Fractional Fillings Research Articles

Topological Fractional Pumping with Alkaline-Earth-Like Atoms in Synthetic Lattices.

Alkaline-earth(-like) atoms, trapped in optical lattices and in the presence of an external gauge field, can form insulating states at given fractional fillings. We will show that, by exploiting these properties, it is possible to realize a topological fractional pump. Our analysis is based on a many-body adiabatic expansion, on simulations with time-dependent matrix product states, and, for a specific form of atom-atom interaction, on an exactly solvable model of fractional pump. The numerical simulations allow us to consider a realistic setup amenable of an experimental realization. As a further consequence, the measure of the center-of-mass shift of the atomic cloud would constitute the first measurement of a many-body Chern number in a cold-atom experiment.

Unconventional fractional quantum Hall effect in monolayer and bilayer graphene

The commensurability condition is applied to determine the hierarchy of fractional fillings of Landau levels in monolayer and in bilayer graphene. The filling rates for fractional quantum Hall effect (FQHE) in graphene are found in the first three Landau levels in one-to-one agreement with the experimental data. The presence of even denominator filling fractions in the hierarchy for FQHE in bilayer graphene is explained. Experimentally observed hierarchy of FQHE in the first and second Landau levels in monolayer graphene and in the zeroth Landau level in bilayer graphene is beyond the conventional composite fermion interpretation but fits to the presented nonlocal topology commensurability condition.

Commensurability condition and hierarchy of fillings for FQHE in higher Landau levels in conventional 2DEG systems and in graphene—monolayer and bilayer

The structure of the filling rate hierarchy referred to as the fractional quantum Hall effect is studied in higher Landau levels using the commensurability condition. The hierarchy of fillings that are derived in this manner is consistent with the experimental observations of the first three Landau levels in conventional semiconductor Hall systems. The relative poverty of the fractional structure in higher Landau levels compared with the lowest Landau level is explained using commensurability topological arguments. The commensurability criterion for correlated states for higher Landau levels (with ) including the paired states at half fillings of the spin-subbands of these levels is formulated. The commensurability condition is applied to determine the hierarchy of the fractional fillings of Landau levels in the monolayer and bilayer graphene. Good agreement with current experimental observations of fractional quantum Hall effect in the graphene monolayer and bilayer is achieved. The presence of even denominator rates in the hierarchy for fractional quantum Hall effect in the bilayer graphene is also explained.

Design of Nickel-rich Layered Oxides Using d Electronic Donor for Redox Reactions

Through first-principles calculations and experimental observations, we first present the correlation between the Ni and Mn ratio and the redox behaviors of the layered NCM cathodes. The equilibrium potentials based on redox reactions of Ni2+/Ni3+ are highly dependent on the Mn ratio (NCM523 and NCM721: ∼3.7 and 3.5 V) because of a donor electron, in the eg band, transferred from Mn to Ni owing to their crystal field splitting (CFS) with different electronegativities, leading to oxidation states of Ni2+-like and Mn4+. Considering the electronic donor (Mn) based on CFS with electronegativity of transition metals (TMs), we finally expect V as a promising doping source to provide donor electrons for Ni redox reactions in Ni-rich layered oxides, leading to be higher delithiation potentials (NCV523: 3.8 V). From our theoretical calculations in the NCV oxide, the oxidation states of Ni and V are stable Ni2+-like and V5+, respectively, and the fractional d-band fillings of Ni are the highest value as compared wi...

