Fractional quantum Hall effect and Chern-Simons gauge theories

Chern-Simons Modified RPA-Eliashberg Theory of the ν=1/2+1/2 Quantum Hall Bilayer

The ν=1/2+1/2 quantum Hall bilayer has been previsously modeled using Chern-Simons-RPA-Eliashberg (CSRPAE) theory to describe pairing between the two layers. However, these approaches are troubled by a number of divergences and ambiguities. By using a "modified" RPA approximation to account for mass renormalization, we can work in a limit where the cyclotron frequency is taken to infinity, effectively projecting to a single Landau level. This, surprisingly, controls the important divergences and removes ambiguities found in prior attempts at CSRPAE. Examining BCS pairing of composite fermions we find that the angular momentum channel l=+1 dominates for all distances d between layers and at all frequency scales. Examining BCS pairing of composite fermion electrons in one layer with composite fermion holes in the opposite layer, we find the l=0 pairing channel dominates for all d and all frequencies. The strength of the pairing in these two different descriptions of the same phase of matter is found to be almost identical. This agrees well with our understanding that these are two different but dual descriptions of the same phase of matter.

Zero-Field Composite Fermi Liquid in Twisted Semiconductor Bilayers

Recent experiments have produced evidence for fractional quantum anomalous Hall (FQAH) states at zero magnetic field in the semiconductor moiré superlattice system tMoTe_{2}. Here, we argue that a composite fermion description, already a unifying framework for the phenomenology of 2D electron gases at high magnetic fields, provides a similarly powerful perspective in this new context. To this end, we present exact diagonalization evidence for composite Fermi liquid states at zero magnetic field in tMoTe_{2} at fillings n=1/2 and n=3/4. We dub these non-Fermi liquid metals anomalous composite Fermi liquids (ACFLs), and we argue that they play a central organizing role in the FQAH phase diagram. We proceed to develop a long wavelength theory for this ACFL state that offers concrete experimental predictions upon doping the composite Fermi sea, including a Jain sequence of FQAH states and a new type of commensurability oscillations originating from the superlattice potential intrinsic to the system.

Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe_{2}

The pursuit of exotic phases of matter outside of the extreme conditions of a quantizing magnetic field is a long-standing quest of solid state physics. Recent experiments have observed spontaneous valley polarization and fractional Chern insulators in zero magnetic field in twisted bilayers of MoTe_{2}, at partial filling of the topological valence band (ν=-2/3 and -3/5). We study the topological valence band at half filling, using exact diagonalization and density matrix renormalization group calculations. We discover a composite Fermi liquid (CFL) phase even at zero magnetic field that covers a large portion of the phase diagram near twist angle ∼3.6°. The CFL is a non-Fermi liquid phase with metallic behavior despite the absence of Landau quasiparticles. We discuss experimental implications including the competition between the CFL and a Fermi liquid, which can be tuned with a displacement field. The topological valence band has excellent quantum geometry over a wide range of twist angles and a small bandwidth that is, remarkably, reduced by interactions. These key properties stabilize the exotic zero field quantum Hall phases. Finally, we present an optical signature involving "extinguished" optical responses that detects Chern bands with ideal quantum geometry.

Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems

We study, numerically, the charge neutral excitations (magnetorotons) in fractional quantum Hall systems, concentrating on the two Jain states near quarter filling, ν=2/7 and ν=2/9, and the ν=1/4 Fermi-liquid state itself. In contrast to the ν=1/3 states and the Jain states near half filling, on each of the two Jain states ν=2/7 and ν=2/9 the graviton spectral densities show two, instead of one, magnetoroton peaks. The magnetorotons have spin 2 and have opposite chiralities in the ν=2/7 state and the same chirality in the ν=2/9 state. We also provide a numerical verification of a sum rule relating the guiding center spin s[over ¯] with the spectral densities of the stress tensor.

Formal derivation of the Laughlin function and its generalization for other topological phases of FQHE

Using the braid symmetry we demonstrate the derivation of the Laughlin function for the main hierarchy 1/q of FQHE in the lowest Landau level of two-dimensional electron system with a mathematical rigour. This proves that the derivation of Laughlin function unavoidably requires some topological elements and cannot be completed within a local quantum mechanics, i.e., without global topological constraints imposed. The method shows the way for the generalization of this function onto other fractions from the general quantum Hall hierarchy. A generalization of the Laughlin function is here formulated.

