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.     

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.     

Magnetic-field-induced insulating phases at large r s

Exploring a two-dimensional hole system in the large r(s) regime we found a surprisingly rich phase diagram. At the highest densities, beside the nu =1/3, 2/3, and 2/5 fractional quantum Hall states, we observe both of the previously reported high field insulating and reentrant insulating phases. As the density is lowered, the reentrant insulating phase initially strengthens, then it unexpectedly starts weakening until it completely disappears. The intricate behavior of the insulating phases can be explained by a nonmonotonic melting line in the nu-r(s) phase space.     

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.     

Dipolar excitons, spontaneous phase coherence, and superfluid-insulator transition in bilayer quantum Hall systems at nu = 1

The spontaneous interlayer phase coherent (111) state of a bilayer quantum Hall system at filling factor nu = 1 may be viewed as a condensate of interlayer particle-hole pairs or excitons. We show that when the layers are biased in such a way that these excitons are very dilute, they may be viewed as pointlike bosons. We calculate the exciton dispersion relation and show that the exciton-exciton interaction is dominated by the dipole moment they carry. In addition to the phase coherent state, we also find a Wigner crystal/glass phase in the presence/absence of disorder which is an insulating state for the excitons. The position of the phase boundary is estimated and the transition between these two phases is discussed.     

Evidence for two different solid phases of two-dimensional electrons in high magnetic fields

We have observed two different rf resonances in the frequency dependent real diagonal conductivity of very high quality two-dimensional electron systems in the high magnetic field insulating phase and interpret them as coming from two different pinned electron solid phases (labeled as "A" and "B"). The "A" resonance is observable for Landau level filling nu<2/9 [reentrant around the nu=1/5 fractional quantum Hall effect (FQHE)] and then crosses over to the different "B" resonance which dominates at sufficiently low nu. Moreover, the "A" resonance is found to show dispersion with respect to the size of the transmission line, indicating that the "A" phase has a large correlation length. We suggest that quantum correlations such as those responsible for FQHE may play an important role in giving rise to such different solids.     

Fractional quantum Hall effect at high fillings in a two-subband electron system

Magnetotransport measurements in a clean two-dimensional electron system confined to a wide GaAs quantum well reveal that, when the electrons occupy two electric subbands, the sequences of fractional quantum Hall states observed at high fillings (ν>2) are distinctly different from those of a single-subband system. Notably, when the Fermi energy lies in the ground state Landau level of either of the subbands, no quantum Hall states are seen at the even-denominator ν=5/2 and 7/2 fillings; instead, the observed states are at ν=[i+p/(2p±1)], where i=2, 3, 4 and p=1, 2, 3, and include several new states at ν=13/5, 17/5, 18/5, 25/7, and 14/3.     

Multichannel Kondo models in non-Abelian quantum Hall droplets

We study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state which is spatially separated from it by an integer quantum Hall state. Near a resonance, the physics at energy scales below the level spacing of the edge states of the dot is governed by a k-channel Kondo model when the quantum Hall state is a Read-Rezayi state at filling fraction nu=2+k/(k+2) or its particle-hole conjugate at nu=2+2/(k+2). The k-channel Kondo model is channel isotropic even without fine-tuning in the former state; in the latter, it is generically channel anisotropic. In the special case of k=2, our results provide a new venue, realized in a mesoscopic context, to distinguish between the Pfaffian and anti-Pfaffian states at filling fraction nu=5/2.     

Non-Abelian states with negative flux: a new series of quantum Hall states

By applying the idea of parafermionic clustering to composite bosons with positive as well as negative flux, a new series of trial wave functions to describe fractional quantum Hall states is proposed. These states compete at filling factors nu=k/(3k+/-2) with other ground states like stripes or composite-fermion states. These series contain all the states recently discovered by Pan et al. [Phys. Rev. Lett. 90, 016801 (2003)10.1103/Phys. Rev. Lett. 90, 016801(2003)] including the even-denominator cases. Exact diagonalization studies on the sphere and torus point to their relevance for nu=3/7, 3/11, and 3/8.     

Quantum Hall fractions in rotating Bose-Einstein condensates

We study the quantum Hall phases that appear in the dilute limit of rotating Bose-Einstein condensates. By exact diagonalization in a spherical geometry we obtain the ground state and low-lying excited states of a small number of bosons as a function of the filling fraction nu, the ratio of the number of bosons to the number of vortices. We show the occurrence of the Jain principal sequence of incompressible liquids for nu=2/3,3/4,4/3,5/4 in addition to the Laughlin state nu=1/2 as well as the Pfaffian state for nu=1. We give gap estimates by finite-size scaling of both charged and neutral excitations.     

High-Resolution Fourier Transform and Diode-Laser Spectroscopy of the nu(6) Fundamental of C(2)F(6) and Associated Hot Bands

High-resolution infrared spectra of the nu(6) (713 cm(-1)) band region of C(2)F(6) vapor have been recorded at several temperatures. Spectra at 77, 200, and 300 K were recorded using a Fourier transform spectrometer with unapodized resolutions of 0.0018 cm(-1) (200 and 300 K) and 0.008 cm(-1) (77 K). Spectra with rotational temperatures in the range 5-50 K were recorded in a supersonic jet using diode-laser absorption spectroscopy. The nu(6) band contains two clear sequences of hot-bands: one arises from the nu(4) torsional vibration at 67.5 cm(-1); the other, shorter, weaker progression is built on the doubly degenerate nu(9) vibration at 220 cm(-1). They lie to high and low wavenumbers of the fundamental band, respectively. Eleven series were assigned and fitted to these hot bands. A perturbed series in the nu(4) sequence is considered, by analogy with the infrared spectrum of C(2)H(6) vapor, to be caused by an xy-Coriolis interaction either between 5nu(4) and nu(9) + 2nu(4) in the ground state or, in the upper state, nu(6) + 5nu(4) with nu(6) + nu(9) + 2nu(4) or nu(6) + 5nu(4) with 2nu(8). One further series resolved only in the jet spectrum and lying very close to the fundamental is almost certainly due to the nu(6) fundamental of the isotopomer (13)C(12)CF(6). Copyright 2000 Academic Press.     

