Integer Fillings Research Articles

Large intrinsic inductance in strongly correlated GaAs two-dimensional holes in the integer quantum hall regime

Quantum Hall measurements are performed for a two-dimensional hole system (2DHS) confined to a 20 nm quantum well in ⟨100⟩ GaAs. Quantum oscillations reveal a density of 4 - 5×1010 cm−2 with mobility μ = 1 × 106 cm2/V s. For temperatures less than ∼350 mK, anomalous insulating peaks are observed between integer fillings 1-2, 2-3, and 3-4. A large out-of-phase signal appears at these peaks, which indicates a substantial inductance inherent to the charge carriers.

Proposed formation and dynamical signature of a chiral Bose liquid in an optical lattice

Recent experiments on p-orbital atomic bosons have suggested the emergence of a spectacular ultracold superfluid with staggered orbital currents in optical lattices. This raises fundamental questions concerning the effects of thermal fluctuations as well as possible ways of directly observing such chiral order. Here we show via Monte Carlo simulations that thermal fluctuations destroy this superfluid in an unexpected two-step process, unveiling an intermediate normal phase with spontaneously broken time-reversal symmetry, dubbed a 'chiral Bose liquid'. For integer fillings (n≥2) in the chiral Mott regime, thermal fluctuations are captured by an effective orbital Ising model, and Onsager's powerful exact solution is adopted to determine the transition from this intermediate liquid to the para-orbital normal phase at high temperature. A lattice quench is designed to convert the staggered angular momentum, previously thought by experts difficult to directly probe, into coherent orbital oscillations, providing a time-resolved dynamical signature of chiral order.

Fractional and integer quantum Hall effects in the zeroth Landau level in graphene

Experiments on the fractional quantized Hall effect in the zeroth Landau level of graphene have revealed some striking differences between filling factors in the ranges $0<|\ensuremath{\nu}|<1$ and $1<|\ensuremath{\nu}|<2$. We argue that these differences can be largely understood as a consequence of the effects of terms in the Hamiltonian which break SU(2) valley symmetry, which we find to be important for $|\ensuremath{\nu}|<1$ but negligible for $|\ensuremath{\nu}|>1$. The effective absence of valley anisotropy for $|\ensuremath{\nu}|>1$ means that states with an odd numerator, such as $|\ensuremath{\nu}|=5/3$ or 7/5, can accommodate charged excitations in the form of large-radius valley skyrmions, which should have a low energy cost and may be easily induced by coupling to impurities. The absence of observed quantum Hall states at these fractions is likely due to the effects of valley skyrmions. For $|\ensuremath{\nu}|<1$, the anisotropy terms favor phases in which electrons occupy states with opposite spins, similar to the antiferromagnetic state previously hypothesized to be the ground state at $\ensuremath{\nu}=0$. The anisotropy and Zeeman energies suppress large-area skyrmions, so that quantized Hall states can be observable at a set of fractions similar to those in GaAs two-dimensional electron systems. In a perpendicular magnetic field $B$, the competition between the Coulomb energy, which varies as ${B}^{1/2}$, and the Zeeman energy, which varies as $B$, can explain the observation of apparent phase transitions as a function of $B$ for fixed $\ensuremath{\nu}$, as transitions between states with different degrees of spin polarization. In addition to an analysis of various fractional states from this point of view and an examination of the effects of disorder on valley skyrmions, we present new experimental data for the energy gaps at integer fillings $\ensuremath{\nu}=0$ and $\ensuremath{\nu}=\ensuremath{-}1$, as a function of magnetic field, and we examine the possibility that valley skyrmions may account for the smaller energy gaps observed at $\ensuremath{\nu}=\ensuremath{-}1$.

Diffusion Thermopower of Quantum Hall States Measured in Corbino Geometry

We have measured the diffusion thermopower of a quantum Hall system in a Corbino setup. A concentric electron-temperature gradient is introduced by irradiating microwaves, via a coplanar waveguide, near the outer rim of a circular mesa of a two-dimensional electron gas. The resulting radial thermovoltages exhibit sawtooth-like oscillations with the magnetic field, taking large positive (negative) values just below (above) integer fillings with sign reversal at the center of the quantum Hall plateaus. The behavior is in agreement with a recent theory [Y. Barlas and K. Yang: Phys. Rev. B 85 (2012) 195107], which treats disorder within the self-consistent Born approximation.

