We directly measure the chemical potential jump in the low-temperature limit when the filling factor traverses the nu = 1/3 and nu = 2/5 fractional gaps in two-dimensional (2D) electron system in GaAs/AlGaAs single heterojunctions. In high magnetic fields B, both gaps are linear functions of B with slopes proportional to the inverse fraction denominator, 1/q. The fractional gaps close partially when the Fermi level lies outside. An empirical analysis indicates that the chemical potential jump for an IDEAL 2D electron system, in the highest accessible magnetic fields, is proportional to q^{-1}B^{1/2}.
We explore both analytically and numerically the properties of doped t-J models on a class of highly frustrated lattices, such as the kagome and the pyrochlore lattice. Focussing on a particular sign of the hopping integral and antiferromagnetic exchange, we find a generic symmetry breaking instability towards a twofold degenerate ground state at a fractional filling below half filling. These states show modulated bond strengths and only break lattice symmetries. They can be seen as a generalization of the well-known valence bond solid states to fractional filling.
We investigate the infinite-dimensional two-orbital Hubbard model at arbitrary band fillings. By means of the self-energy functional approach, we discuss the stability of the metallic state in the systems with same and different bandwidths. It is found that the Mott insulating phases are realized at commensurate band fillings. Furthermore, it is clarified that the orbital selective Mott phase with one orbital localized and the other itinerant is stabilized even at fractional band fillings in the system with different bandwidths.
Quantum Hall effects with multicomponent internal degrees of freedom facilitate the playground of novel emergent topological orders. Here, we explore the correlated topological phases of two-component hardcore bosons at a total filling factor $ν=2/5$ in both lattice Chern band models and Landau level continuum model under the interplay of intracomponent and intercomponent repulsions. We give the numerically theoretical demonstration of the emergence of two competing distinct fractional quantum Hall states: Halperin (441) fractional quantum Hall effect and Halperin (223) fractional quantum Hall…
We study a spinless hardcore boson model on checkerboard lattices by Green function Monte Carlo method. At half filling, the ground state energy is obtained up to $28\times 28$ lattice and extrapolated to infinite size, the staggered pseudospin magnetization is found to vanish in the thermodynamic limit. Thus the $(π,π)$ charge order is absent in this system. Away from half filling, two defects induced by each hole (particle) may carry fractional charge ($\pm e/2$). For one hole case, we study how the defect-defect correlation changes with $t/J$, which is the ratio between the hopping integral…
We propose a systematical approach to construct generic fractional quantum anomalous Hall (FQAH) states, which are generalizations of the fractional quantum Hall states to lattice models with zero net magnetic field and full lattice translation symmetry. Local and translationally invariant Hamiltonians can also be constructed, for which the proposed states are unique ground states. Our result demonstrates that generic chiral topologically ordered states can be realized in lattice models, without requiring magnetic translation symmetry and Landau level structure. We further generalize our appro…
We study the fractional quantum Hall effect at filling fractions 7/3 and 5/2 in the presence of the spin-orbit interaction, using the exact diagonalization method and the density matrix renormalization group (DMRG) method in a spherical geometry. Trial wave functions at these fillings are the Laughlin state and the Moore-Reed-Pfaffian state. The ground state excitation energy gaps and pair-correlation functions at fractional filling factor 7/3 and 5/2 in the second Landau level are calculated. We find that the spin-orbit interaction stabilizes the fractional quantum Hall states.
Viewpoint on Nigel R. Cooper and Jean Dalibard, "Reaching Fractional Quantum Hall States with Optical Flux Lattices", Phys. Rev. Lett. 110, 185301 (2013), and N. Y. Yao, A. V. Gorshkov, C. R. Laumann, A. M. Läuchli, J. Ye, and M. D. Lukin, "Realizing Fractional Chern Insulators in Dipolar Spin Systems", Phys. Rev. Lett. 110, 185302 (2013). Researchers propose new ways to recreate fractional quantum Hall physics using ultracold atoms and molecules.
