Enhancing the stability of a fractional Chern insulator against competing phases

We construct a two-band lattice model whose bands can carry the Chern numbers C=0,pm1,pm2. By means of numerical exact diagonalization, we show that the most favorable situation that selects fractional Chern insulators (FCIs) is not necessarily the one that mimics Landau levels, namely a flat band with Chern number 1. First, we find that the gap, measured in units of the on-site electron-electron repulsion, can increase by almost two orders of magnitude when the bands are flat and carry a Chern number C=2 instead of C=1. Second, we show that giving a width to the bands can help to stabilize a FCI. Finally, we put forward a tool to characterize the real-space density profile of the ground state that is useful to distinguish FCI from other competing phases of matter supporting charge density waves or phase separation.Comment: 10 pages, 6 figure

Noncommutative geometry for three-dimensional topological insulators

We generalize the noncommutative relations obeyed by the guiding centers in the two-dimensional quantum Hall effect to those obeyed by the projected position operators in three-dimensional (3D) topological band insulators. The noncommutativity in 3D space is tied to the integral over the 3D Brillouin zone of a Chern-Simons invariant in momentum-space. We provide an example of a model on the cubic lattice for which the chiral symmetry guarantees a macroscopic number of zero-energy modes that form a perfectly flat band. This lattice model realizes a chiral 3D noncommutative geometry. Finally, we find conditions on the density-density structure factors that lead to a gapped 3D fractional chiral topological insulator within Feynman's single-mode approximation.Comment: 41 pages, 3 figure

Gaussian field theories, random Cantor sets and multifractality

The computation of multifractal scaling properties associated with a critical field theory involves non-local operators and remains an open problem using conventional techniques of field theory. We propose a new description of Gaussian field theories in terms of random Cantor sets and show how universal multifractal scaling exponents can be calculated. We use this approach to characterize the multifractal critical wave function of Dirac fermions interacting with a random vector potential in two spatial dimensions. We show that the multifractal scaling exponents are self-averaging.Comment: Extensive modifications of previous version; exact results replace numerical calculation

Incidences de pluies exceptionnelles sur un aquifère libre côtier en zone semi-aride (Chaouia, Maroc)