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.     

Two-flux composite fermion series of the fractional quantum Hall states in strained Si

Magnetotransport properties are investigated in a high-mobility two-dimensional electron system in the strained Si quantum well of a (100) Si(0.75)Ge(0.25)/Si/Si(0.75)Ge0.25 heterostructure, at temperatures down to 30 mK and in magnetic fields up to 45 T. We observe around nu=1/2 the two-flux composite fermion (CF) series of the fractional quantum Hall effect (FQHE) at nu=2/3, 3/5, 4/7, and at nu=4/9, 2/5, 1/3. Among these FQHE states, the nu=1/3, 4/7, and 4/9 states are seen for the first time in the Si/SiGe system. Interestingly, of the CF series, the 3/5 state is weaker than the nearby 4/7 state and the 3/7 state is conspicuously missing, resembling the observation in the IQHE regime that the nu=3 is weaker than the nearby nu=4 state. Our results can be quantitatively understood in the picture of CF's with the valley degree of freedom.     

High-Resolution Study of the Mid-Infrared Region of FNO(2)

Of the gas-phase IR spectrum of nitrylfluoride, FNO(2), between 1200 and 1900 cm(-1), the bands nu(4), 2nu(6), nu(2) + nu(3), and nu(1) have been studied at a resolution of ca. 0.003 cm(-1). Improved ground state rotational and centrifugal distortion constants have been obtained from a simultaneous analysis of the data from F. Hegelund, H. Bürger, and G. Pawelke [J. Mol. Spectrosc. 184, 350-361 (1997)] and the present data from nu(4) and nu(1). The nu(4) and 2nu(6) bands are free from local perturbations, and upper state spectroscopic constants have been obtained from the conventional Watson Hamiltonian. The bands nu(1) and nu(2) + nu(3) are strongly perturbed by Coriolis interactions with the nearby dark levels nu(5) + nu(6), nu(3) + nu(6), and nu(2) + nu(5). Upper state constants for nu(1) and nu(2) + nu(3) are obtained from triad and tetrad models, respectively, including Coriolis resonances within this system. In addition Coriolis interaction parameters and the vibrational energies for the three dark states together with some of their rotational constants are determined from the observed perturbation effects on nu(1) and nu(2) + nu(3). Copyright 2000 Academic Press.     

Evolution of quasiparticle charge in the fractional quantum hall regime

The charge of quasiparticles in a fractional quantum Hall (FQH) liquid, tunneling through a partly reflecting constriction with transmission t, was determined via shot noise measurements. In the nu = 1/3 FQH state, a charge smoothly evolving from e(*) = e/3 for t(1/3) congruent with 1 to e(*) = e for t(1/3)<1 was determined, agreeing with chiral Luttinger liquid theory. In the nu = 2/5 FQH state the quasiparticle charge evolves smoothly from e(*) = e/5 at t(2/5) congruent with 1 to a maximum charge less than e(*) = e/3 at t(2/5)<1. Thus it appears that quasiparticles with an approximate charge e/5 pass a barrier they see as almost opaque.     

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.     

The Absorption Spectrum of HDO in the 16 300-16 670 and 18 000-18 350 cm(-1) Spectral Regions

The absorption spectrum of HDO has been recorded by Intracavity Laser Absorption Spectroscopy in the 16 300-16 670 and 18 000-18 350 cm(-1) spectral regions corresponding to the weak 2nu(2) + 4nu(3) and nu(2) + 5nu(3) bands, respectively. The nu(2) + 5nu(3) band centered at 18 208.434 cm(-1) was found almost isolated and has been satisfactorily reproduced in the frame of the effective Hamiltonian model. On the other hand, the 2nu(2) + 4nu(3) band at 16 456.201 cm(-1) is strongly perturbed as the (0 2 4) bright state is involved in a complex interaction scheme including the (1 0 4), (5 0 1), (1 5 2), and (1 11 0) states. The rovibrational assignment of these interacting states was greatly helped by the high-accuracy ab initio predictions performed by D. Schwenke and H. Partridge [J. Chem. Phys. 000-000 (2000)]. They could be partly modeled by an effective Hamiltonian which has allowed the assignment and reproduction of most of the observed transitions. Copyright 2000 Academic Press.     

Topologically protected qubits from a possible non-Abelian fractional quantum Hall state

The Pfaffian state is an attractive candidate for the observed quantized Hall plateau at a Landau-level filling fraction nu=5/2. This is particularly intriguing because this state has unusual topological properties, including quasiparticle excitations with non-Abelian braiding statistics. In order to determine the nature of the nu=5/2 state, one must measure the quasiparticle braiding statistics. Here, we propose an experiment which can simultaneously determine the braiding statistics of quasiparticle excitations and, if they prove to be non-Abelian, produce a topologically protected qubit on which a logical Not operation is performed by quasiparticle braiding. Using the measured excitation gap at nu=5/2, we estimate the error rate to be 10(-30) or lower.     

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.     

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.