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.     

Spin-dependent resistivity and quantum Hall ferromagnetism in two-dimensional electrons confined to AlAs quantum wells

We observe a strong dependence of the amplitude and field position of longitudinal resistivity (ρ_xx) peaks in the spin-resolved integer quantum Hall regime on the spin orientation of the Landau level (LL) in which the Fermi energy resides. The amplitude of a given peak is maximal when the partially filled LL has the same spin as the lowest LL, and amplitude changes as large as an order of magnitude are observed as the sample is tilted in field. In addition, the field position of both the ρ_xx peaks and plateau–plateau transitions in the Hall resistance shift depending on the spin orientation of the LLs. The spin dependence of the resistivity points to a new explanation for resistivity spikes, associated with first-order quantum Hall ferromagnetic transitions, that occur at the edges of quantum Hall states.     

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.     

Landau-level interplay in InGaAs double quantum wells

Shubnikov–de Haas (SdH) and Hall measurements have been used to investigate a pair of adjacent two-dimensional electron gases (2DEGs) which were formed in two n_0.53Ga_0.47As quantum-wells, separated by a thin In_0.52Al_0.48As barrier, grown lattice-matched on InP. This double quantum-well system consists of two asymmetric InGaAs quantum wells, 9 nm and 7 nm respectively, separated by a 4.5 nm InAlAs barrier. The existence of two occupied electronic subbands with differing electron densities can clearly be identified by beating effects in the SdH oscillations. By applying a substrate bias the electron densities can be tuned and the beating is shifted. In the simultaneously performed Hall measurements additional features can be observed: Hall measurements with different total electron densities reveal plateaus for integer filling factors ν (with ν = ν₁ + ν₂, ν₁and ν₂both integers, corresponding to the two subbands). Some even filling factors become suppressed and recover with changing electron density. Also, for some densities an odd filling factor is observed. The systematic tuning of the electron densities via the application of a bias voltage to the front gate reveals two Landau fans, one for each electronic system, respectively, crossing each other. The electron densities for both electronic systems can be identified by analysing the SdH spectra. As a function of the front-gate voltage, these densities seem to show evidence for an anticrossing of the two electronic states and therefore for a strong coupling between the states.     

Scaling in the quantum Hall effect regime in n-InGaAs/GaAs nanostructures

The longitudinal ρ _xx (B) and Hall ρ _xy (B) magnetoresistances are investigated experimentally in the integer quantum Hall effect (QHE) regime in n-InGaAs/GaAs double quantum well nanostructures in the range of magnetic fields B = (0–16) T and temperatures T = (0.05–70) K before and after IR illumination. The results are evaluated within the scaling hypothesis with regard to electron-electron interaction.     

Sunlight assisted photodegradation by tin oxide quantum dots

Rutile phase of SnO₂ quantum dots of average size of 2.5 nm were synthesized at a growth temperature of 70 °C and characterized with XRD, TEM, FTIR and Raman analysis. The effective strain within the lattice of SnO₂ quantum dots was calculated by Williamson–Hall method. The broad peaks in XRD as well as Raman spectra and the presence of Raman bands at 569 and 432 cm⁻¹ are due to lower crystallinity of nanoparticles. The optical band gap of SnO₂ quantum dots was increased to 3.75 eV attributed to the quantum size effect. SnO₂ quantum dots were annealed in air atmosphere and the crystallite size of the particles increased with annealing temperature. Sunlight assisted photodegration property of SnO₂ quantum dots was investigated with vanillin as a model system and it shows the photodegradation efficiency of 87%. The photoluminescence and photodegradation efficiency of nanocrystallite SnO₂ decreases with increase of crystallite size contributed to the reduction in population of defects and surface area.     

Breakdown of the quantum hall effect in regularly inhomogeneous 2D electron systems

A breakdown mechanism is discussed for the current-voltage characteristic of the system of integer Hall channels in a 2D sample with a regularly inhomogeneous 2D electron density. It has been shown that the appearance of an external potential V on the “edges” of such strips leads to two alternatives: as V increases, the strip width decreases to zero or increases geometrically but “deteriorates qualitatively.” In both cases with their (different) thresholds, integer strips lose their properties inherent in them in the quantum Hall effect regime. These thresholds are attributed here to the asymmetric breakdown of the quantum Hall effect for the system of integer channels.     

Universal scaling of plateau width in the quantum Hall effect

The plateau width in the quantum Hall effect follows a general scaling rule with ΔB/B₀² being a constant for all the filling factors of integer intervals. This scaling rule can be derived based on the energy spectrum of two-dimensional electrons forming a crystal lattice in the presence of a strong magnetic field.     

Inhomogeneous Hall-geometry sample in the quantum Hall regime

A generalization of the known theory describing the Hall channels with integer filling factors in inhomogeneous 2D electronic samples to the case of a stationary nonequilibrium state (with a nonzero Hall voltage V _H across the 2D system) is proposed. For the central strip located near the extremum of the electron density, the theory predicts a change in its width and a shift of the whole strip from the equilibrium position as functions of V _H . The theoretical results are used to interpret recent experiments on measuring the local electric fields along the Hall samples both in equilibrium conditions and in the presence of transport in the quantum Hall regime.     

