controlled by the transverse dielectric constant or by the first-order dielectric susceptibility. They are strongly affected by many-body interactions between the different species of photogenerated quasi-particles, resulting in dramatic changes of the emission properties of the semiconductor.

The systematic investigation of these radiative recombination processes allows us to selectively monitor the many-body induced changes in the linear and non-linear optical transitions involving quantized states of the quantum wells. The importance of these effects, belonging to the physics of highly excited semiconductors, lies in the possibility of achieving population inversion of states associated with different radiative recombination channels and strong optical non-linearities causing laser action and bistable behaviour of two-dimensional heterostructures, respectively.     

Disorder and the fractional quantum Hall effect

The fractional quantum Hall effect is studied in the 2D electron gas of four GaAs-Al_xGa_1?xAs heterostructures. Localization due to disorder, known to give rise to the wide integral quantum Hall plateaus, is demonstrated to inhibit the fractional effect, which is observed only in the higher mobility samples.     

Ultra-low temperature study of the even-denominator FQHE state

We present experimental data showing unambiguously an even-denominator fractional quantum Hall effect (FQHE) state at . At a bath temperature T_b=8 mK, we observe a Hall plateau quantized to a value of 2h/5e² with an uncertainty smaller than 2 parts in 10⁶ and a vanishing R_xx (R_xx=1.7±1.7 Ω). The thermal activation energy gaps Δ at Landau level filling factors , and are 0.11, 0.10, and 0.055 K, respectively. Adding a disorder broadening (typically 2 K) to these values, we deduce that all three FQHE states have probably very similar energy gaps. The electron heating experiment shows that the 2D electrons are efficiently cooled to the bath temperature for T_b8 mK. We also explore the density dependence of the activation gap at . Preliminary results at T_b25 mK show that the state is very sensitive to disorder.     

Energy gaps for fractional quantum Hall states described by a Chern-Simons composite fermion wavefunction

The Jain's composite fermion wavefunction has proven quite succesful to describe most of the fractional quantum Hall states. Its mathematical foundation lies in the Chern-Simons field theory for the electrons in the lowest Landau level, despite the fact that such wavefunction is different from a typical mean-field level Chern-Simons wavefunction. It is known that the energy excitation gaps for fractional Hall states described by Jain's composite fermion wavefunction cannot be calculated analytically. We note that analytic results for the energy excitation gaps of fractional Hall states described by a fermion Chern-Simons wavefunction are readily obtained by using a technique originating from nuclear matter studies. By adopting this technique to the fractional quantum Hall effect we obtained analytical results for the excitation energy gaps of all fractional Hall states described by a Chern-Simons wavefunction. Received 9 March 2001     

Spin polarization dependent optical transition rates observed in the integer quantum Hall region

We report on a field-dependent photoluminescence (PL) emission rate for the transitions between band states in modulation-doped CdTe/Cd_1−xMg_xTe single quantum wells in the integer quantum Hall region. The recombination time observed for the magneto-PL spectra varies in concomitance with the integer quantum Hall plateaus. Furthermore, different PL decay times were observed for the two circular polarizations, i.e. for the transitions between the Zeeman split subbands of the Landau levels. We analyzed the data in comparison with the experimentally determined spin polarization of the conduction electrons and the Zeeman splitting of the valence band. Furthermore, we discuss the relevance of the spin polarization of the conduction electrons, the electron–hole exchange interaction and the spin-flip processes of the hole states for the PL decay time.     

Time-resolved spectroscopy of soantaneous luminescence of CdSSe1−x quantum dots

Picosecond time-resolved spectroscopy of the edge luminescence band of CdS _x Se_1–x quantum dots with crystallite diameters as small as a few nanometers under band-to-band excitation reveals strong enhancement of the radiative recombination rate compared to bulk CdS owing to quantum confinement. The splitting of the luminescence band into two lines originates from near-band-gap absorption. Analysis of the temperature as well as the spectral dependence of the decay time (leading to a red shift of the luminescence with increasing time) and of the total-light-decay law result in a new model for the dominant radiative recombination channel: donor-acceptor pair recombination instead of an excitonic mechanism as claimed in previous publications.Dedicated to H.-J. Queisser on the occasion of his 60th birthday     