We studied neutral excitations in a two-dimensional electron system with an orbital momentum $ΔM = 1$ and spin projection over magnetic field axis $ΔS_z = 1$ in the vicinity of a filling factor of 3/2. It is shown that the 3/2 state is a singular point in the filling factor dependence of the spin ordering of the two-dimensional electron system. In the vicinity of $ν=3/2$, a significant increase in the relaxation time ($τ= 13$ $μ\text{s}$) for the excitations to the ground state is exhibited even though the number of vacancies in the lowest energy level is macroscopically large. The decrease of…
We discuss quantum Hall effects in a gapped insulator on a periodic two-dimensional lattice. We derive a universal relation among the the quantized Hall conductivity, and charge and flux densities per physical unit cell. This follows from the magnetic translation symmetry and the large gauge invariance, and holds for a very general class of interacting many-body systems. It can be understood as a combination of Laughlin's gauge invariance argument and Lieb-Schultz-Mattis-type theorem. A variety of complementary arguments, based on a cut-and-glue procedure, the many-body electric polarization, …
We note an implication of chiral Luttinger liquid based edge state description of the fractional quantum Hall effect. By considering several examples that involve backward moving neutral modes, arising from either composite fermions with reverse flux attached or edge reconstruction, we show that non-universality of the edge exponent implies non-universality of the Hall conductance, as measured in the two-terminal conductance.
Hall coefficient implies the mechanism for reconstruction of a Fermi surface, distinguishing competing scenarios for Mott criticality such as electron fractionalization, dynamical mean-field theory, and metal-insulator transition driven by symmetry breaking. We find that electron fractionalization leaves a signature for the Hall coefficient at Mott criticality in two dimensions, a unique feature differentiated from other theories. We evaluate the Hall coefficient based on the quantum Boltzman equation approach, guaranteeing gauge invariance in both longitudinal and transverse transport coeffic…
We formulate the Kohn-Sham equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field. Self-consistent solutions of the KS equations demonstrate that our formulation captures not only configurations with non-uniform densities but also topological properties such as fractional charge and fractional braid statistics for the quasiparticles excitations. This method should enable a realistic modeling of the edge structure, the effect of disorder, spin physics, …
Alternative $ν+ν$-picture of bosonic fractional Chern insulators at high filling factors in multiple flat-band systems
National Laboratory of Solid State Microstructure, Department of Physics, Nanjing University（南京大学固体微结构物理国家重点实验室）；College of Physics Science and Technology, Yangzhou University（扬州大学物理科学与技术学院）；Jiangsu Key Laboratory of Quantum Information Science and Technology, Nanjing University（南京大学江苏省量子信息科学与技术重点实验室）
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the sma…
We present a generalization of the composite Fermion picture for a muticomponent quantum Hall plasma which contains particle with different effective charges. The model predicts very well the low-lying states of a $ν=5/2$ quantum Hall state found in numerical diagonalization.
The entanglement entropy of $ν=1/2$ and $ν=9/2$ quantum Hall states in the presence of short range disorder has been calculated by direct diagonalization. Spin polarized electrons are confined to a single Landau level and interact with long range Coulomb interaction. For $ν=1/2$ the entanglement entropy is a smooth monotonic function of disorder strength. For $ν=9/2$ the entanglement entropy is non monotonic suggestive of a solid-liquid phase transition. As a model of the transition at $ν=1/2$ free fermions with disorder in 2 dimensions were studied. Numerical evidence suggests the entanglemen…
We construct a class of lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be controllably solved in their low energy sectors, through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem and is generalizable.
We experimentally study equilibration across the sample edge at high fractional filling factors 4/3, 5/3 under experimental conditions, which allow us to obtain high imbalance conditions. We find a lack of the full equilibration across the edge even in the flat-band situation, where no potential barrier survives at the sample edge. We interpret this result as the manifestation of complicated edge excitation structure at high fractional filling factors 4/3, 5/3. Also, a mobility gap in the $ν_c=1$ incompressible strip is determined in normal and tilted magnetic fields.