Topological Field Theory of Non-Hermitian Systems

Non-Hermiticity gives rise to unique topological phases without Hermitian analogs. However, the effective field theory has yet to be established. Here, we develop a field-theoretical description of the intrinsic non-Hermitian topological phases. Because of the dissipative and nonequilibrium nature of non-Hermiticity, our theory is formulated solely in terms of spatial degrees of freedom, which contrasts with the conventional theory defined in spacetime. Our theory provides a universal understanding of non-Hermitian topological phenomena such as the unidirectional transport in one dimension and the chiral magnetic skin effect in three dimensions. Furthermore, it systematically predicts new physics; we illustrate this by revealing transport phenomena and skin effects in two dimensions induced by a perpendicular spatial texture. From the field-theoretical perspective, the non-Hermitian skin effect, i.e., the anomalous localization due to non-Hermiticity, is shown to be a signature of an anomaly.

Numerical Study of a Dual Representation of the Integer Quantum Hall Transition

We study the critical properties of the noninteracting integer quantum Hall to insulator transition (IQHIT) in a "dual" composite-fermion (CF) representation. A key advantage of the CF representation over electron coordinates is that at criticality CF states are delocalized at all energies. The CF approach thus enables us to study the transition from a new vantage point. Using a lattice representation of CF mean-field theory, we compute the critical and multifractal exponents of the IQHIT. We obtain ν=2.56±0.02 and η=0.51±0.01, both of which are consistent with the predictions of the Chalker-Coddington network model formulated in the electron representation.

Classification of Topological Phase Transitions and van Hove Singularity Steering Mechanism in Graphene Superlattices

We study quantum phase transitions in graphene superlattices in external magnetic fields, where a framework is presented to classify multiflavor Dirac fermion critical points describing hopping-tuned topological phase transitions of integer and fractional Hofstadter-Chern insulators. We argue and provide numerical support for the existence of transitions that can be explained by a nontrivial interplay of Chern bands and van Hove singularities near charge neutrality. This work provides a route to critical phenomena beyond conventional quantum Hall plateau transitions.

Homotopy Phases of FQHE with Long-Range Quantum Entanglement in Monolayer and Bilayer Hall Systems

Correlated phases in Hall systems have topological character. Multilayer configurations of planar electron systems create the opportunity to change topological phases on demand using macroscopic factors, such as vertical voltage. We present an analysis of such phenomena in close relation to recent experiments with multilayer Hall setups including GaAs and graphene multi-layers. The consequences of the blocking or not of the inter-layer electron tunneling in stacked Hall configurations are analyzed and presented in detail. Multilayer Hall systems are thus tunable topological composite nanomaterials, in the case of graphene-stacked systems by both intra- and inter-layer voltage.

Topological Field Theory Far from Equilibrium

The observable properties of topological quantum matter are often described by topological field theories. Here, we demonstrate that this principle extends beyond thermal equilibrium. To this end, we construct a model of two-dimensional driven open dynamics with a Chern insulator steady state. Within a Keldysh field theory approach, we show that under mild assumptions-particle number conservation and purity of the stationary state-an abelian Chern-Simons theory describes its response to external perturbations. As a corollary, we predict chiral edge modes stabilized by a dissipative bulk.

Local Two-Body Parent Hamiltonians for the Entire Jain Sequence

Using an algebra of second-quantized operators, we develop local two-body parent Hamiltonians for all unprojected Jain states at filling factor n/(2np+1), with integer n and (half-)integer p. We rigorously establish that these states are uniquely stabilized and that zero mode counting reproduces mode counting in the associated edge conformal field theory. We further establish the organizing "entangled Pauli principle" behind the resulting zero mode paradigm and unveil an emergent SU(n) symmetry characteristic of the fixed point physics of the Jain quantum Hall fluid.