Kinetics of indirect photoluminescence in GaAs/AlxGa1−x As double quantum wells in a random potential with a large amplitude

The kinetics of indirect photoluminescence of GaAs/Al_xGa_1−x As double quantum wells, characterized by a random potential with a large amplitude (the linewidth of the indirect photoluminescence is comparable to the binding energy of an indirect exciton) in magnetic fields B≤12 T at low temperatures T≥1.3 K is investigated. It is found that the indirect-recombination time increases with the magnetic field and decreases with increasing temperature. It is shown that the kinetics of indirect photoluminescence corresponds to single-exciton recombination in the presence of a random potential in the plane of the double quantum wells. The variation of the nonradiative recombination time is discussed in terms of the variation of the transport of indirect excitons to nonradiative recombination centers, and the variation of the radiative recombination time is discussed in terms of the variation of the population of optically active excitonic states and the localization radius of indirect excitons. The photoluminescence kinetics of indirect excitons, which is observed in the studied GaAs/Al_xGa_1−x As double quantum wells for which the random potential has a large amplitude, is qualitatively different from the photoluminescence kinetics of indirect excitons in AlAs/GaAs wells and GaAs/Al_xGa_1−x As double quantum wells with a random potential having a small amplitude. The temporal evolution of the photoluminescence spectra in the direct and indirect regimes is studied. It is shown that the evolution of the photoluminescence spectra corresponds to excitonic recombination in a random potential. Zh. éksp. Teor. Fiz. 115, 1890–1905 (May 1999)     

Properties of excitons in a wide CdTe-based quantum well with irregular insertions of a fractional monolayer of ZnTe

The irregular short period CdTe/ZnTe superlattice structure is investigated by both stationary and time-resolved optical spectroscopy with and without an external magnetic field as a perturbation. This study is aimed to emphasize the properties of radiative excitonic recombination in a superlattice of this type in comparison with the excitons confined in a single QW structure. The decay time of the excitons is about 400 ps which is deduced from the time-resolved measurements. Theg-factors of electrons and holes are obtained by the spin quantum beat measurements combined with Zeeman measurements. The experimental results show that theg-factors of holes in the irregular short period CdTe/ZnTe superlattice become dramatically different in comparison with the single CdTe/CdMgTe quantum wells.     

Integer and fractional quantum Hall effect in a strip of stripes

We study anisotropic stripe models of interacting electrons in the presence of magnetic fields in the quantum Hall regime with integer and fractional filling factors. The model consists of an infinite strip of finite width that contains periodically arranged stripes (forming supercells) to which the electrons are confined and between which they can hop with associated magnetic phases. The interacting electron system within the one-dimensional stripes are described by Luttinger liquids and shown to give rise to charge and spin density waves that lead to periodic structures within the stripe with a reciprocal wavevector 8k _F in a mean field approximation. This wavevector gives rise to Umklapp scattering and resonant scattering that results in gaps and chiral edge states at all known integer and fractional filling factors ν. The integer and odd denominator filling factors arise for a uniform distribution of stripes, whereas the even denominator filling factors arise for a non-uniform stripe distribution. We focus on the ground state of the system, and identify the quantum Hall regime via the quantized Hall conductance. For this we calculate the Hall conductance via the Streda formula and show that it is given by σ _H = νe ²/h for all filling factors. In addition, we show that the composite fermion picture follows directly from the condition of the resonant Umklapp scattering.     

Transport studies of Kondo behavior,ferromagnetic and antiferromagnetic order in U1−xThxSb

We report electrical resistivity, Hall effect and magnetization measurements in the system U_1?xTh_xSb for magnetic fields up to 100 kOe. In U_0.14Th_0.86Sb a Kondo-like behavior of the resistivity is detected and the interaction J_df between the conduction d electrons and the uranium f electrons is found to be about ?0.2 eV. The dilution of USb by ThSb leads to large modifications of the electrical transport properties, reflecting the change from antiferromagnetism to ferromagnetism and simultaneously a decrease of the ordered magnetic moment per uranium atom occurs. A simple model is presented which accounts for this decrease assuming that all the conduction electrons added by thorium are polarized antiparallel to the remaining uranium f electrons due to the negative J_df. The Kondo temperature is used to estimate the band width and the binding energy of the 5f state.     