Fractional quantum Hall-superconductor heterostructures may provide a platform towards non-abelian topological modes beyond Majoranas. However their quantitative theoretical study remains extremely challenging. We propose and implement a numerical setup for studying edge states of fractional quantum Hall droplets with a superconducting instability. The fully gapped edges carry a topological degree of freedom that can encode quantum information protected against local perturbations. We simulate such a system numerically using exact diagonalization by restricting the calculation to the quasihole…
By allowing the spin degrees of freedom, we present a generalized spin allowed $U(1)\times U(1)$ Chern-Simons theory of fractional quantum Hall effects for odd and even denominator filling factors in single layers. This theory is shown to reproduce all possible odd denominator filling factors corresponding to spin-unpolarized, partially polarized, and fully polarized fractional quantum Hall states. Closely following our earlier theory, we derive the formal expressions of electromagnetic polarization tensors and Hall conductivity for the spin-unpolarized and partially polarized fractional quant…
We develop a hydrodynamic field theory of the three-dimensional fractional quantum Hall effect, which was recently proposed to exist in magnetic Weyl semimetals, when the Weyl nodes are gapped by strong repulsive interactions. This theory takes the form of a BF theory, which contains both one-form and two-form gauge fields, coupling to quasiparticle and loop excitations correspondingly. It may be regarded as a generalization of the Chern-Simons theory of two-dimensional fractional quantum Hall liquids to three dimensions.
New trial wave functions corresponding to half filling quantum Hall states are proposed. These wave functions are constructed by first pairing up the quasielectrons of the 1/3 Laughlin quantum Hall state, with the same relative angular momentum for each pair, and then making the paired quasielectrons condense into a 1/4 Laughlin state. The quasiparticle excitations of the proposed wave functions carry $\pm1/4$ of electron charge, and obey Abelian fractional statistics. In the spherical geometry, the total flux quanta $N_ϕ$ is shown to be related to the number of electrons $N$ by $N_ϕ = 2N-(5-q…
In this letter, we discuss the recently proposed fractional quantum Hall effect in the absence of Landau levels. It is shown that the parton construction can explain all properties of 1/3 state, including the effective charge of quasi-particles, their statistics and the many-body ground-state degeneracy. The low energy description of these states has been discussed. We also generalize our model to construct the hierarchical quantum Hall states at filling fractions other than $1/m$.
The integer quantum Hall state occurs when the Landau levels are fully occupied by the fermions, while the fractional quantum Hall state usually emerges when the Landau level is partially filled by the strongly correlated fermions or bosons. Here, we report two fractional Chern insulating states of the hard-core bosons in a multi-band lattice model hosting topological flat bands with high Chern number. The previously proposed $ν=1/3$ fractional Chern insulating state inherited from the high Chern number $C=2$ of the lowest topological flat band is revisited by the infinite density matrix renor…
We report the observation of developing fractional quantum Hall states at Landau level filling factors $ν= 1/2$ and 1/4 in electron systems confined to wide GaAs quantum wells with significantly $asymmetric$ charge distributions. The very large electric subband separation and the highly asymmetric charge distribution at which we observe these quantum Hall states, together with the fact that they disappear when the charge distribution is made symmetric, suggest that these are one-component states, possibly described by the Moore-Read Pfaffian wavefunction.
We construct a holographic model of a system of strongly-coupled fermions in 2+1 dimensions based on a D8-brane probe in the background of D2-branes. The Minkowski embeddings of the D8-brane represent gapped quantum Hall states with filling fraction one. By computing the conductivity and phase structure, we find results qualitatively similar to the experimental observations and also to the recent D3-D7' model.
We report experiments in a large, 2.5 micron diameter Fabry-Perot quantum Hall interferometer with two tunneling constrictions. Interference fringes are observed as conductance oscillations as a function of applied magnetic field (the Aharonov-Bohm flux through the electron island) or a global backgate voltage (electronic charge in the island). Depletion is such that in the fractional quantum Hall regime, filling 1/3 current-carrying chiral edge channels pass through constrictions when the island filling is 2/5. The interferometer device is calibrated with fermionic electrons in the integer qu…
We study the recently observed graphene fractional quantum Hall state at a filling factor $ν_G=1/3$ using a four-component trial wave function and exact diagonalization calculations. Although it is adiabatically connected to a 1/3 Laughlin state in the upper spin branch, with SU(2) valley-isospin ferromagnetic ordering and a completely filled lower spin branch, it reveals physical properties beyond such a state that is the natural ground state for a large Zeeman effect. Most saliently, it possesses at experimentally relevant values of the Zeeman gap low-energy spin-flip excitations that may be…
We consider stripe formation in quantum Hall systems at integer filling factors. We use Hartree-Fock calculations to obtain the phase diagram of bilayer quantum Hall systems at $ν=4n+1$ in a tilted magnetic field. We derive and analyze an effective low energy theory for the stripe phases which may be present in such systems. We discuss the possibility of stripe formation in wide well systems in a tilted magnetic field and suggest that the resistance anisotropy, observed recently by W. Pan et.al. [phys. Rev. B 64 (2001) 121305], may be due to the existence of a skyrmion stripe phase.
