Exact results for systems of electrons in the fractional quantum Hall regime

There has been a great deal of interest over the last two decades on the fractional quantum Hall effect, a novel quantum many-body liquid state of strongly correlated two-dimensional electronic systems in a strong perpendicular magnetic field. The most pronounced fractional quantum Hall states occur at odd denominator filling factors of the lowest Landau level and are described by the Laughlin wave function. It is well known that exact closed-form solutions for many-body wave functions, including the Laughlin wave function, are generally very rare and hard to obtain. In this work we present some exact results corresponding to small systems of electrons in the fractional quantum Hall regime at odd denominator filling factors. Use of Jacobi coordinates is the key tool that facilitates the exact calculation of various quantities. Expressions involving integrals over many variables are considerably simplified with the help of Jacobi coordinates allowing us to calculate exactly various quantities corresponding to systems with several electrons.     

Exact results for systems of electrons in the fractional quantum Hall regime II

In a previous work [O. Ciftja, Physica B 404 (2009) 227] we reported the exact calculation of energies for the fractional quantum Hall Laughlin state at filling factor for systems with up to N=4 electrons in a disk geometry. The purpose of this brief extension of the earlier work is to report similar exact results for the other Laughlin state at filling factor . We use the same method of orthogonal Jacobi variables adopted in the earlier work.     

Inelastic light scattering by collective excitations in the fractional quantum Hall regime

We report an inelastic light scattering study of long wavelength collective gap excitations of fractional quantum Hall (FQH) states at ν=p/(2p+1) for . The ν-dependence of the gap energy suggests a collapse of the collective excitation gap near . In a range of filling factors close to , where the FQH gap is believed to collapse, we observe a collective excitation mode that exists only at temperatures below 150 mK.     

Light scattering observations of spin reversal excitations in the fractional quantum Hall regime

Resonant inelastic light scattering experiments access the low lying excitations of electron liquids in the fractional quantum Hall regime in the range 2/5≥ν≥1/3. Modes associated with changes in the charge and spin degrees of freedom are measured. Spectra of spin reversed excitations at filling factor ν?1/3 and at ν?2/5 identify a structure of lowest spin-split Landau levels of composite fermions (CFs) that is similar to that of electrons. Observations of spin wave excitations enable determinations of energies required to reverse spin. The spin reversal energies obtained from the spectra illustrate the significant residual interactions of composite fermions. At ν=1/3 energies of spin reversal modes are larger but relatively close to spin conserving excitations that are linked to activated transport. Predictions of composite fermion theory are in good quantitative agreement with experimental results.     

Interedge strong-to-weak scattering evolution at a constriction in the fractional quantum Hall regime

Gate-voltage control of interedge tunneling at a split-gate constriction in the fractional quantum Hall regime is reported. Quantitative agreement with the behavior predicted for out-of-equilibrium quasiparticle transport between chiral Luttinger liquids is shown at low temperatures at specific values of the backscattering strength. When the latter is lowered by changing the gate voltage, the zero-bias peak of the tunneling conductance evolves into a minimum, and a nonlinear quasiholelike characteristic emerges. Our analysis emphasizes the role of the local filling factor in the split-gate constriction region.     

Resonant rayleigh scattering from bilayer quantum Hall phases

We observe resonant Rayleigh scattering of light from quantum Hall bilayers at Landau level filling factor nu = 1. The effect arises below 1 Kelvin when electrons are in the incompressible quantum Hall phase with strong interlayer correlations. Marked changes in the Rayleigh scattering signal in response to application of an in-plane magnetic field indicate that the unexpected temperature dependence is linked to formation of a nonuniform electron fluid close to the phase transition towards the compressible state. These results demonstrate a new realm of study in which resonant Rayleigh scattering methods probe quantum phases of electrons in semiconductor heterostructures.     

Resonant enhancement of inelastic light scattering in the fractional quantum Hall regime at ν=1/3

Strong resonant enhancements of inelastic light scattering from the long wavelength inter-Landau level magnetoplasmon and the intra-Landau level spin wave excitations are seen for the fractional quantum Hall state at ν=1/3. The energies of the sharp peaks (FWHM 0.2 meV) in the profiles of resonant enhancement of inelastic light scattering intensities coincide with the energies of photoluminescence bands assigned to negatively charged exciton recombination. To interpret the observed enhancement profiles, we propose three-step light scattering mechanisms in which the intermediate resonant transitions are to states with charged excitonic excitations.     