Bosonic Hard-Rods in One Dimensional Optical Lattices

Diffusion Monte Carlo simulations on the subject of bosonic hard rods trapped in one dimensional optical lattices are presented. The existence of Mott Insulator phases for integer fillings is deduced from the behavior of the energy per particle as a function of the density. The analysis of the pair distribution functions and structure factors suggest the existence of fluid-like phases for shallow optical lattices that evolve to solid-like arrangements when the confinement is deep enough.

Complete phase diagram for three-band Hubbard model with orbital degeneracy lifted by crystal field splitting

Motivated by the unexplored complexity of the phase diagrams for multi-orbital Hubbard models, a three-band Hubbard model at integer fillings (N=4) with orbital degeneracy lifted partially by crystal field splitting is analyzed systematically in this work. By using single site dynamical mean-field theory and rotationally invariant Gutzwiller approximation, we have computed the full phase diagram with Coulomb interaction strength $U$ and crystal field splitting $\Delta$. We find a large region in the phase diagram, where an orbital selective Mott phase will be stabilized by the positive crystal field lifting the orbital degeneracy. Further analysis indicates that the Hund's rule coupling is essential for the orbital selective Mott phase and the transition toward this phase is accompanied by a high-spin to low-spin transition. Such a model may be relevant for the recently discovered pnictides and ruthenates correlated materials.

Static and dynamic properties of type-II composite fermion Wigner crystals

The Wigner crystal of composite fermions is a strongly correlated state of complex emergent particles in two dimensions, and therefore its unambiguous detection would be of significant importance. A recent observation of optical resonances in the vicinity of filling factor $\ensuremath{\nu}=1/3$ has been interpreted as evidence for a pinned Wigner crystal of composite fermions [Phys. Rev. Lett. 105, 126803 (2010)]. We evaluate in a microscopic theory the shear modulus and the magnetophonon and magnetoplasmon dispersions of the composite fermion Wigner crystal in the vicinity of filling factors 1/3, 2/5, and 3/7. We determine the region of stability of the crystal phase, and also relate the frequency of its pinning mode to that of the corresponding electron crystal near integer fillings. These results are in good semiquantitative agreement with experiment, and therefore support the identification of the optical resonance as the pinning mode of the composite fermion Wigner crystal. Our calculations also bring out certain puzzling features, such as a relatively small melting temperature for the composite fermion Wigner crystal, and also suggest a higher asymmetry between Wigner crystals of composite fermion particles and holes than that observed experimentally.

Orbital and interlayer skyrmion crystals in bilayer graphene

A graphene bilayer in a transverse magnetic field has a set of Landau levels with energies $E=\pm \sqrt{N(N+1)}\hslash \omega_{c}^{\ast}$ where $\omega_{c}^{\ast}$ is the effective cyclotron frequency and $% N=0,1,2,...$ All Landau levels but N=0 are four times degenerate counting spin and valley degrees of freedom. The Landau level N=0 has an extra degeneracy due to the fact that orbitals $n=0$ and $n=1$ both have zero kinetic energies. At integer filling factors, Coulomb interactions produce a set of broken-symmetry states with partial or full alignement in space of the valley and orbital pseudospins. These quantum Hall pseudo-ferromagnetic states support topological charged excitations in the form of orbital and valley Skyrmions. Away from integer fillings, these topological excitations can condense to form a rich variety of Skyrme crystals with interesting properties. We study in this paper different crystal phases that occur when an electric field is applied between the layers. We show that orbital Skyrmions, in analogy with spin Skyrmions, have a texture of electrical dipoles that can be controlled by an in-plane electric field. Moreover, the modulation of electronic density in the crystalline phases are experimentally accessible through a measurement of their local density of states

Skyrme and Wigner crystals in graphene

At low-energy, the band structure of graphene can be approximated by two degenerate valleys $(K,K^{\prime})$ about which the electronic spectra of the valence and conduction bands have linear dispersion relations. An electronic state in this band spectrum is a linear superposition of states from the $A$ and $B$ sublattices of the honeycomb lattice of graphene. In a quantizing magnetic field, the band spectrum is split into Landau levels with level N=0 having zero weight on the $B(A)$ sublattice for the $% K(K^{\prime})$ valley. Treating the valley index as a pseudospin and assuming the real spins to be fully polarized, we compute the energy of Wigner and Skyrme crystals in the Hartree-Fock approximation. We show that Skyrme crystals have lower energy than Wigner crystals \textit{i.e.} crystals with no pseudospin texture in some range of filling factor $\nu $ around integer fillings. The collective mode spectrum of the valley-skyrmion crystal has three linearly-dispersing Goldstone modes in addition to the usual phonon mode while a Wigner crystal has only one extra Goldstone mode with a quadratic dispersion. We comment on how these modes should be affected by disorder and how, in principle, a microwave absorption experiment could distinguish between Wigner and Skyrme crystals.