Particle-Hole Symmetry and the Fractional Quantum Hall Effect in the Lowest Landau Level

We report on detailed experimental studies of a high-quality heterojunction insulated-gate field-effect transistor (HIGFET) to probe the particle-hole symmetry of the fractional quantum Hall effect (FQHE) states about half-filling in the lowest Landau level. The HIGFET is specially designed to vary the density of a two-dimensional electronic system under constant magnetic fields. We find in our constant magnetic field, variable density measurements that the sequence of FQHE states at filling factors ν=1/3,2/5,3/7… and its particle-hole conjugate states at filling factors 1-ν=2/3,3/5,4/7… have a very similar energy gap. Moreover, a reflection symmetry can be established in the magnetoconductivities between the ν and 1-ν states about half-filling. Our results demonstrate that the FQHE states in the lowest Landau level are manifestly particle-hole symmetric.

Berry Phase and Model Wave Function in the Half-Filled Landau Level

We construct model wave functions for the half-filled Landau level parametrized by "composite fermion occupation-number configurations" in a two-dimensional momentum space, which correspond to a Fermi sea with particle-hole excitations. When these correspond to a weakly excited Fermi sea, they have a large overlap with wave functions obtained by the exact diagonalization of lowest-Landau-level electrons interacting with a Coulomb interaction, allowing exact states to be identified with quasiparticle configurations. We then formulate a many-body version of the single-particle Berry phase for adiabatic transport of a single quasiparticle around a path in momentum space, and evaluate it using a sequence of exact eigenstates in which a single quasiparticle moves incrementally. In this formulation the standard free-particle construction in terms of the overlap between "periodic parts of successive Bloch wave functions" is reinterpreted as the matrix element of a "momentum boost" operator between the full Bloch states, which becomes the matrix elements of a Girvin-MacDonald-Platzman density operator in the many-body context. This allows the computation of the Berry phase for the transport of a single composite fermion around the Fermi surface. In addition to a phase contributed by the density operator, we find a phase of exactly π for this process.

Crystallization in the Fractional Quantum Hall Regime Induced by Landau-Level Mixing

The interplay between strongly correlated liquid and crystal phases for two-dimensional electrons exposed to a high transverse magnetic field is of fundamental interest. Through the nonperturbative fixed-phase diffusion Monte Carlo method, we determine the phase diagram of the Wigner crystal in the ν-κ plane, where ν is the filling factor and κ is the strength of Landau-level (LL) mixing. The phase boundary is seen to exhibit a striking ν dependence, with the states away from the magic filling factors ν=n/(2pn+1) being much more susceptible to crystallization due to Landau-level mixing than those at ν=n/(2pn+1). Our results explain the qualitative difference between the experimental behaviors observed in n- and p-doped gallium arsenide quantum wells and, in particular, the existence of an insulating state for ν<1/3 and also for 1/3<ν<2/5 in low-density p-doped systems. We predict that, in the vicinity of ν=1/5 and ν=2/9, increasing LL mixing causes a transition not into an ordinary electron Wigner crystal, but rather into a strongly correlated crystal of composite fermions carrying two vortices.

Many-body wave functions for correlated systems in magnetic fields: Monte Carlo simulations in the lowest Landau level

We put forward possible wave functions for quantum Hall states in the lowest Landau level. These were deduced from the topological approach based on the relation between braid groups and the quantum statistics, as well as the commensurability condition unavoidable for collective states in magnetic fields. In this paper we demonstrate that the [Formula: see text]-field imposes restrictions on braid trajectories (i.e. elements of the full braid group). This results in the appearance of cyclotron subgroups, instead of the full braid group, for certain filling factors. The fermion representation of cyclotron subgroups defines transformations of wave functions in the quantum Hall regime. Hence, it sets quantum statistics (transformations of [Formula: see text] under exchanges of arguments), which is unavoidable for collective states (in compliance with the framework of Feynman's path integrals). Finally, the topological approach allows to define the hierarchy of fillings in the lowest Landau level, which agree with the hierarchy observed in quantum Hall devices (i.e. in transport measurements). The symmetry of a many-body wave function (i.e. quantum statistics) is always determined by a 1D unitary representation of the system's braid group. Using this topologically-originated property, we demonstrate that many-body wave functions for selected fillings of the lowest Landau level may not be purely antisymmetric. Only systems composed of fermions are investigated. Additionally, we present Monte Carlo calculations in a disc geometry, which remain in a nice agreement with predictions of exact diagonalizations (expected values of potential energy and pair distribution functions are presented). No boundary potential is assumed.