Fractional quantum Hall states of dipolar gases in Chern bands

We study fermions and hard-core bosons with long-range dipolar interactions at fractional fillings in a topological checkerboard lattice with short-range hoppings up to next-next-nearest neighbors [T. Neupert, L. Santos, C. Chamon, and C. Mudry, Phys. Rev. Lett. 106, 236804 (2011)]. We consider the case that the dipoles are aligned in the perpendicular direction by an external field without the complication of anisotropic interaction. Using exact diagonalization, we find clear signatures of fractional quantum Hall (FQH) states at filling factors 1/3 and 1/5 for fermions (1/2 and 1/4 for bosons) in the lowest Chern band with a robust spectrum gap at moderate dipolar interaction strength. The robustness of these FQH states against a long-range interaction tail and band flatness is investigated. When the dipolar interaction decreases, the fermionic FQH states turn into normal states, and the bosonic 1/4 FQH state turns into a superfluid state. The bosonic 1/2 FQH state survives even in the absence of the dipolar interaction, but vanishes when the hard core becomes a soft core with a critical on-site repulsion. In the thin torus limit, the static density structure factors indicate that the FQH state turns into a commensurate charge density wave state.

Imaging quantum-dot-confined electron density in transition to fractional quantum Hall regime

We consider mapping the charge density confined in quantum dots by the Coulomb blockade microscopy (CBM) at the transition to the fractional quantum Hall regime. We apply an exact diagonalization method to determine the exact charge density and its reaction to the scanning probe as well as to calculate the energy maps as functions of the position of the probe. From the energy maps—which are the only experimentally accessible quantity in CBM—we evaluate an apparent charge density solving an inverse integral problem given by the perturbation theory. We discuss the exact and apparent charge densities derived from the energy maps. We find that for magnetic fields corresponding to the integer fillings of the lowest Landau level, when the electron system exhibits a liquid-like reaction to the potential of the probe, the confined charge density can be quite accurately mapped by the CBM. For fractional fillings of the lowest Landau level the probe induces nucleation of single-electron islands which in circular quantum dots evade imaging by CBM. We demonstrate that mapping the molecular charge densities is possible for confinement potentials of lower symmetry that is consistent with the geometry of the single-electron islands distribution.

Generalizing quantum Hall ferromagnetism to fractional Chern bands

We study the interplay between quantum Hall ordering and spontaneous sublattice symmetry breaking in multiple-Chern-number bands at fractional fillings. Primarily, we study fermions with repulsive interactions near half filling in a family of square lattice models with flat $C=2$ bands and a wide band gap. By perturbing about the particularly transparent limit of two decoupled $C=1$ bands and by exact diagonalization studies of small systems in the more general case, we show that the system generically breaks sublattice symmetry with a transition temperature ${T}_{c}>0$ and additionally exhibits a quantized Hall conductance of ${e}^{2}/h$ as $T\ensuremath{\rightarrow}0$. We note the close analogy to quantum Hall ferromagnetism in the multicomponent problem and the connection to topological Mott insulators. We also discuss generalizations to other fillings and higher Chern numbers.

Simulation study of the energy-size reduction of MPS vertical spindle pulverizer

As an important pulverizing equipment, the vertical spindle pulverizer (VSP) is widely used in power plants to produce fines for combustion. But high temperature and pressure in VSP limit the study of grinding process. Herein, a laboratory roller mill, with the addition of a power recorder, has been designed for the simulated study. Parameters of loading force, table revolution rate and fractional filling in this device can be adjusted. Grinding tests for different combinations of these three parameters are conducted. Confidence analyses of the experimental data illustrate the reliability of results, with a 90% confidence limit being 5% of the mean measured value. Breakage characteristics of the top size show the first-order law and the initial samples of narrow size fraction are all broken and disappear with less than 20s. Both the loading force and table revolution rate have a positive effect on t10 and the tests for condition of lower fractional fillings also generate the high value of t10. For the analyses of energy-size reduction, t10 and specific energy are conducted as the response results. The mathematical relationship between t10 and specific energy of the grinding test with fixed parameters can be described well by the classical energy-size reduction breakage model, t10=A(1-e-b·Ecs),with the R2>0.97. Due to the difference of values of t10 generated at the unit specific energy for the conditions of different parameter combinations, this model only can simulate the grinding process with changes of loading forces or fractional fillings. 10 Sets of additional experimental data demonstrate this conclusion. Reasons of this phenomenon are discussed.