In this paper, the density-matrix renormalization group method is employed to investigate the fractional quantum Hall effect at filling fractions $ν=1/3$ and 5/2. We first present benchmark results at both filling fractions for large system sizes to show the accuracy as well as the capability of the numerical algorithm. Furthermore, we show that by keeping a large number of basis states, one can also obtain accurate entanglement spectrum at $ν=5/2$ for large system with electron number up to $N_e=34$, much larger than systems previously studied. Based on a finite-size scaling analysis, we demo…
The nature of the state at low Landau-level filling factors has been a longstanding puzzle in the field of the fractional quantum Hall effect. While theoretical calculations suggest that a crystal is favored at filling factors $ν\lesssim 1/6$, experiments show, at somewhat elevated temperatures, minima in the longitudinal resistance that are associated with fractional quantum Hall effect at $ν=$ 1/7, 2/11, 2/13, 3/17, 3/19, 1/9, 2/15 and 2/17, which belong to the standard sequences $ν=n/(6n\pm 1)$ and $ν=n/(8n\pm 1)$. To address this paradox, we investigate the nature of some of the low-$ν$ st…
We consider tunneling through two point contacts between two edges of Quantum Hall liquids of different filling factors $ν_{0,1}=1/ (2m_{0,1}+1)$ with $m_0-m_1\equiv m>0$. Properties of the antidot formed between the point contacts in the strong-tunneling limit are shown to be very different from the $ν_0 =ν_1$ case, and include vanishing average total current in the two contacts and quasiparticles of charge $e/m$. For $m>1$, quasiparticle tunneling leads to non-trivial $m$-state dynamics of effective flux through the antidot which restores the regular ``electron'' periodicity of the current i…
We compute the physical properties of non-Abelian Fractional Quantum Hall (FQH) states described by Jack polynomials at general filling $ν=\frac{k}{r}$. For $r=2$, these states are identical to the $Z_k$ Read-Rezayi parafermions, whereas for $r>2$ they represent new FQH states. The $r=k+1$ states, multiplied by a Vandermonde determinant, are a non-Abelian alternative construction of states at fermionic filling $2/5, 3/7, 4/9...$. We obtain the thermal Hall coefficient, the quantum dimensions, the electron scaling exponent, and show that the non-Abelian quasihole has a well-defined propagator f…
We calculate a topological invariant, whose value would coincide with the Chern number in case of integer quantum Hall effect, for fractional quantum Hall states. In case of Abelian fractional quantum Hall states, this invariant is shown to be equal to the trace of the K-matrix. In case of non-Abelian fractional quantum Hall states, this invariant can be calculated on a case by case basis from the conformal field theory describing these states. This invariant can be used, for example, to distinguish between different fractional Hall states numerically even though, as a single number, it cannot…
We investigate the algebraic structure of flat energy bands a partial filling of which may give rise to a fractional quantum anomalous Hall effect (or a fractional Chern insulator) and a fractional quantum spin Hall effect. Both effects arise in the case of a sufficiently flat energy band as well as a roughly flat and homogeneous Berry curvature, such that the global Chern number, which is a topological invariant, may be associated with a local non-commutative geometry. This geometry is similar to the more familiar situation of the fractional quantum Hall effect in two-dimensional electron sys…
We derive the low-energy theory of semi-quantized quantum Hall states, a recently observed class of gapless bilayer fractional quantum Hall states. Our theory shows these states to feature gapless quasiparticles of fractional charge coupled to an emergent Chern-Simons gauge field. These gapless quasiparticles can be understood as composites of electrons and Laughlin-like quasiparticles. We show that semi-quantized quantum Hall states exhibit perfect interlayer drag, host non-Fermi liquid physics, and serve as versatile parent states for fully gapped topological phases hosting anyonic excitatio…
We present results of extensive numerical calculations on the ground state of electrons in the first excited (n=1) Landau level with Coulomb interactions, and including non-zero thickness effects, for filling factors 12/5 and 13/5 in the torus geometry. In a region that includes these experimentally-relevant values, we find that the energy spectrum and the overlaps with the trial states support the previous hypothesis that the system is in the non-Abelian k = 3 liquid phase we introduced in a previous paper.