Quantum Hall Effect with Composites of Magnetic Flux Tubes and Charged Particles

Composites formed from charged particles and magnetic flux tubes, proposed by Wilczek, are one model for anyons-particles obeying fractional statistics. Here we propose a scheme for realizing charged flux tubes, in which a charged object with an intrinsic magnetic dipole moment is placed between two semi-infinite blocks of a high-permeability (μ_{r}) material, and the images of the magnetic moment create an effective flux tube. We show that the scheme can lead to a realization of Wilczek's anyons, when a two-dimensional electron system, which exhibits the integer quantum Hall effect, is sandwiched between two blocks of the high-μ_{r} material with a temporally fast response (in the cyclotron and Larmor frequency range). The signature of Wilczek's anyons is a slight shift of the resistivity at the plateau of the IQHE. Thus, the quest for high-μ_{r} materials at high frequencies, which is underway in the field of metamaterials, and the quest for anyons, are here found to be on the same avenue.

Exact Boson-Fermion Duality on a 3D Euclidean Lattice

The idea of statistical transmutation plays a crucial role in descriptions of the fractional quantum Hall effect. However, a recently conjectured duality between a critical boson and a massless two-component Dirac fermion extends this notion to gapless systems. This duality sheds light on highly nontrivial problems such as the half-filled Landau level, the superconductor-insulator transition, and surface states of strongly coupled topological insulators. Although this boson-fermion duality has undergone many consistency checks, it has remained unproven. We describe the duality in a nonperturbative fashion using an exact UV mapping of partition functions on a 3D Euclidean lattice.

Investigating Anisotropic Quantum Hall States with Bimetric Geometry

We construct a low energy effective theory of anisotropic fractional quantum Hall (FQH) states. We develop a formalism similar to that used in the bimetric approach to massive gravity, and apply it to describe Abelian anisotropic FQH states in the presence of external electromagnetic and geometric backgrounds. We derive a relationship between the shift, the Hall viscosity, and a new quantized coupling to anisotropy, which we term anisospin. We verify this relationship by numerically computing the Hall viscosity for a variety of anisotropic quantum Hall states using the density matrix renormalization group. Finally, we apply these techniques to the problem of nematic order and clarify certain disagreements that exist in the literature about the meaning of the coefficient of the Berry phase term in the nematic effective action.

Density-Functional Theory of the Fractional Quantum Hall Effect

A conceptual difficulty in formulating the density-functional theory of the fractional quantum Hall effect is that while in the standard approach the Kohn-Sham orbitals are either fully occupied or unoccupied, the physics of the fractional quantum Hall effect calls for fractionally occupied Kohn-Sham orbitals. This has necessitated averaging over an ensemble of Slater determinants to obtain meaningful results. We develop an alternative approach in which we express and minimize the grand canonical potential in terms of the composite fermion variables. This provides a natural resolution of the fractional-occupation problem because the fully occupied orbitals of composite fermions automatically correspond to fractionally occupied orbitals of electrons. We demonstrate the quantitative validity of our approach by evaluating the density profile of fractional Hall edge as a function of temperature and the distance from the delta dopant layer and showing that it reproduces edge reconstruction in the expected parameter region.

Statistical Transmutation in Floquet Driven Optical Lattices

We show that interacting bosons in a periodically driven two dimensional (2D) optical lattice may effectively exhibit fermionic statistics. The phenomenon is similar to the celebrated Tonks-Girardeau regime in 1D. The Floquet band of a driven lattice develops the moat shape, i.e., a minimum along a closed contour in the Brillouin zone. Such degeneracy of the kinetic energy favors fermionic quasiparticles. The statistical transmutation is achieved by the Chern-Simons flux attachment similar to the fractional quantum Hall case. We show that the velocity distribution of the released bosons is a sensitive probe of the fermionic nature of their stationary Floquet state.

Luttinger Theorem for the Strongly Correlated Fermi Liquid of Composite Fermions

While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion (CF) Fermi sea arises as a nonperturbative consequence of emergent gauge fields in a system where there was no Fermi sea to begin with. A mean-field picture suggests two Fermi seas, of composite fermions made from electrons or holes in the lowest Landau level, which occupy different areas away from half filling and thus appear to represent distinct states. Using the microscopic theory of composite fermions, which satisfies particle-hole symmetry in the lowest Landau level to an excellent approximation, we show that the Fermi wave vectors at filling factors ν and 1-ν are equal when expressed in units of the inverse magnetic length, and are generally consistent with the experimental findings of Kamburov et al. [Phys. Rev. Lett. 113, 196801 (2014)]. Our calculations suggest that the area of the CF Fermi sea may slightly violate the Luttinger area rule.