Charge gaps at fractional fillings in boson Hubbard ladders

The Bose-Hubbard Hamiltonian describes the competition between superfluidity and Mott insulating behavior at zero temperature and commensurate filling as the strength of the on-site repulsion is varied. Gapped insulating phases also occur at noninteger densities as a consequence of longer ranged repulsive interactions. In this paper we explore the formation of gapped phases in coupled chains due instead to anisotropies ${t}_{x}\ensuremath{\ne}{t}_{y}$ in the bosonic hopping, extending the work of Crepin et al. [Phys. Rev. B 84, 054517 (2011).] on two coupled chains, where a gap was shown to occur at half filling for arbitrarily small interchain hopping ${t}_{y}$. Our main result is that, unlike the two-leg chains, for three- and four-leg chains, a charge gap requires a finite nonzero critical ${t}_{y}$ to open. However, these finite values are surprisingly small, well below the analogous values required for a fermionic band gap to open.

Thermal phase transitions in a honeycomb lattice gas with three-body interactions

We study the thermal phase transitions in a classical (hard-core) lattice gas model with nearest-neighbor three-body interactions on the honeycomb lattice, based on parallel tempering Monte Carlo simulations. This system realizes incompressible low-temperature phases at fractional fillings of 9/16, 5/8, and 3/4 that were identified in a previous study of a related quantum model. In particular, both the 9/16 and the 5/8 phase exhibit an extensive ground-state degeneracy reflecting the frustrated nature of the three-body interactions on the honeycomb lattice. The thermal melting of the 9/16 phase is found to be a first-order, discontinuous phase transition. On the other hand, from the thermodynamic behavior we obtain indications for a four-states Potts-model thermal transition out of the 5/8 phase. We find that this thermal Potts-model transition relates to the selection of one out of four extensive sectors within the low-energy manifold of the 5/8 phase, which we obtain via an exact mapping of the ground-state manifold to a hard-core dimer model on an embedded honeycomb superlattice.

Fractional topological phase in one-dimensional flat bands with nontrivial topology

We consider a topologically nontrivial flat-band structure in one spatial dimension in the presence of nearest- and next-nearest-neighbor Hubbard interaction. The noninteracting band structure is characterized by a symmetry-protected topologically quantized Berry phase. At certain fractional fillings, a gapped phase with a filling-dependent ground-state degeneracy and fractionally charged quasiparticles emerges. At filling $\frac{1}{3}$, the ground states carry a fractional Berry phase in the momentum basis. These features at first glance suggest a certain analogy to the fractional quantum Hall scenario in two dimensions. We solve the interacting model analytically in the physically relevant limit of a large band gap in the underlying band structure, the analog of a lowest Landau level projection. Our solution affords a simple physical understanding of the properties of the gapped interacting phase. We pinpoint crucial differences to the fractional quantum Hall case by studying the Berry phase and the entanglement entropy associated with the degenerate ground states. In particular, we conclude that the ``fractional topological phase in one-dimensional flat bands'' is not a one-dimensional analog of the two-dimensional fractional quantum Hall states, but rather a charge density wave with a nontrivial Berry phase. Finally, the symmetry-protected nature of the Berry phase of the interacting phase is demonstrated by explicitly constructing a gapped interpolation to a state with a trivial Berry phase.

Quantum Hall effect of two-component bosons at fractional and integral fillings

We investigate the feasibility of many candidate quantum Hall states for two-component bosons in the lowest Landau level. We identify interactions for which spin-singlet incompressible states occur at filling factors $\nu=2/3$, 4/5 and 4/3, and spin-partially-polarized states at filling factors 3/4 and 3/2, where "spin" serves as a generic label for the two components. We study ground states, excitations, edge states and entanglement spectrum for systems with up to 16 bosons, and construct explicit trial wave functions to clarify the underlying physics. The composite fermion theory very accurately describes the ground states as well as excitations at $\nu=2/3$, 4/5 and 3/4, although it is less satisfactory for the $\nu=3/2$ state. For $\nu=4/3$ a "non-Abelian spin-singlet" state has been proposed to occur for a 2-body contact interaction; we find that it is more likely that the actual state here is a spin-singlet state of reverse-flux-attached composite fermions at filling $\nu^*=4$. We also consider incompressible states at integral filling factors $\nu=1$ and 2. The incompressible state at $\nu=1$ is shown to be well described by the parton-based Jain spin-singlet wave function, and the incompressible state at $\nu=2$ as the spin-singlet state of reverse-flux-attached composite fermions at $\nu^*=2$.