The electronic excitations at the edges of a Hall bar not much wider than a few magnetic lengths are studied theoretically at filling $ν= 2$. Both mean-field theory and Luttinger liquid theory techniques are employed for the case of a null Zeeman energy splitting. The first calculation yields a stable spin-density wave state along the bar, while the second one predicts dominant Wigner-crystal correlations along the edges of the bar. We propose an antiferromagnetic Wigner-crystal groundstate for the edge electrons that reconciles the two results. A net Zeeman splitting is found to produce canti…
The concept of fractional charge is central to the theory of the fractional quantum Hall effect (FQHE). Here I use exact diagonalization as well as configuration space renormalization (CSR) to study finite clusters which are large enough to contain two independent edges. I analyze the conditions of resonant tunneling between the two edges. The "computer experiment" reveals a periodic sequence of resonant tunneling events consistent with the experimentally observed fractional quantization of electric charge in units of e/3 and e/5.
We use the non-equilibrium bosonization technique to study the effects of Coulomb interactions in mesoscopic electron colliders based on quantum Hall (QH) edge states at filing factor $ν= 2$. The current cross-correlations and Fano factor, which carry the information about the exclusion statistics, are calculated. It is shown that both these quantities have a non-analytical dependence on the source transparency, which scales as $\log(1/T_s)$ at small $T_s \ll 1$. This is the consequence of electron-electron interactions in the outgoing non-equilibrium states of the collider.
We explain effective charge anomalies recently observed for fractional quantum Hall edge states at $ν=5/2$ [M. Dolev, Y. Gross, Y. C. Chung, M. Heiblum, V. Umansky, and D. Mahalu, Phys.Rev. B. \textbf{81}, 161303(R) (2010)]. The experimental data of differential conductance and excess noise are fitted, using the anti-Pfaffian model, by properly take into account renormalizations of the Luttinger parameters induced by the coupling of the system with an intrinsic $1/f$ noise. We demonstrate that a peculiar agglomerate excitation with charge $e/2$, double of the expected $e/4$ charge, dominates t…
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 $+(-)1/m^3$ in the total configuration space CP$^3$. The density correlation function of the Zhang-Hu states indicates that they are incompressible liquid.
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.
We elucidate the nature of neutral collective excitations of fractional quantum Hall liquids in the long-wavelength limit. We demonstrate that they are chiral gravitons carrying angular momentum - 2, which are quanta of quantum motion of an internal metric, and show up as resonance peaks in the systems response to what is the fractional Hall analog of gravitational waves. Relation with existing and possible future experimental work that can detect these fractional quantum Hall gravitons and reveal their chirality are discussed.
A quasiclassical theory for dc magnetotransport in a modulated quantum Hall system near filling factor $ν={1/2}$ is presented. A weak one-dimensional electrostatic potential acts on the two-dimensional electron gas. Closed form analytic expressions are obtained for the resistivity $ρ_\perp$ corresponding to a current at right angles to the direction of the modulation lines as well as a smaller component $ρ_{||}$ for a current along the direction of the modulation lines. It is shown that both resistivity components are affected by the presence of the modulation. Numerical results are presented …
We propose ways to create and detect fractionally charged excitations in \emph{integer} quantum Hall edge states. The charge fractionalization occurs due to the Coulomb interaction between electrons propagating on different edge channels. The fractional charge of the soliton-like collective excitations can be observed in time resolved or frequency dependent shot noise measurements.
