Fractional Quantum Hall Effect Regime Research Articles

Electrical and thermal transport of composite fermions

The resistivity and the diffusion thermopower are calculated for a two-dimensional electron and hole gas at low temperatures in the fractional quantum Hall effect regime. The composite fermions picture enables us to use the integer quantum Hall effect and Shubnikov--de Haas conductivity models for a quantitative comparison with experiment. Satisfactory agreement with experiments on electron and hole gases is obtained.

Aharonov-Bohm effect in the chiral Luttinger liquid

Edge states of the quantum Hall fluid provide an almost unparalled opportunity to study mesoscopic effects in a highly correlated electron system. In this paper we develop a bosonization formalism for the finite-size edge state, as described by chiral Luttinger liquid theory, and use it to study the Aharonov-Bohm effect. The problem we address may be realized experimentally by measuring the tunneling current between two edge states through a third edge state formed around an antidot in the fractional quantum Hall effect regime. A renormalization group analysis reveals the existence of a two-parameter universal scaling function G(X,Y) that describes the Aharonov-Bohm resonances. We also show that the strong renormalization of the tunneling amplitudes that couple the antidot to the incident edge states, together with the nature of the Aharonov-Bohm interference process in a chiral system, prevent the occurrence of perfect resonances as the magnetic field is varied, even at zero temperature.

Mesoscopic effects in the fractional quantum Hall regime

Edge states of the quantum Hall fluid provide an opportunity to study mesoscopic effects in a highly correlated electron system that is both experimentally accessible and theoretically tractable. In this paper we review recent work on the persistent current and Aharonov-Bohm magnetoconductance oscillations in the fractional quantum Hall effect regime.

Thermally activated dissipative conductivity in the fractional quantum Hall effect regime

Experimental investigations of thermally activated dissipative conductivity σxx 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.

Evidence for Charge-Flux Duality near the Quantum Hall Liquid-to-Insulator Transition

A remarkable symmetry has been observed between the diagonal, nonlinear, current-voltage ( I-V xx ) characteristics taken in the fractional quantum Hall effect (FQHE) liquid state of the two-dimensional electron system and those taken in the bordering insulating phase. When properly selected, the I-V xx traces in the FQHE regime are identical, within experimental errors, to V xx -I traces in the insulator, that is, with the roles of the currents and voltages exchanged. These results can be interpreted as evidence for the existence of charge-flux duality symmetry in the system.

Determination of the transport properties of composite fermions under high hydrostatic pressure

We describe a series of low temperature magneto-transport measurements on two high mobility, low carrier density, GaAs/AlGaAs heterojunctions under conditions of reduced Landé spin g-factor. The magnitude of the effective Landé spin g-factor was reduced with the application of hydrostatic pressure and under these experimental conditions we demonstrate the existence of unpolarised spin states of composite fermions in the fractional quantum Hall effect regime down to filling factors v ~ 1 5 . The activation energies of states at filling factors, v = 2 3 and 2 5 in the lowest composite fermion hierarchy show a variation with effective Landé g-factor that is consistent with a spin unpolarised ground state at these filling factors in the dilute electron system. However, this is less clear in a moderate carrier density system, with concentrations > 1 × 10 11 cm −2. We also show that under conditions of reduced effective Landé g-factor and varying levels of disorder, structure in ϱ xx absent at ambient pressure develops at even filling factor fractions corresponding to metallic states predicted within the composite fermion model. The variation of disorder with hydrostatic pressure in the fractional quantum Hall effect is discussed with respect to the underlying electronic scattering mechanisms.

Experimental determination of the transport properties of composite fermions with reduced Lande g-factor

We demonstrate experimentally the existence of unpolarized spin states of composite fermions in the fractional quantum Hall effect regime. The modulus of the effective Lande g-factor was reduced using hydrostatic pressure and the transport properties of the first and second hierarchy of composite fermion states were studied in an AlGaAs/GaAs heterojunction in perpendicular magnetic fields. The activation energy of states at filling factor, nu =2/3 and 2/5 show a variation with effective Lande g-factor that is consistent with a spin-unpolarized ground state at these filling factors. The rapid destruction of the energy gap in the first composite fermion hierarchy at nu =2/5 follows the pressure dependence of the effective Lande g-factor of free electrons in GaAs. We show that structure in sigma xx, initially absent at ambient pressure, develops at even filling factor fractions corresponding to metallic states at nu =3/8 and nu =5/12 under reduced Lande g-factor conditions. Consistent behaviour is observed independent of the carrier density in the dilute electron system at 4.4*1010 and 6.8*1010 cm-2.