Coupled charge and valley excitations in graphene quantum Hall ferromagnets

Graphene is a two-dimensional carbon material with a honeycomb lattice and Dirac-type low-energy spectrum. In a strong magnetic field, where Coulomb interactions dominate against disorder broadening, quantum Hall ferromagnetic states realize at integer fillings. Extending the quantum Hall ferromagnetism to the fractional filling case of massless Dirac fermions, we study the elementally charge excitations which couple with the valley degrees of freedom (so-called valley skyrmions). With the use of the density matrix renomalization group (DMRG) method, the excitation gaps are calculated and extrapolated to the thermodynamic limit. These results exhibit numerical evidences and criterions of the skyrmion excitations in graphene.

Zero-Bias Conductance in Carbon Nanotube Quantum Dots

We present numerical renormalization group calculations for the zero-bias conductance of quantum dots made from semiconducting carbon nanotubes. These explain and reproduce the thermal evolution of the conductance for different groups of orbitals, as the dot-lead tunnel coupling is varied and the system evolves from correlated Kondo behavior to more weakly correlated regimes. For integer fillings N=1, 2, 3 of an SU(4) model, we find universal scaling behavior of the conductance that is distinct from the standard SU(2) universal conductance, and concurs quantitatively with experiment. Our results also agree qualitatively with experimental differential conductance maps.

Quantum phase transitions and the hidden order in a two-chain extended boson Hubbard model at half-odd-integer fillings

We study the phase diagram of two weakly coupled one-dimensional dipolar boson chains at half-odd-integer fillings. We find that the system contains a rich phase diagram. Four different phases are found. They are the Mott insulators, the single-particle resonant superfluid, the paired superfluid, and the bond-density or interchain density waves. Moreover, the Mott insulating phase can be further classified according to a hidden string order parameter, which is analogous to the one investigated recently in the one-dimensional boson Mott insulator at integer fillings.

Phases and transitions in the spin-1 Bose-Hubbard model: Systematics of a mean-field theory

We generalize the mean-field theory for the spinless Bose-Hubbard model to account for the different types of superfluid phases that can arise in the spin-1 case. In particular, our mean-field theory can distinguish polar and ferromagnetic superfluids, Mott insulator, that arise at integer fillings at zero temperature, and normal Bose liquids into which the Mott insulators evolve at finite temperatures. We find, in contrast to the spinless case, that several of the superfluid-Mott insulator transitions are of first order at finite temperatures. Our systematic study yields rich phase diagrams that include first-order and second-order transitions and a variety of tricritical points. We discuss the possibility of realizing such phase diagrams in experimental systems.

Vortex molecular crystal and vortex plastic crystal states in honeycomb and kagomé pinning arrays

Using numerical simulations, we investigate vortex configurations and pinning in superconductors with honeycomb and kagom\'e pinning arrays. We find that a variety of vortex crystal states can be stabilized at integer and fractional matching field densities. The honeycomb and kagom\'e pinning arrays produce considerably more pronounced commensuration peaks in the critical depinning force than triangular pinning arrays, and also cause additional peaks at noninteger matching fields where a portion of the vortices are located in the large interstitial regions of the pinning lattices. For the honeycomb pinning array, we find matching effects of equal strength at most fillings $B∕{B}_{\ensuremath{\phi}}=n∕2$ for $ng2$, where $n$ is an integer, in agreement with recent experiments. For kagom\'e pinning arrays, pronounced matching effects generally occur at $B∕{B}_{\ensuremath{\phi}}=n∕3$ for $ng3$, while for triangular pinning arrays pronounced matching effects are observed only at integer fillings $B∕{B}_{\ensuremath{\phi}}=n$. At the noninteger matching field peaks in the honeycomb and kagom\'e pinning arrays, the interstitial vortices are arranged in dimer, trimer, and higher order $n$-mer states that have an overall orientational order. We call these $n$-mer states ``vortex molecular crystals'' and ``vortex plastic crystals'' since they are similar to the states recently observed in colloidal molecular crystal systems. We argue that the vortex molecular crystals have properties in common with certain spin systems such as Ising and $n$-state Potts models. We show that kagom\'e and honeycomb pinning arrays can be useful for increasing the critical current above that of purely triangular pinning arrays.

Low-energy effective theory for one-dimensional lattice bosons near integer filling

A low-energy effective theory for interacting bosons on a one-dimensional lattice at and near integer fillings is proposed. It is found that two sets of bosonic phase fields are necessary in order to explain the complete phase diagram. Using the present effective theory, the nature of the quantum phase transitions among various phases can be identified. Moreover, the general condition for the appearance of the recently proposed Pfaffian-like state can be realized from our effective action.

