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.     

Edge state propagation direction in the fractional quantum Hall regime: multi-terminal magnetocapacitance experiment

The propagation direction of fractional quantum Hall effect (FQHE) edge states has been investigated experimentally via the symmetry properties of the multi-terminal capacitances of a two-dimensional electron gas. Although strong asymmetries with respect to zero magnetic field appear, no asymmetries with respect to even denominator Landau level filling factor ν are seen. This indicates that current-carrying FQHE edge states propagate in the same direction as integer QHE edge states. In addition, anomalous capacitance features, indicative of enhanced bulk conduction, are observed at and .     

Geometry of quantum Hall states: Gravitational anomaly and transport coefficients

We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local transformation properties of these states are examined through local geometric variations. We introduce the notion of a generating functional and relate it to geometric invariant functionals recently studied in geometry. We develop two complementary methods to study the geometry of the FQHE. One method is based on iterating a Ward identity, while the other is based on a field theoretical formulation of the FQHE through a path integral formalism.     

Resonant tunneling into a biased fractional quantum Hall edge

We observe resonant tunneling into a voltage biased fractional quantum Hall effect (FQHE) edge, using atomically sharp tunnel barriers unique to cleaved-edge overgrown devices. The resonances demonstrate different tunnel couplings to the metallic lead and the FQHE edge. Weak coupling to the FQHE edge produces clear non-Fermi liquid behavior with a sixfold increase in resonance area under bias arising from the power law density of states at the FQHE edge. A simple device model uses the resonant tunneling formalism for chiral Luttinger liquids to successfully describe the data.     

Transition from an electron solid to the sequence of fractional quantum Hall states at very low Landau level filling factor

At low Landau level filling of a two-dimensional electron system, typically associated with the formation of an electron crystal, we observe local minima in Rxx at filling factors nu = 2/11, 3/17, 3/19, 2/13, 1/7, 2/15, 2/17, and 1/9. Each of these developing fractional quantum Hall (FQHE) states appears only above a filling-factor-specific temperature. This can be interpreted as the melting of an electron crystal and subsequent FQHE liquid formation. The observed sequence of FQHE states follows the series of composite fermion states emanating from nu = 1/6 and nu = 1/8.     

Quark confinement and the fractional quantum Hall effect

Working in the physics of Wilson factor and Aharonov-Bohm effect, we find in the fluxtube-quark system the topology of a baryon consisting of three heavy flavor quarks resembles that of the fractional quantum Hall effect (FQHE) in condensed matter. This similarity yields the result that the constituent quarks of baryon have the ``filling factor' 1/3, thus the previous conjecture that quark confinement is a correlation effect is confirmed. Moreover, by deriving a Hamiltonian of the system analogous to that of FQHE, we predict an energy gap for the ground state of a heavy three-quark system.     

Quark confinement and the fractional quantum Hall effect

Working in the physics of Wilson factor and Aharonov-Bohm effect,we find in the fluxtubequark system the topology of a baryon consisting of three heavy flavor quarks resembles that of the fractional quantum Hall effect(FQHE)in condensed matter.This similarity yields the result that the constituent quarks of baryon have the"filling factor"1/3.thus the previous conjecture that quark confinement is a correlation effect is confirmed.Moreover,by deriving a Hamiltonian of the system analogous to that of FQHE,we predict an energy gap for the ground state of a heavy three-quark system.     

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.     

Ultra-low temperature study of the even-denominator FQHE state

We present experimental data showing unambiguously an even-denominator fractional quantum Hall effect (FQHE) state at . At a bath temperature T_b=8 mK, we observe a Hall plateau quantized to a value of 2h/5e² with an uncertainty smaller than 2 parts in 10⁶ and a vanishing R_xx (R_xx=1.7±1.7 Ω). The thermal activation energy gaps Δ at Landau level filling factors , and are 0.11, 0.10, and 0.055 K, respectively. Adding a disorder broadening (typically 2 K) to these values, we deduce that all three FQHE states have probably very similar energy gaps. The electron heating experiment shows that the 2D electrons are efficiently cooled to the bath temperature for T_b8 mK. We also explore the density dependence of the activation gap at . Preliminary results at T_b25 mK show that the state is very sensitive to disorder.     