Electronic topological transition in an <Emphasis Type="Italic">n</Emphasis>-BiSb semiconductor alloy in the quantum limit range of magnetic fields for H‖<Emphasis Type="Italic">C</Emphasis><Subscript>2</Subscript>

The galvanomagnetic properties of single-crystal samples of the Bi_0.93Sb_0.07 semiconductor alloy with the electron density n = 1.6 × 10¹⁷ cm⁻³ in magnetic fields up to 14 T at T = 1.6 K have been investigated. The resistivity ρ and Hall coefficient R have been measured as functions of the magnetic field directed along the binary axis of a crystal for a current flowing through a sample along the bisector axis; i.e., the components ρ₂₂ and R _{32, 1} have been measured. The strong anisotropy of the electron spectrum of the samples makes it possible to separately observe quantum oscillations of the magnetoresistance ρ₂₂(H) for H ‖ C ₂ in low magnetic fields for two equivalent ellipsoids with small extremal cross sections (secondary ellipsoids) and in high magnetic fields for electrons of the ellipsoid with a large extremal cross section (main ellipsoid). An increase in the energy of the electrons of secondary ellipsoids in the quantum limit magnetic fields is accompanied by the flow of electrons to the main ellipsoid; i.e., an electronic topological transition occurs from the three-valley electron spectrum to the single-valley one. After the flow stops, the Fermi energy E _F increases from 18 meV to 27.8 meV. With an increase in the quantizing magnetic field, the Fermi energy of the electrons decreases both in the region of quantum oscillations of the resistance that are attributed to the electrons of the secondary ellipsoids and in the region of oscillations associated with the electrons of the main ellipsoid. The Hall coefficient R _{32, 1} decreases in high magnetic fields; this behavior indicates the absence of the electron magnetic freezing effect.     

Classical and quantum hall effect measurements in GaInNAs/GaAs quantum wells

We have performed magneto-transport experiments in modulation-doped Ga_0.7In_0.3N_yAs_1−y/GaAs quantum wells with nitrogen mole fractions 0.4%, 1.0% and 1.5%. Classical magnetotransport (resistivity and low-field Hall effect) measurements have been performed in the temperatures between 1.8 and 275 K, while quantum Hall effect measurements in the temperatures between 1.8 and 47 K and magnetic fields up to 11 T.The variations of Hall mobility and Hall carrier density with nitrogen mole fractions and temperature have been obtained from the classical magnetotransport measurements. The results are used to investigate the scattering mechanisms of electrons in the modulation-doped Ga_0.7In_0.3N_yAs_1−y/GaAs quantum wells. It is shown that the alloy disorder scattering is the major scattering mechanism at investigated temperatures.The quantum oscillations in Hall resistance have been used to determine the carrier density, effective mass, transport mobility, quantum mobility and Fermi energy of two-dimensional (2D) electrons in the modulation-doped Ga_0.7In_0.3N_yAs_1−y/GaAs quantum wells. The carrier density, in-plane effective mass and Fermi energy of the 2D electrons increases when the nitrogen mole fraction is increased from y=0.004 to 0.015. The results found for these parameters are in good agreement with those determined from the Shubnikov-de Haas effect in magnetoresistance.     

Two-dimensional electron gas in double quantum wells with tilted bands

When a voltage is applied to double quantum wells based on AlGaAs/GaAs heterostructures with contact regions (n-i-n structures), a two-dimensional (2D) electron gas appears in one of the quantum wells. Under illumination which generates electron-hole pairs, the photoexcited holes become localized in a neighboring quantum well and recombine radiatively with the 2D electrons (tunneling recombination through the barrier). The appearance, ground-state energy, and density of the degenerate 2D electron gas are determined from the structure of the Landau levels in the luminescence and luminescence excitation spectra as well as from the oscillations of the radiative recombination intensity in a magnetic field with detection directly at the Fermi level. The electron density is regulated by the voltage between the contact regions and increases with the slope of the bands. For a fixed slope of the bands the 2D-electron density has an upper limit determined by the resonance tunneling of electrons into a neighboring quantum well and subsequent direct recombination with photoexcited holes. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 11, 840–845 (10 June 1997)     