Anyonic ions, energy bands, and photoluminescence of fractional quantum Hall systems.

A two-dimensional electron liquid interacting with free or localized valence-band holes located a distance d away from the electron layer is studied by exactly diagonalizing the Hamiltonian of a finite-size system. For a coplanar electron-hole system, our calculation does not show the usual sign of an imcompressible state or a fractional quantum Hall effect. For the case where the separation d is about 1.5 times the magnetic length, pronounced cusps are revealed in a plot of the ground-state energy versus the Landau-level degeneracy. Detailed analysis suggests that the ground state responsible for the cusps consists of anyonic ions (composed of Laughlin quasielectrons bound to a hole) weakly coupled to an incompressible fluid of the remaining electrons. The hypothesis of stable anyonic ions is further supported by the structure displayed in the photoluminescence (PL) spectrum. Three PL systems, namely, electron--free-hole (e-h), electron--localized-hole (e-${\mathit{A}}^{+}$), and electron--neutral-acceptor (e-${\mathit{A}}^{0}$), have been investigated as functions of separation d, filling factor ${\ensuremath{\nu}}_{\mathit{e}}$, and temperature T. Multipeaked spectra are obtained for all three systems; they can be understood in terms of quasielectron-hole recombination processes and the ``band structure'' of two-dimensional electrons in the fractional quantum Hall effect regime. The connections between the calculated spectrum and some recent experimental results are also discussed.

Nonlinear conductivity of a Wigner crystal in a strong magnetic field.

We investigate the sliding state of a two-dimensional Wigner crystal in a strong magnetic field in the presence of randomness and free carriers, using a high-velocity perturbation theory. We find that the Hall resistivity retains its classical value within the second order Born approximation, and that disorder induces predominantly transverse distortions. We calculate the interference effects that arise in combined ac+dc fields for the present system. We examine recent experiments that measure the nonlinear conductivity for the insulating phases in the fractional quantum Hall effect regime.

Experimental evidence for finite-width edge channels in integer and fractional quantum Hall effects.

We report our transport study of a narrow and low-density two-dimensional electron system (2DES) defined by a pair of split gates, in the integer (IQHE) and fractional quantum Hall effect (FQHE) regimes. The gate-bias-dependent breakdown on the high and low magnetic field side of the IQHE and FQHE diagonal resistance minima is studied. In the IQHE case, edge states of width comparable to the magnetic length, in the single-electron Landau-level picture, cannot explain the observed breakdown data and much wider edge channels (wide band of edge states) are needed. These wide edge channels are interpreted as the compressible regions when the 2DES near the sample boundary phase separates into compressible and incompressible regions. The same breakdown behavior is observed in the fractional quantum Hall state and is interpreted as a similar phase separation in the FQHE regime.

The role of accumulation layers in quantum dot arrays and quantum Hall effect devices

The two-dimensional electron gas in field-effect devices is influenced by an accumulation layer close to the 2DEG. It is populated when the chemical potential lies in a gap of the energy spectrum of the 2DEG and is required to assure overall electrical neutrality. The existence of an accumulation layer explains the far-infrared response of quantum dot arrays as well as optical measurements in the integer and fractional quantum Hall effect regime.

Single-electron tunneling in the fractional quantum Hall effect regime

A recent mean-field approach to the fractional quantum Hall effect (QHE) isreviewed, with a special emphasis on the application to single-electron tunneling through a quantum dot in a high magnetic field. The theory is based on the adiabatic principle of Greiter and Wilczek, which maps an incompressible state in the integer QHE on the fractional QHE. The single-particle contribution to the addition spectrum is analyzed, for a quantum dot with a parabolic confining potential. The spectrum is shown to be related to the Fock-Darwin spectrum in the integer QHE, upon substitution of the electron charge by the fractional quasiparticle charge.Implications for the periodicity of the Aharonov-Bohm oscillations in the conductance are discussed.

Wigner crystallization in the fractional quantum Hall regime: A variational quantum Monte Carlo study.