Topological invariants for fractional quantum hall states

We calculate a topological invariant, whose value would coincide with the Chern number in the case of integer quantum Hall effect, for fractional quantum Hall states. In the case of Abelian fractional quantum Hall states, this invariant is shown to be equal to the trace of the K-matrix. In the case of non-Abelian fractional quantum Hall states, this invariant can be calculated on a case by case basis from the conformal field theory describing these states. This invariant can be used, for example, to distinguish between different fractional Hall states numerically even though, as a single number, it cannot uniquely label distinct states.     

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.     

Conductance fluctuations of chiral metals

We study conductance fluctuations of the edge-state sheath that forms in the integer quantum Hall effect from the coupled edge states of a GaAs/Al_xGa_1 − xAs multilayer. Comparison of the measured variance in the vertical conductance to recent theoretical predictions for mesoscopic fluctuations suggests dephasing lengths of 1–10 μm around the sheath perimeter at low temperatures. However, inconsistencies in the estimated inelastic lengths indicate that present understanding of dephasing on the sheath is incomplete.     

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.     

Role of electron spin in integer quantum hall photoluminescence

We investigate numerically the photoluminescence (PL) spectrum in the integer quantum Hall regime and find that the electron spins play important roles. The spectra for the left circularly polarized light show peak splittings when the Fermi levels lies in the excited Landau level, which is caused by the inter Landau level scattering between electrons with anti-parallel spins. At around ν_e∼1 the PL energy is strongly affected by the interplay between the screening and multiple spin flipping (skyrmion) effects.     

Universal explicit expression for quantum Hall conductance at any temperatures and chemical potentials

This paper generalises the theorem already obtained [Solid State Commun. 127 (2003) 505] for the high mobility, dissipationless, integer quantum Hall systems at T=0 K to the T>0 K situations. The results obtained are again suitable at both microscopic and macroscopic scales. In comparison [Solid State Commun. 127 (2003) 505], this generalised form gives a universal explicit expression for the Hall conductance σ_xy(μ,T) between any two points selected in such a system as a function of chemical potential and temperature. Further, thermal deviation Δσ_xy(μ,T) from the exact quantised values of σ_xy(μ,T) and the minimum slopes of Hall plateaux in the T>0 cases, observed already in experiments, are also derived in theory. Similar to those in the T=0 K case [Solid State Commun. 127 (2003) 505], the overall quantum Hall behaviour of the system can again be obtained from this theory by simply selecting two points on the two Hall contacts.     

Giant fluctuations of radiation intensity of two-dimensional electrons in double quantum wells

Giant fluctuations of the recombination-radiation intensity of two-dimensional electrons were studied in double quantum wells with different well and barrier widths in the regime of the integer quantum Hall effect. It was found that the giant fluctuations of photoluminescence intensity in double quantum wells with a narrow barrier (l<150 Å) occur in a narrow magnetic-field interval, where the sum of electron concentrations in both wells corresponds to the integer filling factors 4, 8, and 12. It was established that, under these conditions, the coefficient C₁₂ of correlation between the radiation intensities from different wells is close to unity. It is shown that, as the barrier width increases (l>200 Å), the coefficient C₁₂ decreases, changes sign, and goes to zero at l=400 Å.     

Excitations in a quantum Hall ferromagnet with strong Coulomb interaction

A quantum Hall ferromagnet is considered at integer fillings ν, provided typical Coulomb interaction energy E _c is large compared to the cyclotron energy ω_H. Low-energy collective modes consist of a magnetoplasmon exciton and a gapless spin exciton. All charged excitations have a gap. The activation energy gap for a pair of charged topological excitations—skyrmion and antiskyrmion—is small, i.e., Δ< vω_H. The electric charge of a skyrmion is the multiple q=eνQ, where Q is the integer topological charge.     

Studies of the quantum Hall to quantum Hall insulator transition in InSb-based 2DESs

The temperature dependence of ρ_xx is studied in the vicinity of the quantum Hall to quantum Hall insulator transition (ν=1→0) in InSb/InAlSb based 2DESs. ρ_xx displays a symmetric temperature dependence about the transition with on the QH side and on the insulating side. A plot of 1/T₀ for successive ν displays power-law divergence with 1/T₀∝|ν−ν_c|^−γ,² with γ=2.2±0.3. This critical behavior in addition to the behavior expected of the quantum transport regime confirms that the QH/QHI transition is indeed a good quantum phase transition.     

On the structure of strips exhibiting the integral quantum Hall effect in an inhomogeneous 2D electron system

A formalism is developed to generalize the results obtained for “incompressible” strips exhibiting the integral quantum Hall effect in a spatially inhomogeneous 2D electron system to the cases of finite temperatures, significant electron density gradients, etc. Specifically, the concept of the “quality” of a given integer quantum Hall effect strip (channel) is introduced; the quality is proportional to the derivative dn(x)/dx in the central part of the channel [n(x) is the electron density distribution over the channel]. For a well-defined channel, this derivative tends to zero. If a noticeable gradient arises in the n(x) distribution, the channel does not exhibit the quantum Hall effect and ceases to exist. The conditions are determined under which a channel exhibiting the integral quantum Hall effect breaks down. The results of calculations are used to interpret the available experimental data.