Strongly Correlated Phases in Rapidly Rotating Bose Gases

We consider a system of trapped spinless bosons interacting with a repulsive potential and subject to rotation. In the limit of rapid rotation and small scattering length, we rigorously show that the ground state energy converges to that of a simplified model Hamiltonian with contact interaction projected onto the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles, we also prove convergence of states; in particular, in a certain regime we show convergence towards the bosonic Laughlin wavefunction. This is the first rigorous justification of the effective FQHE Hamiltonian for rapidly rotating Bose gases. We review previous results on this effective Hamiltonian and outline open problems.     

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.     

On triggering role of carrier mobility for Laughlin state organization

Recent experiments with suspended graphene have corroborated an important role of carrier mobility in the competition between Laughlin state and insulating state, presumably of Wigner-type electron crystal. Moreover, the fractional quantum Hall effect (FQHE) in graphene has been observed at low carrier densities when the interaction was reduced due to carrier dilution. This suggests that not solely interaction and the flat band with quenched kinetic energy may be important for formation of FQHE. Here, some exclusive for 2D topological arguments are supposed to explain the triggering role of carrier mobility in formation of the collective FQHE state, when conditions of sufficient flattening of a band and interaction presence are fulfilled.     

Quasihole Tunneling in Disordered Fractional Quantum Hall Systems

Fractional quantum Hall systems are often described by model wave functions,which are the ground states of pure systems with short-range interaction.A primary example is the Laughlin wave function,which supports Abelian quasiparticles with fractionalized charge.In the presence of disorder,the wave function of the ground state is expected to deviate from the Laughlin form.We study the disorder-driven colla.pse of the quantum Hall state by analyzing the evolution of the ground state and the single-quasihole state.In particular,we demonstrate that the quasihole tunneling amplitude can signal the fractional quantum Hall phase to insulator transition.     

Theory of four-dimensional fractional quantum Hall states

We propose a pseudo-potential Hamiltonian for the Zhang-Hu’s generalized fractional quantum Hall states to be the exact and unique ground states. Analogously to Laughlin’s quasi-hole (quasi-particle), the excitations in the generalized fractional quantum Hall states are extended objects. They are vortex-like excitations with fractional charges +(−)1/m³ in the total configuration space CP³. The density correlation function of the Zhang-Hu states indicates that they are incompressible liquid.     

Topological investigation of the fractionally quantized Hall conductivity

Using the fiber bundle concept developed in geometry and topology, the fractionally quantized Hall conductivity is discussed in the relevant many-particle configuration space. Electronmagnetic field and electron-electron interactions under FQHE conditions are treated as functional connections over the torus, the torus being the underlying two-dimensional manifold. Relations to the (2 + 1)-dimensional Chern-Simons theory are indicated. The conductivity being a topological invariant is given as e²/h times a linking number which is the quotient of the winding numbers of the self-consistent field and the magnetic field, respectively. Odd denominators are explained by the two spin structures which have been considered for the FQHE correlated electron system.     

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.     

From quantum Hall ferromagnetism to huge longitudinal resistance at the 2/3 fractional quantum Hall state

We observe the transition from a spin-unpolarized to a polarized nu=2/3 fractional quantum Hall state at low currents (<5 nA), recently described in terms of quantum Hall ferromagnetism, versus density and parallel magnetic field. At larger currents the time and current dependent huge longitudinal resistance (HLR) is always initiated at the transition. Transport in the HLR regime is linear and the amount of current-induced nuclear polarization in the HLR is comparable to the thermal nuclear polarization at approximately 20 mK and 10 T. A current-induced disorder in the nuclear polarization is speculated to cause the enhanced resistance in the HLR regime.