Spontaneous formation of a nonuniform chiral spin liquid in a moat-band lattice

A number of lattices exhibit moatlike band structures, i.e., a band with infinitely degenerate energy minima attained along a closed line in the Brillouin zone. If such a lattice is populated with hard-core bosons, the degeneracy prevents their condensation. At half-filling, the system is equivalent to the s=1/2  XY model at a zero magnetic field, while the absence of condensation translates into the absence of magnetic order in the XY plane. Here, we show that the ground state breaks time reversal as well as inversion symmetries. This state, which may be identified with the chiral spin liquid, has a bulk gap and chiral gapless edge excitations. The applications of the developed analytical theory include an explanation of recent numerical findings and a suggestion for the chiral spin liquid realizations in experiments with cold atoms in optical lattices.

Framing anomaly in the effective theory of the fractional quantum Hall effect

We consider the geometric part of the effective action for the fractional quantum Hall effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions. In the lowest order in gradients, the linear response generating functional includes Chern-Simons, Wen-Zee, and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states.

Quantum anomalous Hall insulator of composite fermions

We show that a weak hexagonal periodic potential can transform a two-dimensional electron gas with an even-denominator magnetic filling factor into an quantum anomalous hall insulator of composite fermions, giving rise to the fractionally quantized Hall effect. The system provides a realization of the Haldane honeycomb-net model, albeit in a composite fermion system. We further propose a trial wave function for the state, and numerically evaluate its relative stability against the competing Hofstadter state. Possible sets of experimental parameters are proposed.

Organization of strongly interacting directed polymer liquids in the presence of stringent constraints

The impact of impenetrable obstacles on the energetics and equilibrium structure of strongly repulsive directed polymers is investigated. As a result of the strong interactions, regions of severe polymer depletion and excess are found in the vicinity of the obstacle, and the associated free-energy cost is found to scale quadratically with the average polymer density. The polymer-polymer interactions are accounted for via a sequence of transformations: from the 3D line liquid to a 2D fluid of Bose particles to a 2D composite fermion fluid and, finally, to a 2D one-component plasma. The results presented here are applicable to a range of systems consisting of noncrossing directed lines.

Phase diagram of the two-component fractional quantum Hall effect

We calculate the phase diagram of the two component fractional quantum Hall effect as a function of the spin or valley Zeeman energy and the filling factor, which reveals new phase transitions and phase boundaries spanning many fractional plateaus. This phase diagram is relevant to the fractional quantum Hall effect in graphene and in GaAs and AlAs quantum wells, when either the spin or valley degree of freedom is active.

Spin transition in the ν=8/3 fractional quantum Hall effect

We present here the results from a density dependent study of the activation energy gaps of the fractional quantum Hall effect states at Landau level fillings ν=8/3 and 7/3 in a series of high quality quantum wells. In the density range from 0.5×10(11) to 3×10(11) cm(-2), the 7/3 energy gap increases monotonically with increasing density, supporting its ground state being spin polarized. For the 8/3 state, however, its energy gap first decreases with increasing density, almost vanishes at n~0.8×10(11) cm(-2), and then turns around and increases with increasing density, clearly demonstrating a spin transition.

Weakly coupled Pfaffian as a type I quantum Hall liquid

The Pfaffian phase in the proximity of a half-filled Landau level is understood to be a p+ip superconductor of composite fermions. We consider the properties of this paired quantum Hall phase when the pairing energy is small, i.e., in the weak-coupling, BCS limit, where the coherence length is much larger than the charge screening length. We find that, as in a type I superconductor, vortices attract so that, upon varying the magnetic field from its magic value at ν=5/2, the system exhibits Coulomb frustrated phase separation. We propose that the weakly and strongly coupled Pfaffians exemplify a general dichotomy between type I and type II quantum Hall fluids.