Topological Bose-Mott insulators in a one-dimensional optical superlattice.

We study topological properties of the Bose-Hubbard model with repulsive interactions in a one-dimensional optical superlattice. We find that the Mott insulator states of the single-component (two-component) Bose-Hubbard model under fractional fillings are topological insulators characterized by a nonzero charge (or spin) Chern number with nontrivial edge states. For ultracold atomic experiments, we show that the topological Chern number can be detected through measuring the density profiles of the bosonic atoms in a harmonic trap.

Electron-electron interactions and topology in the electronic properties of gated graphene nanoribbon rings in Möbius and cylindrical configurations

We present a theory of the electronic properties of gated graphene nanoribbon rings with zigzag edges in M\obius and cylindrical configurations. The finite width opens a gap and nontrivial topology of the M\obius ring leads to a single edge with edge states with an induced, effective gauge field, in analogy to topological insulators. The single zigzag edge leads to a shell of degenerate states at the Fermi level and a ferromagnetic (FM) ground state at half-filling, i.e., at charge neutrality, due to electron-electron interactions. For fractional fillings, both the magnetic moment and the energy gap are found to oscillate as a function of the shell filling. In cylindrical rings, the two edges lead to AF ground state at half-filling but FM ground state at fractional fillings.

Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene

Graphene provides a rich platform to study many-body effects, owing to its massless chiral charge carriers and the fourfold degeneracy arising from their spin and valley degrees of freedom. We use a scanning single-electron transistor to measure the local electronic compressibility of suspended graphene, and we observed an unusual pattern of incompressible fractional quantum Hall states that follows the standard composite fermion sequence between filling factors ν = 0 and 1 but involves only even-numerator fractions between ν = 1 and 2. We further investigated this surprising hierarchy by extracting the corresponding energy gaps as a function of the magnetic field. The sequence and relative strengths of the fractional quantum Hall states provide insight into the interplay between electronic correlations and the inherent symmetries of graphene.

Interaction-Induced Topological Insulator States in Strained Graphene

The electronic properties of graphene can be manipulated via mechanical deformations, which opens prospects for both studying the Dirac fermions in new regimes and for new device applications. Certain natural configurations of strain generate large nearly uniform pseudomagnetic fields, which have opposite signs in the two valleys, and give rise to flat spin- and valley-degenerate pseudo-Landau levels (PLLs). Here we consider the effect of the Coulomb interactions in strained graphene with a uniform pseudomagnetic field. We show that the spin or valley degeneracies of the PLLs get lifted by the interactions, giving rise to topological insulator states. In particular, when a nonzero PLL is quarter or three-quarter filled, an anomalous quantum Hall state spontaneously breaking time-reversal symmetry emerges. At half-filled PLLs, a weak spin-orbital interaction stabilizes the time-reversal-symmetric quantum spin-Hall state. These many-body states are characterized by the quantized conductance and persist to a high temperature scale set by the Coulomb interactions, which we estimate to be a few hundreds Kelvin at moderate strain values. At fractional fillings, fractional quantum Hall states breaking valley symmetry emerge. These results suggest a new route to realizing robust topological states in mesoscopic graphene.

