Possible pairing-induced even-denominator fractional quantum Hall effect in the lowest Landau level

We report on our theoretical investigations that point to the possibility of a fractional quantum Hall effect with partial spin polarization at nu = 3/8. The physics of the incompressible state proposed here involves p-wave pairing of composite fermions in the spin reversed sector. The temperature and magnetic field regimes for the realization of this state are estimated.     

Possible reentrance of the fractional quantum Hall effect in the lowest Landau level

In the framework of a recently developed model of interacting composite fermions, we calculate the energy of different solid and Laughlin-type liquid phases of spin-polarized composite fermions. The liquid phases have a lower energy than the competing solids around the electronic filling factors nu = 4/11,6/17, and 4/19 and may thus be responsible for the fractional quantum Hall effect at nu = 4/11. The alternation between solid and liquid phases when varying the magnetic field may lead to reentrance phenomena in analogy with the observed reentrant integral quantum Hall effect.     

Nonconventional odd-denominator fractional quantum Hall states in the second Landau level

We report the observation of a new fractional quantum Hall state in the second Landau level of a two-dimensional electron gas at the Landau level filling factor ν=2+6/13. We find that the model of noninteracting composite fermions can explain the magnitude of gaps of the prominent 2+1/3 and 2+2/3 states. The same model fails, however, to account for the gaps of the 2+2/5 and the newly observed 2+6/13 states suggesting that these two states are of exotic origin.     

Spin order in paired quantum Hall states

We consider quantum Hall states at even-denominator filling fractions, especially nu=5/2, in the limit of small Zeeman energy. Assuming that a paired quantum Hall state forms, we study spin ordering and its interplay with pairing. We give numerical evidence that at nu=5/2 an incompressible ground state will exhibit spontaneous ferromagnetism. The Ginzburg-Landau (GL) theory for the spin degrees of freedom of paired Hall states is a perturbed CP2 model. We compute the coefficients in the GL theory by a BCS Stoner mean-field theory for coexisting order parameters, and show that even if repulsion is smaller than that required for a Stoner instability, ferromagnetic fluctuations can induce a partially or fully polarized superconducting state.     

Collective nature of the reentrant integer quantum Hall states in the second Landau level

We report an unexpected sharp peak in the temperature dependence of the magnetoresistance of the reentrant integer quantum Hall states in the second Landau level. This peak defines the onset temperature of these states. We find that in different spin branches the onset temperatures of the reentrant states scale with the Coulomb energy. This scaling provides direct evidence that Coulomb interactions play an important role in the formation of these reentrant states evincing their collective nature.     

Non-Fermi-liquid behavior of compressible electron states on the lowest Landau level

Experiments show that at even denominator fractions (EDF) (7p = 1=2;3=4;3=2,...) the two-dimensional electron gas (2DEG) in a strong magnetic field becomes compressible, has no energy gap, and demonstrates the presence of an ostensible Fermi surface (FS). Since this phenomenon results from a minimization of the interaction, rather than the kinetic energy, the EDF states might well exhibit deviations from a conventional Fermi liquid (FL). We show that impurity scattering and its interference with electronelectron and electron-phonon interactions provide examples of intrinsically non-Fermi-liquid (NFL) transport at EDFs.     

Effect of the Landau level broadening on the quantum Hall conductance

Summary In a previous paper, Kliroset al. presented a model calculation of the Hall conductivity as a function of the Landau level broadening Γ for finite temperatures. In this paper, the effect of Landau-level broadening on the structure of the Hall conductivity is investigated. The experimental data regarding the Si-MOSFET and GaAs-heterostructure experiments are reproduced including a functional dependence of Γ on the magnetic field. The influence of the effectiveg-factor is considered as well.     

Effective Hamiltonian for striped and paired states at the half-filled Landau level

We study a pairing mechanism for the quantum Hall system using a mean field theory with a basis on the von Neumann lattice, on which the magnetic translations commute. In the Hartree–Fock–Bogoliubov approximation, we solve the gap equation for spin-polarized electrons at the half-filled Landau levels. We obtain an effective Hamiltonian which shows a continuous transition from the compressible striped state to the paired state. Furthermore, a crossover occurs in the pairing phase. The energy spectrum and energy gap of the quasiparticle in the paired state is calculated numerically at the half-filled second Landau level.     

Observation of reentrant integer quantum Hall States in the lowest landau level

Measurements on very low disorder two-dimensional electrons confined to relatively wide GaAs quantum well samples with tunable density reveal a close competition between the electron liquid and solid phases near the Landau level filling factor ν=1. As the density is raised, the fractional quantum Hall liquid at ν=4/5 suddenly disappears at a well-width dependent critical density, and then reappears at higher densities with insulating phases on its flanks. These insulating phases exhibit reentrant ν=1 integer quantum Hall effects and signal the formation of electron Wigner crystal states. Qualitatively similar phenomena are seen near ν=6/5.     

Ballistic phonon studies in the lowest Landau level

We report time-resolved studies of ballistic phonon absorption in the fractional quantum Hall regime at Landau level filling factors of and . The technique used can resolve the interaction of the two-dimensional electron system with LA and TA phonons and has been used to measure the temperature variation of the heat capacity of a single layer of electrons at . The energy gaps at have also been measured and found to be in good agreement with theory. The roles of compressible and incompressible regions in the phonon absorption process are discussed. Angle resolved measurements at are also in good agreement with theory.     

Insulating and fractional quantum hall states in the first excited Landau level

The observation of new insulating phases of two-dimensional electrons in the first excited Landau level is reported. These states, which are manifested as reentrant integer quantized Hall effects, exist alongside well-developed even-denominator fractional quantized Hall states at nu = 7/2 and 5/2 and new odd-denominator states at nu = 3+1/5 and 3+4/5.     

Tuning the effects of Landau level mixing on anisotropic transport in quantum Hall systems

Electron-electron interactions in half-filled high Landau levels in two-dimensional electron gases in a strong perpendicular magnetic field can lead to states with anisotropic longitudinal resistance. This longitudinal resistance is generally believed to arise from broken rotational invariance, which is indicated by charge density wave order in Hartree-Fock calculations. We use the Hartree-Fock approximation to study the influence of externally tuned Landau level mixing on the formation of interaction-induced states that break rotational invariance in two-dimensional electron and hole systems. We focus on the situation when there are two non-interacting states in the vicinity of the Fermi level and construct a Landau theory to study coupled charge density wave order that can occur as interactions are tuned and the filling or mixing are varied. We consider numerically a specific example where mixing is tuned externally through Rashba spin-orbit coupling. We calculate the phase diagram and find the possibility of ordering involving coupled striped or triangular charge density waves in the two levels. Our results may be relevant to recent transport experiments on quantum Hall nematics in which Landau level mixing plays an important role.