Using a variational quantum Monte Carlo method, we study the two-dimensional Wigner crystal induced by a strong magnetic field in the fractional quantum Hall effect regime. Effects of exchange, intra-Landau-level correlation, and inter-Landau-level mixing on the total energy and their dependence on the carrier mass and magnetic field strength are calculated. Our results support that the recently observed reentrant behavior to an insulating phase around \ensuremath{\nu}=1/3 in p-doped GaAs/AlGaAs is a consequence of an increased stability of the Wigner crystal due to the effects of Landau-level mixing.

Measurements and modeling of nonlocal resistance in the fractional quantum Hall effect.

Recently, we have reported the observation of nonlocal resistance in the regime of the fractional quantum Hall effect (FQHE) that clearly demonstrates edge-state conduction over macroscopic distances. In this paper we present measurements of nonlocal resistance with variations of sample geometry, magnetic-field direction, temperature, and applied current. From our results we formulate a picture of transport in the FQHE regime via coexisting edge and bulk states. Scattering of edge currents is largely suppressed over distances of \ensuremath{\sim}1 mm at low temperatures. Edge currents are partially redistributed into the bulk at Ohmic contacts on the sample periphery. This results in potential drops between Ohmic contacts far from the bulk-only current path, i.e., nonlocal resistances. For analysis of our data, we introduce a FQHE extension of the bulk-edge transport model successfully applied by Szafer et al. in the integer QHE regime. We discuss the current and temperature dependence of the data in terms of temperature-dependent scattering between edge and bulk currents, increasing with increasing current or temperature.

Microscopic theory of the fractional quantum Hall effect

Abstract This is a review of the composite fermion theory of the fractional quantum Hall effect (FQHE). This theory provides a microscopic description of the low energy states of the strongly correlated electrons in the FQHE regime in terms of weakly interacting composite fermions, where a composite fermion is an electron bound to an even number of vortices. In the simplest cases, the FQHE can be construed as a manifestation of the integer quantum Hall effect of the composite fermions. Based on these ideas, simple Jastrow-Slater trial wavefunctions are written for the incompressible FQHE states as well as their low energy excitations. Extensive numerical work has been performed to confirm their validity. In particular, these have essentially 100% overlap with the true Coulomb states for few particle systems. Various consequences of the theory are in excellent agreement with experiments. Notably, it provides a unified framework for the fractional and integer quantum Hall effects, consistent with the experimental fact that there is no qualitative distinction between the observation of various plateaus. Also, the prominent fractions are clearly identified and compare well with the experimentally observed fractions.

Optical spectroscopy in the fractional quantum hall effect and wigner solid regimes

Discontinuities have been observed in the spectral position of the magneto-luminescence from GaAs-Al χGa 1−χAs heterojunctions at fractional filling factors ( v) down to 1/9. Below a critical temperature and ( v) = 0.28 an additional luminescence line appears and the integrated intensity decreases drastically indicating formation of a Wigner solid.

Anomalous sound propagation at nu =1/2 in a 2D electron gas: Observation of a spontaneously broken translational symmetry?

Surface-acoustic-wave propagation on high-quality AlGaAs/GaAs heterostructures containing a two-dimensional electron system has been examined in the fractional quantum Hall effect (FQHE) regime. The response of the electron system to the sound wave is found to be similar in the FQHE states to that previously studied in the integral quantum Hall states. However, a striking disparity is observed at Landau-level filling \ensuremath{\nu}=1/2, where sound propagation is distinctly different from that in the neighboring filling-factor range. We propose that phase separation of the 2DEG may be responsible for the feature at \ensuremath{\nu}=1/2.

Magnetooptics of two-dimensional electrons in the integral and fractional quantum Hall effect regimes

Magnetooptics of two-dimensional electrons in the integral and fractional quantum Hall effect regimes

Магнитооптика двумерных электронов в условиях целочисленного и дробного квантового эффекта Холла

Магнитооптика двумерных электронов в условиях целочисленного и дробного квантового эффекта Холла

Collective-excitation gap in the fractional quantum Hall effect.

We present a theory of the collective excitation spectrum in the fractional quantum Hall-effect regimes, in analogy with Feynman's theory for helium. The spectrum is in excellent quantitative agreement with the numerical results of Haldane. Within this approximation we prove that a finite gap is generic to any liquid state in the extreme quantum limit and that in this single-mode approximation gapless excitations can arise only as Goldstone modes for ground states with broken translation symmetry.