Microscopic origin of the next-generation fractional quantum Hall effect

Most of the fractions observed to date belong to the sequences nu=n/(2pn+/-1) and nu=1-n/(2pn+/-1), n and p integers, understood as the familiar integral quantum Hall effect of composite fermions. These sequences fail to accommodate, however, many fractions such as nu=4/11 and 5/13, discovered recently in ultrahigh mobility samples at very low temperatures. We show that these "next generation" fractional quantum Hall states are accurately described as the fractional quantum Hall effect of composite fermions.     

Fractional quantum Hall effect of composite fermions

In a GaAs/AlGaAs quantum well of density 1 x 10(11) cm(-2) we observed a fractional quantum Hall effect (FQHE) at nu = 4/11 and 5/13, and weaker states at nu = 6/17, 4/13, 5/17, and 7/11. These sequences of fractions do not fit into the standard series of integral quantum Hall effects of composite fermions (CF) at nu = p/(2mp +/- 1). They rather can be regarded as the FQHE of CFs attesting to residual interactions between these composite particles. In tilted magnetic fields the nu = 4/11 state remains unchanged, strongly suggesting it to be spin polarized. The weak nu = 7/11 state vanishes quickly with tilt.     

Tilt-induced localization and delocalization in the second Landau level

We have investigated the behavior of electronic phases of the second Landau level under tilted magnetic fields. The fractional quantum Hall liquids at nu=2+1/5 and 2+4/5 and the solid phases at nu=2.30, 2.44, 2.57, and 2.70 are quickly destroyed with tilt. This behavior can be interpreted as a tilt driven localization of the 2+1/5 and 2+4/5 fractional quantum Hall liquids and a delocalization through the melting of solid phases in the top Landau level, respectively. The evolution towards the classical Hall gas of the solid phases is suggestive of antiferromagnetic ordering.     

Hierarchy of composite fermions in the Hamiltonian theory

Most states of the fractional quantum Hall effect may be interpreted in terms of an integral quantum Hall effect of weakly-interacting quasiparticles (composite fermions). The recently discovered state does not belong to these states because its formation is due to the residual interactions between composite fermions, which become relevant when the composite-fermion levels are only partially filled. We have derived a model of interacting composite fermions, which reveals the self-similarity of the fractional quantum Hall effect and which allows for a systematic study of higher generations of composite fermions. Here, we derive the form of the interaction potential between these hierarchical composite fermions and provide some stability criteria for such states.     

Fractional Quantum Hall Effect in SiGe/Si/SiGe Quantum Wells in Weak Quantizing Magnetic Fields

We have experimentally studied the fractional quantum Hall effect in SiGe/Si/SiGe quantum wells in relatively weak magnetic fields, where the Coulomb interaction between electrons exceeds the cyclotron splitting by a factor of a few XX. Minima of the longitudinal resistance have been observed corresponding to the quantum Hall effect of composite fermions with quantum numbers p = 1, 2, 3, and 4. Minima with p = 3 disappear in magnetic fields below 7 T, which may be a consequence of the intersection or even merging of the quantum levels of the composite fermions with different orientations of the pseudo-spin, i.e., those belonging to different valleys. We have also observed minima of the longitudinal resistance at filling factors ν = 4/5 and 4/11, which may be due to the formation of the second generation of the composite fermions.     

Phonon excitations of composite-fermion landau levels

Phonon excitations of fractional quantum Hall states at filling factors nu = 1/3, 2/5, 4/7, 3/5, 4/3, and 5/3 are experimentally shown to be based on Landau-level transitions of composite fermions. At filling factor nu = 2/3, however, a linear field dependence of the excitation energy in the high-field regime rather hints towards a spin transition excited by the phonons. We propose to explain this surprising observation by an only partially polarized 2/3 ground state, making the energetically lower lying spin transition also allowed for phonon excitations.     

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.     

Higher-energy composite fermion levels in the fractional quantum Hall effect

Even though composite fermions in the fractional quantum Hall liquid are well established, it is not yet known up to what energies they remain intact. We probe the high-energy spectrum of the 1/3 liquid directly by resonant inelastic light scattering, and report the observation of a large number of new collective modes. Supported by our theoretical calculations, we associate these with transitions across two or more composite fermions levels. The formation of quasiparticle levels up to high energies is direct evidence for the robustness of topological order in the fractional quantum Hall effect.     