Modulation induced stripe phase at fractional fillings

We have experimentally examined the state of a two-dimensional electron gas subjected to unidirectional periodic potential modulation in the vicinity of the filling ν = 5/3 (equivalent to ν = 1/3 by the particle-hole symmetry). In addition to a peak in the longitudinal resistivity ρxx, we find small amplitude oscillations roughly periodic in the magnetic field B in the Hall resistivity ρyx. The oscillations appear in a narrow range of the electron density ne, and the period ΔB of the oscillations increases with the slight increase in ne. The oscillations are interpreted as resulting from the commensurability between the high harmonics of the modulation potential and the stripe state, which is predicted by the density matrix renormalization group calculations to be the ground state in our system.

DMRG study of fractional quantum Hall effect and valley skyrmions in graphene

The ground state and low-energy excitations of graphene and its bilayer are investigated by the density matrix renormalization group (DMRG) method. We analyze the effect of Coulomb interaction between the electrons including valley degrees of freedoms. The obtained results show finite charge excitation gap at various fractional fillings νn = 1/3, 2/5, 2/3 in the n = 0 and 1 Landau levels of single-layer graphene (SLG) and n = 2 Landau level of bilayer graphene (BLG). The lowest charge excitations at ν = 1/3, and 1 in SLG are valley skyrmions.

Unified microscopic approach to the interplay of pinned-Wigner-solid and liquid behavior of the lowest Landau-level states in the neighborhood ofν=13

Motivated by recent experiments, and using the rotating-and-vibrating electron-molecule (RVEM) theory [Yannouleas and Landman, Phys. Rev. B 66, 115315 (2002); Phys. Rev. A 81, 023609 (2010)], in conjunction with exact diagonalization, we develop a unified microscopic approach for the interplay between liquid fractional-quantum-Hall-effect (FQHE) states and Wigner-solid states in the lowest Landau level (LLL) in the neighborhood of nu=1/3. Liquid characteristics of the FQHE states are associated with the symmetry-conserving rotations and vibrations of the electron molecule. Although the electron densities of the symmetry-conserving LLL states do not exhibit crystalline patterns, the intrinsic crystalline correlations are reflected in the conditional probability distributions and the emergence of cusp yrast states in the LLL spectra. It is shown that away from the exact fractional fillings, weak pinning perturbations (due to weak disorder) may overcome the energy gaps between adjacent global states and generate pinned broken symmetry ground states as a superposition of symmetry-conserving LLL states with different total angular momenta. The electron densities of such mixed states (without good angular momentum quantum numbers) exhibit oscillating patterns that correspond to molecular crystallites. These pinned Wigner crystallites represent finite-size precursors of the bulk Wigner-solid state. It is further shown that the emergence of these molecular crystallites is a consequence of the presence of RVEM components in the symmetry-conserving LLL states. In addition, it is shown that the RVEM approach accounts for the Wigner-solid state in the neighborhood of nu=1, which was also found in the experiments. We utilize results for sizes in a wide range from N=6 to N=29 electrons, and we address the extrapolation to the thermodynamic limit.

Kinetically Forbidden Transformations of Water Molecular Assemblies in Hydrophobic Micropores

Water adsorption hysteresis is one of the most important phenomena observed during the interaction of water with hydrophobic surfaces. Adsorption hysteresis in micropores has strong relevance to the structure of adsorbed water. We used three typical models (cluster, monolayer, and uniform distribution structure models) to determine the structure of the water molecules adsorbed in hydrophobic slit-shaped carbon micropores. In each model, stabilization energy profiles were calculated for various fractional fillings by using the interaction potential theory. Simultaneously, molecular dynamics (MD) simulations of water adsorbed in the micropore of 1.1 nm pore width, which shows significant adsorption hysteresis, were performed to determine the kinetics of the observed structural transformations. The transformations between monolayer and cluster were slow, that is, kinetically forbidden at the fractional filling of 0.2 and 0.6, whereas the cluster-uniform distribution structure and uniform distribution structure-monolayer transformations were kinetically allowed. The kinetically forbidden transformation resulted in the occurrence of metastable structure of adsorbed water and was responsible for the observed adsorption hysteresis.