Resonant tunneling into a biased fractional quantum Hall edge

We observe resonant tunneling into a voltage biased fractional quantum Hall effect (FQHE) edge, using atomically sharp tunnel barriers unique to cleaved-edge overgrown devices. The resonances demonstrate different tunnel couplings to the metallic lead and the FQHE edge. Weak coupling to the FQHE edge produces clear non-Fermi liquid behavior with a sixfold increase in resonance area under bias arising from the power law density of states at the FQHE edge. A simple device model uses the resonant tunneling formalism for chiral Luttinger liquids to successfully describe the data.     

Energy relaxation of two-dimensional electrons in the quantum Hall effect regime

The mm-wave spectroscopy with high temporal resolution is used to measure the energy relaxation times τ_e of 2D electrons in GaAs/AlGaAs heterostructures in magnetic fields B=0–4 T under quasi-equilibrium conditions at T=4.2 K. With increasing B, a considerable increase in τe from 0.9 to 25 ns is observed. For high B and low values of the filling factor ν, the energy relaxation rate τ _e ^?1 oscillates. The depth of these oscillations and the positions of maxima depend on the filling factor ν. For ν>5, the relaxation rate τ _e ^?1 is maximum when the Fermi level lies in the region of the localized states between the Landau levels. For lower values of ν, the relaxation rate is maximum at half-integer values of τ _e ^?1 when the Fermi level is coincident with the Landau level. The characteristic features of the dependence τ _e ^?1 (B) are explained by different contributions of the intralevel and interlevel electron-phonon transitions to the process of the energy relaxation of 2D electrons.     

Ising ferromagnetism and domain morphology in the fractional quantum Hall regime

The density driven quantum phase transition between the unpolarized and fully spin polarized nu = 2/3 fractional quantum Hall state is accompanied by hysteresis in accord with 2D Ising ferromagnetism and domain formation. The temporal behavior is reminiscent of the Barkhausen and time-logarithmic magnetic after-effects ubiquitous in familiar ferromagnets. It too suggests domain morphology and, in conjunction with NMR, intricate domain dynamics, which is partly mediated by the contact hyperfine interaction with nuclear spins of the host semiconductor.     

Thermally activated dissipative conductivity in the fractional quantum Hall effect regime

Experimental investigations of thermally activated dissipative conductivity σ_xx in the fractional quantum Hall effect at filling factors v=1/3 and near zero were performed with GaAs/AlGaAs heterojunction based field-effect transistors with an electronic channel. To within our accuracy of 10%, the pre-exponential factor measured for v=1/3 is equal to 2e*2/h (e*=e/3 is the charge of the quasiparticles), the value expected for the case when the quasielectrons and quasiholes make the same contribution to the conductivity. The observed change in the temperature dependence of the conductivity when n deviates from 1/3 is associated with the change in the filling of the energy levels of the quasielectrons and quasiholes and indicates that there is no gap in the quasiparticle density of states averaged over the sample. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 1, 67–72 (10 January 1996)     

Resonant Raman scattering from CdTe/ZnTe self-assembled quantum dot structures

We report resonant Raman scattering results of CdTe/ZnTe self-assembled quantum dot (QD) structures. Photoluminescence spectra reveal that the band gap energies of the CdTe QDs decrease with the increase of CdTe thickness from 2.0 to 3.5 monolayers, which indicates that the size of the QDs increases. When the CdTe/ZnTe QD structures are excited by non-resonant excitation, a longitudinal optical (LO) phonon response from the ZnTe barrier material is observed at 206 cm⁻¹. In contrast, when the CdTe/ZnTe QD structures are resonantly excited near the band gap energy of the QDs, additional phonon modes emerge at 167 and 200 cm⁻¹, while the ZnTe LO phonon response completely disappears. The 167 cm⁻¹ mode corresponds to the LO phonon of the CdTe QDs. A spatially resolved Raman scattering from the cleaved edge of the QD sample reveals that the 200 cm⁻¹ mode is strongly localized at the interface between the CdTe QDs and ZnTe cap layer. This phonon mode is attributed to the interface optical (IO) phonon. The analytically calculated value of the IO phonon energy using a dielectric continuum approach, assuming a spherical dot boundary, agrees well with the experimental value.