Phase diagram for quantum hall bilayers at nu=1

We present a phase diagram for a double quantum well bilayer electron gas in the quantum Hall regime at a total filling factor nu=1, based on exact numerical calculations of the topological Chern number matrix and the (interlayer) superfluid density. We find three phases: a quantized Hall state with pseudospin superfluidity, a quantized Hall state with pseudospin "gauge-glass" order, and a decoupled composite Fermi liquid. Comparison with experiments provides a consistent explanation of the observed quantum Hall plateau, Hall drag plateau, and vanishing Hall drag resistance, as well as the zero-bias conductance peak effect, and suggests some interesting points to pursue experimentally.     

Composite fermion hofstadter problem: partially polarized density wave states in the nu = 2/5 fractional quantum hall effect

It is well known that the nu = 2/5 state is unpolarized at zero Zeeman energy, while it is fully polarized at large Zeeman energies. A novel state with a charge/spin density wave order for composite fermions is proposed to exist at intermediate values of the Zeeman coupling for nu = 2/5. This state has half the maximum possible polarization, and can be extended to other incompressible fractions. A Hartree-Fock calculation based on the new approach for all fractional quantum Hall states developed by R. Shankar and the author is used to demonstrate the stability of this state to single-particle excitations and to compute gaps. A very recent experiment shows direct evidence for this state.     

Excitation spectrum and effective mass of the even-fraction quantum hall liquid

To probe the nature of the even-fraction quantum Hall system, we have investigated the low-lying excitation spectrum by exact diagonalization for finite systems. We have found (i) a striking one-to-one correspondence (i.e., a shell structure) between the spectrum and those for free (composite) fermions, (ii) a surprisingly straight scaling plot for the excitation energy that gives a zero gap (metal) in the thermodynamic limit, (iii) the effective mass evaluated from the scaling becoming heavier for nu = 1/2,1/4,1/6, but (iv) some deviations from the single-mode or the Hartree-Fock composite fermion approximation.     

Direct measurement of the g factor of composite fermions

The activation gap Delta of the fractional quantum Hall states at constant fillings nu=2/3 and 2/5 has been measured as a function of the perpendicular magnetic field B. A linear dependence of Delta on B is observed while approaching the spin-polarization transition. This feature allows a direct measurement of the g factor of composite fermions which appears to be heavily renormalized by interactions and strongly sensitive to the electronic filling factor.     

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.     

Valley polarization and susceptibility of composite fermions around a filling factor nu=3/2

We report magnetotransport measurements of fractional quantum Hall states in an AlAs quantum well around a Landau level filling factor nu=3/2, demonstrating that the quasiparticles are composite fermions (CFs) with a valley degree of freedom. By monitoring the valley level crossings for these states as a function of applied symmetry-breaking strain, we determine the CF valley susceptibility and polarization. The data can be explained well by a simple Landau level fan diagram for CFs, and are in nearly quantitative agreement with the results reported for CF spin polarization.     

Half-polarized quantum hall states

We report a theoretical analysis of the half-polarized quantum Hall states observed in a recent experiment. Our numerical results indicate that the ground state energy of the quantum Hall nu = 2 / 3 and nu = 2 / 5 states versus spin polarization has a downward cusp at half the maximal spin polarization. We map the two-component fermion system onto a system of excitons and describe the ground state as a liquid state of excitons with nonzero values of exciton angular momentum.     

Phase diagram of interacting composite fermions in the bilayer nu=2/3 quantum hall effect

We study the phase diagram of composite fermions (CFs) in the presence of spin and pseudospin degrees of freedom in the bilayer nu=2/3 quantum Hall (QH) state. Activation studies elucidate the existence of three different QH states with two different types of hysteresis in the magnetotransport. While a noninteracting CF model provides a qualitative account of the phase diagram, the observed renormalization of tunneling gap and a non-QH state at high densities are not explained in the noninteracting CF model, and are suggested to be manifestations of interactions between CFs.     

Contrasting behavior of the 5/2 and 7/3 fractional quantum Hall effect in a tilted field

Using a tilted-field geometry, the effect of an in-plane magnetic field on the even denominator nu=5/2 fractional quantum Hall state is studied. The energy gap of the nu=5/2 state is found to collapse linearly with the in-plane magnetic field above approximately 0.5 T. In contrast, a strong enhancement of the gap is observed for the nu=7/3 state. The radically distinct tilted-field behavior between the two states is discussed in terms of Zeeman and magneto-orbital coupling within the context of the proposed Moore-Read Pfaffian wave function for the 5/2 fractional quantum Hall effect.