A microscopic confirmation of the fractional statistics of the {\em quasiparticles} in the fractional quantum Hall effect has so far been lacking. We calculate the statistics of the composite-fermion quasiparticles at $ν=1/3$ and $ν=2/5$ by evaluating the Berry phase for a closed loop encircling another composite-fermion quasiparticle. A careful consideration of subtle perturbations in the trajectory due to the presence of an additional quasiparticle is crucial for obtaining the correct value of the statistics. The conditions for the applicability of the fractional statistics concept are discu…
The Bose-Hubbard model is extended to include nearest and far neighbor interactions and is related to the fractional quantum Hall effect (FQHE). Both models may be studied in optical lattices with quantum gases. The ground state is calculated for the extended Bose-Hubbard model with strong repulsive interactions (weak hopping). Incompressible Mott insulator states are found at rational filling fractions compatible with the principal and secondary FQHE filling fractions of the lowest Landau levels observed experimentally. It is discussed to which extent these states at fractional filling surviv…
We establish a variational principle for properly mapping a fractional quantum Hall (FQH) state to a fractional Chern insulator (FCI). We find that the mapping has a gauge freedom which could generate a class of FCI ground state wave functions appropriate for different forms of interactions. Therefore, the gauge should be fixed by a variational principle that minimizes the interaction energy of the FCI model. For a soft and isotropic electron-electron interaction, the principle leads to a gauge coinciding with that for maximally localized \emph{two-dimensional} projected Wannier functions of a…
We address the issue of an apparent disagreement between theory and experiment on the I-V characteristic of electron tunneling from a metal to the edge of a two-dimensional electron gas in the fractional quantum Hall regime. A part of our result is a theory for the edge of the half-filled Landau level.
We discuss the orbital effect of a tilted magnetic field on the quantum Hall effect in parabolic quantum wells. Many-body states realized at the fractional 1/3 and 1/2 filling of the second electronic subband are studied using finite-size exact diagonalization. In both cases, we obtain the phase diagram consisting of a fractional quantum Hall fluid phase that persists for moderate tilts, and eventually undergoes a direct transition to the stripe phase. It is shown that tilting of the field probes the geometrical degree of freedom of fractional quantum Hall fluids, and can be partly related to …
We show that in quantum Hall systems at half-filling, edge potentials alone can drive transitions between the Pfaffian and anti-Pfaffian topological phases. We conjecture this is true in realistic systems even in the presence of weak bulk interactions that break the particle-hole symmetry. The strong effects of edge potentials could be understood from different topological shifts of competing phases, manifested on the disk geometry as the variation of orbital numbers at fixed number of particles. In particular, we show analytically particle-hole conjugation of Hamiltonians on the disk is equiv…
We numerically study the fractional quantum Hall effect at filling factors $ν=12/5$ and 13/5 (the particle-hole conjugate of 12/5) in high-quality two-dimensional GaAs heterostructures via exact diagonalization including finite well width and Landau level mixing. We find that Landau level mixing suppresses $ν=13/5$ fractional quantum Hall effect relative to $ν=12/5$. By contrast, we find both $ν=2/5$ and (its particle-hole conjugate) $ν=3/5$ fractional quantum Hall effects in the lowest Landau level to be robust under Landau level mixing and finite well-width corrections. Our results provide a…
Because of the spin and Dirac-valley degrees of freedom, graphene allows the observation of one-, two- or four-component fractional quantum Hall effect in different parameter regions. We argue that some, though not all, apparently puzzling features observed in recent experiments are consistent with a two-component fractional quantum Hall effect, with the electron spin frozen but the Dirac-valley symmetry approximately intact. In the SU(4) limit, we predict that new low-energy Goldstone modes determine the stability of the fractional quantum Hall states at 2/5, 3/7 etc.; SU(4) skyrmions are not…
The observation of new insulating phases of two-dimensional electrons in the first excited Landau level is reported. These states, which are manifested as re-entrant 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.
We study theoretically resonant tunneling of composite fermions through their quasi-bound states around a fractional quantum Hall island, and find a rich set of possible transitions of the island state as a function of the magnetic field or the backgate voltage. These considerations have possible relevance to a recent experimental study, and bring out many subtleties involved in deducing fractional braiding statistics.