Cyclotron braid group structure for composite fermions

Although they describe properties of 2D Hall systems in the fractional quantum regime well, composite fermions suffer from the unexplained character of the localized magnetic field flux-tubes attached to each particle in order to reproduce the Laughlin correlations via Aharonov-Bohm phase shifts. The identification of the cyclotron trajectories of 2D charged particles as accessible classical trajectories within the braid group approach at the magnetic field presence, allows, however, for the avoidance of the construction with fluxes. We introduce cyclotron braid subgroups for charged 2D systems at the fractional Landau-level filling associated in a more natural way with composite fermions without invoking field flux-tubes. The Aharonov-Bohm phase shifts caused by fluxes are replaced with the phase gain due to multi-loop cyclotron trajectories unavoidably occurring at the fractional filling of 1/p (p is an odd integer). Another approach to composite particles, using so-called vortices, is also discussed from the point of view of the cyclotron braid group description (for both odd and even p integers).

Hamiltonian theory of disorder at nu = 1/3

The Hamiltonian theory of the fractional quantum Hall regime provides a simple and tractable approach to calculating gaps, polarizations, and many other physical quantities. In this Letter we include disorder in our treatment and show that a simple model with minimal assumptions produces results consistent with a range of experiments. In particular, the interplay between disorder and interactions can result in experimental signatures which mimic those of spin textures.

Lorentz shear modulus of fractional quantum Hall states

We show that the Lorentz shear modulus of macroscopically homogeneous electronic states in the lowest Landau level is proportional to the bulk modulus of an equivalent system of interacting classical particles in the thermodynamic limit. Making use of this correspondence, we calculate the Lorentz shear modulus of Laughlin's fractional quantum Hall states at filling factor ν = 1/m (m an odd integer) and find that it is equal to [Formula: see text], where n is the density of particles and the sign depends on the direction of magnetic field.

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.

Aharanov-Bohm interference and fractional statistics in a quantum Hall interferometer

We compute the temperature, voltage, and magnetic field dependences of the conductance oscillations of a model interferometer designed to measure the fractional statistics of the quasiparticles in the fractional quantum Hall effect. The geometry is the same as that used in recent experiments. With appropriate assumptions concerning the relative areas of the inner and outer rings of the interferometer, we find the theoretical results, including the existence of super periodic Aharonov-Bohm oscillations, to be in remarkably good agreement with experiment. We then make additional experimental predictions with no adjustable parameters which, if verified, would confirm the proposed interpretation of the experiment as a measurement of fractional statistics.

Microscopic verification of topological electron-vortex binding in the lowest Landau-level crystal state

When two-dimensional electrons are subjected to a very strong magnetic field, they are believed to form a triangular crystal. By a direct comparison with the exact wave function, we demonstrate that this crystal is not a simple Hartree-Fock crystal of electrons but an inherently quantum mechanical crystal characterized by a nonperturbative binding of quantized vortices to electrons. It is suggested that this has qualitative consequences for experiment.

Competition between a fractional quantum hall liquid and bubble and Wigner crystal phases in the third Landau level

Magnetotransport measurements were performed in an ultrahigh mobility GaAs/AlGaAs quantum well of density approximately 3.0 x 10(11) cm(-2). The temperature dependence of the magnetoresistance Rxx was studied in detail in the vicinity of nu=9/2. In particular, we discovered new minima in Rxx at a filling factor nu approximately 41/5 and 44/5, but only at intermediate temperatures 80 approximately less than T approximately less than 120 mK. We interpret these as evidence for a fractional quantum Hall liquid forming in the N=2 Landau level and competing with bubble and Wigner crystal phases favored at lower temperatures. Our data suggest that a magnetically driven insulator-insulator quantum phase transition occurs between the bubble and Wigner crystal phases at T=0.

Dynamical role of anyonic excitation statistics in rapidly rotating bose gases

We show that for rotating harmonically trapped Bose gases in a fractional quantum Hall state, the anyonic excitation statistics in the rotating gas can effectively play a dynamical role. For particular values of the two-dimensional coupling constant g=-2pih2(2k-1)/m, where k is a positive integer, the system becomes a noninteracting gas of anyons, with exactly obtainable solutions satisfying Bogomol'nyi self-dual order parameter equations. Attractive Bose gases under rapid rotation thus can be stabilized in the thermodynamic limit due to the anyonic statistics of their quasiparticle excitations.

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.

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.

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.

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.