Optical and electrical properties of modulation-doped n and p-type Ga x In1-x N y As1-y /GaAs quantum wells for 1.3 μm laser applications

We present a comprehensive study of spectral photoluminescence (PL), photoconductivity and Hall mobility in undoped, n and p-type modulation-doped quantum wells of Ga_1-x In _x N _y As_1-y /GaAs with varying nitrogen concentration. We show that the increasing nitrogen composition red shifts the energy gap and this red shift is accompanied with a reduction of the 2D electron mobility in the quantum wells. True temperature dependence of the band gap, free from errors associated with nitrogen induced exciton trapping effects, is observed because in the modulation doped QW samples PL emission is dominated by band-to-band recombination and the S-shape temperature dependence is eliminated. Excellent fit to semi-experimental Varshni equation is obtained and the temperature dependence of the band gap in the linear regime (dE/dT) is tabulated as a function of nitrogen concentration and the type of dopant.     

Quantum corrections to the conductivity of a natural Nd<Subscript>2−<Emphasis Type="Italic">x</Emphasis></Subscript> Ce<Subscript>x</Subscript>CuO<Subscript>4</Subscript> superlattice

Temperature and magnetic field dependences of the resistivity and Hall coefficient in layered single-crystal Nd_2?xCe_xCuO₄ (x = 0.12) films are experimentally investigated and analyzed. It is shown that this material clearly exhibits quantum effects characteristic of 2D semiconductor structures: negative magnetoresistance caused by suppression of the interference quantum correction by a magnetic field, a near-logarithmic temperature dependence of the conductivity, and a temperature dependence of the Hall coefficient related to e-e interaction. It is shown that, when analyzing experimental data, it is necessary to take interlayer transitions into account. Such an approach provides quantitative agreement between experiment and the standard theory of quantum corrections.     

The lattices with the continuous vorticity as a model for fractional quantum hall effect

It was shown that the including spin of 2d electrons at high magnetic field is possible to remove the divergences in the cores of the vortex lattice and construct the topologically stable states. These states can be considered as the lattices of skyrmions where the unit cell is mapped on the whole sphere of spin directions. That gives the gapped ground state for electrons and can be used as a model for fractional quantum Hall effect.     

Spatial evolution of the generation and relaxation of excited carriers near the breakdown of the quantum Hall effect

We have measured the generation and relaxation of excited carriers along their drift direction near the breakdown of the quantum Hall effect (QHE). The dissipative resistivity ρ_xx(x) at current densities close to the critical value for the QHE breakdown was measured as a function of the distance x from the electron injection at x=0. By injecting “cold” electrons into constrictions at supercritical current levels, the evolution of the breakdown along the drift direction was monitored. After a smooth increase of the resistivity with the drifting distance, an avalanche-like rise towards a saturation value occurs. Drastic changes of the resistivity profiles with the applied current were found in a narrow range around the critical current. The observed behavior is attributed to impurity-assisted tunneling between Landau levels. By injecting hot electrons (excited in a periodic set of constrictions) into a region with subcritical current density, the relaxation process was analyzed. Inelastic relaxation lengths with typical values in the range from 0.3 to 4 μm were found, which agree within 10% with the elastic mean free path determined from the Hall mobility at zero magnetic field. We conclude that the energy relaxation process is triggered by scattering at impurity potentials.     

Fractional quantum Hall States of Dirac electrons in graphene

We have investigated the fractional quantum Hall states of Dirac electrons in a graphene layer in different Landau levels. The relativistic nature of the energy dispersion relation of electrons in graphene significantly modifies the interelectron interactions. This results in a specific dependence of the ground state energy and the energy gaps for electrons on the Landau-level index. For the valley-polarized states, i.e., at nu=1/m, m being an odd integer, the energy gaps have the largest values in the n=1 Landau level. For the valley-unpolarized states, e.g., for the 2/3 state, the energy gaps are suppressed for n=1 as compared to those at n=0. For both n=1 and n=0, the ground state of the 2/3 system is fully valley-unpolarized.