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.     

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.     

Metamorphosis of the quantum Hall ferromagnet at nu=2/5

We report on the dramatic evolution of the quantum Hall ferromagnet in the fractional quantum Hall regime at nu=2/5 filling. A large enhancement in the characteristic time scale gives rise to a dynamical transition into a novel quantized Hall state. The observed Hall state is determined to be a zero-temperature phase distinct from the spin-polarized and spin-unpolarized nu=2/5 fractional quantum Hall states. It is characterized by a strong temperature dependence and puzzling correlation between temperature and time.     

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.     

Pairing of spin excitations in lateral quantum dots

We demonstrate the existence of correlated electronic states as paired spin excitations of lateral quantum dots in the integer quantum Hall regime. Starting from the spin-singlet filling-factor nu=2 droplet, by increasing the magnetic field we force the electrons to flip spins and increase the spin polarization. We identify the second spin-flip process as one accompanied by correlated, spin depolarized phases, interpreted as pairs of spin excitons. The correlated states are identified experimentally in few-electron lateral quantum dots using high source-drain voltage spectroscopy.     

Switching noise as a probe of statistics in the fractional quantum Hall effect

We propose an experiment to probe the unconventional quantum statistics of quasiparticles in fractional quantum Hall states by measurement of current noise. The geometry we consider is that of a Hall bar where two quantum point contacts introduce two interfering amplitudes for backscattering. Thermal fluctuations of the number of quasiparticles enclosed between the two point contacts introduce current noise, which reflects the statistics of the quasiparticles. We analyze Abelian nu=1/q states and the non-Abelian nu=5/2 state.     

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.     

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.     

Competing topological orders in the ν=12/5 quantum Hall state

We provide numerical evidence that a p(x)-ip(y) paired Bonderson-Slingerland (BS) non-Abelian hierarchy state is a strong candidate for the observed ν=12/5 quantum Hall plateau. We confirm the existence of a gapped incompressible ν=12/5 quantum Hall state with shift S=2 on the sphere, matching that of the BS state. The exact ground state of the Coulomb interaction at S=2 is shown to have a large overlap with the BS trial wave function. Larger overlaps are obtained with BS-type wave functions that are hierarchical descendants of general p(x)-ip(y) weakly paired states at ν=5/2. We perform a finite-size scaling analysis of the ground-state energies for ν=12/5 states at shifts corresponding to the BS (S=2) and 3-clustered Read-Rezayi (S=-2) universality classes. This analysis reveals very tight competition between these two non-Abelian topological orders.     

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.     

Observation of collapse of pseudospin order in bilayer quantum Hall ferromagnets

The Hartree-Fock paradigm of bilayer quantum Hall states with finite tunneling at filling factor nu=1 has full pseudospin ferromagnetic order with all the electrons in the lowest symmetric Landau level. Inelastic light scattering measurements of low energy spin excitations reveal major departures from the paradigm at relatively large tunneling gaps. The results indicate the emergence of a novel correlated quantum Hall state at nu=1 characterized by reduced pseudospin order. Marked anomalies occur in spin excitations when pseudospin polarization collapses by application of in-plane magnetic fields.     

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.     

Spin degree of freedom in the nu=1 bilayer electron system investigated by nuclear spin relaxation

The nuclear-spin-relaxation rate 1/T(1) has been measured in a bilayer electron system at and around total Landau level filling factor nu=1. The measured 1/T(1), which probes electron spin fluctuations, is found to increase gradually from the quantum Hall (QH) state at low fields through a phase transition to the compressible state at high fields. Furthermore, 1/T(1) in the QH state shows a noticeable increase away from nu=1. These results demonstrate that, as opposed to common assumption, the electron spin degree of freedom is not completely frozen either in the QH or the compressible states.     

Quantum Hall ferrimagnetism in lateral quantum dot molecules

We demonstrate the existence of ferrimagnetic and ferromagnetic phases in a spin phase diagram of coupled lateral quantum dot molecules in the quantum Hall regime. The spin phase diagram is determined from the Hartree-Fock configuration interaction method as a function of electron number N and magnetic field B. The quantum Hall ferrimagnetic phase corresponds to spatially imbalanced spin droplets resulting from strong interdot coupling of identical dots. The quantum Hall ferromagnetic phases correspond to ferromagnetic coupling of spin polarization at filling factors between nu=2 and nu=1.     

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.     

Particle-hole symmetry and the Pfaffian state

We show that the particle-hole conjugate of the Pfaffian state-or "anti-Pfaffian" state-is in a different universality class from the Pfaffian state, with different topological order. The two states can be distinguished easily by their edge physics: their edges differ in both their thermal Hall conductance and their tunneling exponents. At the same time, the two states are exactly degenerate in energy for a nu=5/2 quantum Hall system in the idealized limit of zero Landau level mixing. Thus, both are good candidates for the observed sigma_{xy}=5/2(e;{2}/h) quantum Hall plateau.     

Optical investigation of spin-wave excitations in fractional quantum hall states and of interaction between composite fermions

We demonstrate that the temperature dependence of the electron spin polarization for the fractional states nu = 1/3 and nu = 2/3 displays activated behavior. This study enables the first measurement of the fractional quantum Hall spin-flip gaps. They are found to be systematically larger in comparison with the gaps simultaneously measured in transport. For nu = 1/3 and nu = 1/2, these spin-flip gaps allow the determination of the composite fermion interaction energy. This energy is investigated as a function of the finite width of the 2D channel.     

Quantum Hall states near the charge-neutral Dirac point in graphene

We investigate the quantum Hall (QH) states near the charge-neutral Dirac point of a high mobility graphene sample in high magnetic fields. We find that the QH states at filling factors nu=+/-1 depend only on the perpendicular component of the field with respect to the graphene plane, indicating that they are not spin related. A nonlinear magnetic field dependence of the activation energy gap at filling factor nu=1 suggests a many-body origin. We therefore propose that the nu=0 and +/-1 states arise from the lifting of the spin and sublattice degeneracy of the n=0 Landau level, respectively.     

New phase transition between partially and fully polarized quantum Hall states with charge and spin gaps at nu = 2/3

The average electron spin polarization Rho of a two-dimensional electron gas confined in GaAs/GaAlAs multiple quantum wells was measured by NMR near the fractional quantum Hall state with filling factor nu = 2/3. Above this filling factor (2/3< or = nu < 0.85), a strong depolarization is observed corresponding to two spin flips per additional flux quantum. The most remarkable behavior of the polarization is observed at nu = 2/3, where a quantum phase transition from a partially polarized (Rho approximately 3/4) to a fully polarized (Rho = 1) state can be driven by increasing the ratio between the Zeeman and the Coulomb energy above a critical value eta(c) = Delta(Z)/Delta(C) = 0.0185.     

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.