Quantum Phases in Partially Filled Landau Levels

We compare the energies of different electron solids, such as bubble crystals with triangular and square symmetry and stripe phases, to those of correlated quantum liquids in partially filled intermediate Landau levels. Multiple transitions between these phases when varying the filling of the top-most partially filled Landau level explain the observed reentrance of the integer quantum Hall effect. The phase transitions are identified as first-order. This leads to a variety of measurable phenomena such as the phase coexistence between a Wigner crystal and a two-electron bubble phase in a Landau-level filling-factor range $4.15 < nu < 4.26$, which has recently been observed in transport measurements under micro-wave irradiation.Comment: 6 pages, 2 figures; to appear in "Proceedings of the 16th International Conference on High Magnetic Fields in Semiconductor Physics (SemiMag-16)

Second Generation of Composite Fermions and the Self-Similarity of the Fractional Quantum Hall Effect

A recently developed model of interacting composite fermions, is used to investigate different composite-fermion phases. Their interaction potential allows for the formation of both solid and new quantum-liquid phases, which are interpreted in terms of second-generation composite fermions and which may be responsible for the fractional quantum Hall states observed at unusual filling factors, such as nu=4/11. Projection of the composite-fermion dynamics to a single level, involved in the derivation of the Hamiltonian of interacting composite fermions, reveals the underlying self-similarity of the model.Comment: 4 pages, 1 figure; to appear in "Proceedings of the 16th International Conference on High Magnetic Fields in Semiconductor Physics (SemiMag-16)", only change with respect to v1: correction in authors line, no changes in manuscrip

Supersolid phases of dipolar bosons in optical lattices with a staggered flux

We present the theoretical mean-field zero-temperature phase diagram of a Bose-Einstein condensate (BEC) with dipolar interactions loaded into an optical lattice with a staggered flux. Apart from uniform superfluid, checkerboard supersolid and striped supersolid phases, we identify several supersolid phases with staggered vortices, which can be seen as combinations of supersolid phases found in earlier work on dipolar BECs and a staggered-vortex phase found for bosons in optical lattices with staggered flux. By allowing for different phases and densities on each of the four sites of the elementary plaquette, more complex phase patterns are found.Comment: 11 pages; added references, minor changes in tex

Possible Reentrance of the Fractional Quantum Hall Effect in the Lowest Landau Level

In the framework of a recently developed model of interacting composite fermions, we calculate the energy of different solid and Laughlin-type liquid phases of spin-polarized composite fermions. The liquid phases have a lower energy than the competing solids around the electronic filling factors nu=4/11,6/17, and 4/19 and may thus be responsible for the fractional quantum Hall effect at nu=4/11. The alternation between solid and liquid phases when varying the magnetic field may lead to reentrance phenomena in analogy with the observed reentrant integral quantum Hall effect.Comment: 4 pages, 3 figures; revised version accepted for publication in Phys. Rev. Let

Unitarity of theories containing fractional powers of the d'Alembertian operator

We examine the unitarity of a class of generalized Maxwell U(1) gauge theories in (2+1) D containing the pseudodifferential operator $\Box^{1-\alpha}$, for $\alpha \in [0,1)$. We show that only Quantum Electrodynamics (QED$_3$) and its generalization known as Pseudo Quantum Electrodynamics (PQED), for which $\alpha =0$ and $\alpha = 1/2$, respectively, satisfy unitarity. The latter plays an important role in the description of the electromagnetic interactions of charged particles confined to a plane, such as in graphene or in hetero-junctions displaying the quantum Hall effect.Comment: 6 pages, no figure

Local density of states of electron-crystal phases in graphene in the quantum Hall regime

We calculate, within a self-consistent Hartree-Fock approximation, the local density of states for different electron crystals in graphene subject to a strong magnetic field. We investigate both the Wigner crystal and bubble crystals with M_e electrons per lattice site. The total density of states consists of several pronounced peaks, the number of which in the negative energy range coincides with the number of electrons M_e per lattice site, as for the case of electron-solid phases in the conventional two-dimensional electron gas. Analyzing the local density of states at the peak energies, we find particular scaling properties of the density patterns if one fixes the ratio nu_N/M_e between the filling factor nu_N of the last partially filled Landau level and the number of electrons per bubble. Although the total density profile depends explicitly on M_e, the local density of states of the lowest peaks turns out to be identical regardless the number of electrons M_e. Whereas these electron-solid phases are reminiscent to those expected in the conventional two-dimensional electron gas in GaAs heterostructures in the quantum Hall regime, the local density of states and the scaling relations we highlight in this paper may be, in graphene, directly measured by spectroscopic means, such as e.g. scanning tunneling microscopy.Comment: 8 pages, 7 figures; minor correction

Assimetrias regionais na região Norte de Portugal: uma análise de cluster

Portugal, como todos os restantes países do mundo é constituído por regiões heterogéneas. O aspecto económico só por si é insuficiente para a caracterização de um país ou região, pelo que se torna necessário analisar outros indicadores. O Norte de Portugal continental encontra-se dividido em 8 regiões (NUT III), regiões estas que diferem entre si originando assimetrias. As assimetrias regionais normalmente traduzem-se, em diferentes níveis de desenvolvimento económico e social, que poderá induzir a processos de vulnerabilidade das regiões levando a aplicação de políticas de desenvolvimento regionais incoerentes, com consequências preocupantes para a coesão social e territorial. Assim, com o presente artigo pretende-se quantificar, caracterizar e classificar as diferentes NUTS III, da região Norte de Portugal, aplicando uma análise de clusters no sentido de encontrar uma homogeneidade sócio-económica. Para tal, utilizaram-se diferentes indicadores que permitem caracterizar sócio e economicamente as NUT III, para os anos de 2004 e 2008. Dos resultados obtidos visualiza-se nitidamente 3 regiões diversificadas, diferenciadas e classificadas com distintos graus de desenvolvimento, sendo elas, “Regiões Menos Desenvolvidas”, “Regiões Desenvolvidas” e “Regiões Mais Desenvolvidas”. Esta classificação revela a “velha” assimetria regional vs interior. Pretende-se ainda com este estudo facultar dados que sejam úteis para a aplicação de políticas de desenvolvimento regionais coesas

Dynamics of topological defects in a spiral: a scenario for the spin-glass phase of cuprates

We propose that the dissipative dynamics of topological defects in a spiral state is responsible for the transport properties in the spin-glass phase of cuprates. Using the collective-coordinate method, we show that topological defects are coupled to a bath of magnetic excitations. By integrating out the bath degrees of freedom, we find that the dynamical properties of the topological defects are dissipative. The calculated damping matrix is related to the in-plane resistivity, which exhibits an anisotropy and linear temperature dependence in agreement with experimental data.Comment: 4 pages, as publishe

Scaling Approach to the Phase Diagram of Quantum Hall Systems

We present a simple classification of the different liquid and solid phases of quantum Hall systems in the limit where the Coulomb interaction between the electrons is significant, i.e. away from integral filling factors. This classification, and a criterion for the validity of the mean-field approximation in the charge-density-wave phase, is based on scaling arguments concerning the effective interaction potential of electrons restricted to an arbitrary Landau level. Finite-temperature effects are investigated within the same formalism, and a good agreement with recent experiments is obtained.Comment: 4 pages, 3 figures; to be published in Europhys. Lett.; new version contains more detailed description of finite-temperature effect