Wigner crystal and bubble phases in graphene in the quantum Hall regime

Graphene, a single freestanding sheet of graphite with honeycomb lattice structure, is a semimetal with carriers that have linear dispersion. A consequence of this dispersion is the absence of Wigner crystallization in graphene, since the kinetic and potential energies both scale identically with density of carriers. We study the ground state of graphene in the presence of strong magnetic field focusing on states with broken translational symmetry. Our mean-field calculations show that at integer fillings a uniform state is preferred, whereas at noninteger fillings, Wigner crystal states (with broken translational symmetry) have lower energy. We obtain the phase diagram of the system. We find that it is qualitatively similar to that of quantum Hall systems in semiconductor heterostructures. Our analysis predicts that nonuniform states, including Wigner crystal state, will occur in graphene in the presence of a magnetic field and will lead to anisotropic transport in high Landau levels.

Electron Correlations and Single-Particle Physics in the Integer Quantum Hall Effect

The compressibility of a two-dimensional electron system with spin in a spatially correlated random potential and a quantizing magnetic field is investigated. Electron-electron interaction is treated with the Hartree-Fock method. Numerical results for the influences of interaction and disorder on the compressibility as a function of the particle density and the strength of the magnetic field are presented. Localization-delocalization transitions associated with a highly compressible region in the energy spectrum are found at half-integer filling factors. Coulomb blockade effects are found near integer fillings in the regions of low compressibility. Results are compared with recent experiments.

Collective modes and skyrmion excitations in grapheneSU(4)quantum Hall ferromagnets

Graphene exhibits quantum Hall ferromagnetism in which an approximate SU(4) symmetry involving spin and valley degrees of freedom is spontaneously broken. We construct a set of integer and fractional quantum Hall states that break the SU(4) spin/valley symmetry, and study their neutral and charged excitations. Several properties of these ferromagnets can be evaluated analytically in the SU(4) symmetric limit, including the full collective mode spectrum at integer fillings. By constructing explicit wave functions we show that the lowest energy skyrmion states carry charge $\pm 1$ for {\em any} integer filling, and that skyrmions are the lowest energy charged excitations for graphene Landau level index $|n| \le 3$. We also show that the skyrmion lattice states which occur near integer filling factors support four gapless collective mode branches in the presence of full SU(4) symmetry. Comparisons are made with the more familiar SU(2) quantum Hall ferromagnets studied previously.

Exact study of the one-dimensional boson Hubbard model with a superlattice potential

We use Quantum Monte Carlo simulations and exact diagonalization to explore the phase diagram of the Bose-Hubbard model with an additional superlattice potential. We first analyze the properties of superfluid and insulating phases present in the hard-core limit where an exact analytic treatment is possible via the Jordan-Wigner transformation. The extension to finite on-site interaction is achieved by means of quantum Monte Carlo simulations. We determine insulator/superfluid phase diagrams as functions of the on-site repulsive interaction, superlattice potential strength, and filling, finding that insulators with fractional occupation numbers, which are present in the hard-core case, extend deep into the soft-core region. Furthermore, at integer fillings, we find that the competition between the on-site repulsion and the superlattice potential can produce a phase transition between a Mott insulator and a charge density wave insulator, with an intermediate superfluid phase. Our results are relevant to the behavior of ultracold atoms in optical superlattices which are beginning to be studied experimentally.

Extended Bose Hubbard model of interacting bosonic atoms in optical lattices: From superfluidity to density waves

For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian of the system in powers of the lattice parameters and of a scale parameter, the {\it lattice attenuation factor}. We identify the dominant terms that need to be retained in realistic experimental conditions, up to nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the on site occupation numbers. In mean field approximation, we determine the free energy of the system and study the phase diagram both at zero and at finite temperature. At variance with the standard on site Bose Hubbard model, the zero temperature phase diagram of the EBH model possesses a dual structure in the Mott insulating regime. Namely, for specific ranges of the lattice parameters, a density wave phase characterizes the system at integer fillings, with domains of alternating mean occupation numbers that are the atomic counterparts of the domains of staggered magnetizations in an antiferromagnetic phase. We show as well that in the EBH model, a zero-temperature quantum phase transition to pair superfluidity is in principle possible, but completely suppressed at lowest order in the lattice attenuation factor. Finally, we determine the possible occurrence of the different phases as a function of the experimentally controllable lattice parameters.