Les eaux souterraines qui représentent les seules ressources en eau de la Chaouia côtière, sont très minéralisées : intrusion marine, évaporation et recyclage des eaux d'irrigation chargées en sels. L'évolution spatio-temporelle piézométrique et hydrochimique de cet aquifère a été observée sur 179 puits, de 1991 à 1998 qui inclue une période exceptionnellement pluvieuse. Une comparaison par rapport à l'état de la nappe en 1971, date du début de l'exploitation des eaux souterraines, a été faite. Les suivis ont montré qu'à la suite des pluies importantes de 1996 (943 mm), un rehaussement important du niveau de la nappe et des dilutions plus ou moins retardées de tous les sels en solution dans l'eau, sont mesurés dans tous les puits. En effet, la nappe qui a accusé des baisses de 10 à 20 m entre 1971 et 1995, remonte en 1996 de 4,5 à 12,5 m en moyenne surtout au centre et à l'amont de la plaine. Quant à la qualité des eaux qui s'était dégradée, elle a connu des améliorations importantes avec des variations de 0,5 à plus de 4 ms/cm au niveau de la conductivité électrique. Ces faits montrent une grande sensibilité de la nappe aux apports par les pluies qui constituent sa principale alimentation.A study of regional pollution in the coastal aquifer system between Oum-er-Rbia River and Bir Jdid (Coastal Moroccan Meseta, Morocco) was based on data gathered from 1995 to 1998. The study improved the hydrogeological and hydrochemical understanding of the aquifers. The study examined the effects of significant rains on the quantity and quality of coastal groundwater. These waters exhibited high sensitivity to the rain input.Measurements undertaken since 1991 on 179 wells in the study area reveal that the groundwaters are highly mineralized - conductivity reaches more than 10 mS/cm, depending on season and well location. These results also show high chloride concentrations (more than 3500 mg/l), sodium concentrations frequently in the 500 - 1000 mg/l range and nitrates between 150 and 250 mg/l.In coastal Chaouia, these high concentrations of dissolved mineral salts aggravate the problem of supplying quality water to the rural population for drinking or even market-gardening irrigation purposes. The area is characterized by increased irrigated surfaces (more than 16000 hectares with 4125 m3 /s) and a demographic rise that has triggered the chaotic boring of more than 2000 wells into a heterogeneous aquifer sensitive to salinity. Possible sources of this high salinity include :Seawater intrusion into coastal aquifer sectors (mainly into a two-kilometre strip of coastline). The degree and the length of the marine intrusion were exacerbated by intensive pumping for irrigation needs, particularly during the dry season. Other factors such as coastal aquifer permeability, saturation zone thickness and basement depth also affect the degree and length of the marine intrusion. Seawater pollution is more marked in the southwestern coastal area.Reuse of irrigation saline waters, especially as groundwater circulates in the coastal and eastern sectors deep in the soil (to depths of 10 m).Several important factors have been highlighted concerning the origin of the chemical elements in solution and the mechanism of hydrochemical distribution: evaporation, lithology of tapped aquifers, water table depth, distance of wells from the coast, type of soil, use of fertilizers, frequency of pumping operations, and rainfall, among others.A regular network of 179 wells was monitored and surveyed in this study. Spatial and temporal changes in the water table and in the hydrochemistry of the aquifer were monitored between 1991 and 1998, a span which included an exceptionally rainy period (1996). Data are compared with those from 1971, the year groundwater exploitation began.The studied region is characterized by a semi-arid climate, mean annual rainfall of 391 mm (between 1977 and 1998), mean temperature of 17.8 °C, and mean rainfall input of 142 mm. In the dry season, high temperature combined with low rainfall and intensive pumping operations give rise to salinization of shallow groundwater. Groundwater in the area of study circulates in two principal hydrogeological matrices :1. Sandy-calcareous Plio-Quaternary and paleozoic strata in costal sectors and the eastern part located between Tnine Chtouka and Bir Jdid. These hydrogeological strata are characterized by significant porosity and permeability and are exploited at a shallow depth, generally less than 14 m, under sandy-clayed soil.2. A Cretaceous aquifer in marly limestone located between Oum-er-Rbia River and Tnine Chtouka. This aquifer is characterized by a low permeability and a water table generally exceeding 24 m in depth.Monitoring showed that after the heavy rains of 1996 (943 mm, with infiltration of 142 mm), the water table rose markedly in all study wells and a lagged dilution (3 to 6 months) was noted for all mineral salts dissolved in water. In fact, the water table, which had dropped between 1971 and 1995 (10 m in the costal sectors and 20 m in the others parts of the studied region), rose by an average 4.5 to 12.5 m in the central and up-gradient parts of the plain. Several factors were at work between 1971 and 1995: decreased pumping times (about 15 minutes) combined with sharp decreases in the thickness of the saturated zone; appearance of a closed piezometric level in the western region between Oum-er-Rbia River and Tnine Chtouka; and desiccation of 59 wells. With the aid of a polynomial model, annual level evolution of the five coastal test piezometers showed correlation factors of 0.76 to 0.93 respectively for years 1996 and 1997. Other quantitative effects of exceptional rains on groundwater identified include: increased pumping time (up from less than 15 minutes prior to the heavy rains of 1996); increased saturated zone thickness; rises in the water-table surpassing former sea-level heights in certain wells ; general advancement of the piezometric levels towards the coastline; and increased aquifer thickness stemming from longer pumping times.In terms of quality, groundwater showed gradually increasing salinity (by a factor of 2) between 1971 and 1995 and significant improvements after the rains of 1996. Between 1971 and 1995, increased mineralization was observed mainly in coastal and eastern parts of the aquifer between Tnine Chtouka and Bir Jdid. Conductivity of the waters in some coastal wells increased from 5 mS/cm to more than 10 mS/cm. After the exceptional rains of 1996, differences ranging from 0.5 to more than 4 mS/cm were observed in 71 % of the 179 wells analysed. Over the same period, chloride concentrations decreased by average values ranging from 150 to 500 mg/l (higher decreases surpassed 1000 mg/l). By contrast, spatial distributions of conductivity and of the main mineral salts remained unchanged and coastal and eastern groundwaters were still the most vulnerable to high salinity.The quantitative and qualitative effects of heavy rain point to the high sensitivity of these groundwaters to rain input, which is the principal recharge source of the studied aquifer

Anderson transition in systems with chiral symmetry

Anderson localization is a universal quantum feature caused by destructive interference. On the other hand chiral symmetry is a key ingredient in different problems of theoretical physics: from nonperturbative QCD to highly doped semiconductors. We investigate the interplay of these two phenomena in the context of a three-dimensional disordered system. We show that chiral symmetry induces an Anderson transition (AT) in the region close to the band center. Typical properties at the AT such as multifractality and critical statistics are quantitatively affected by this additional symmetry. The origin of the AT has been traced back to the power-law decay of the eigenstates; this feature may also be relevant in systems without chiral symmetry.Comment: RevTex4, 4 two-column pages, 3 .eps figures, updated references, final version as published in Phys. Rev.

Isotropic Single Objective (ISO) microscopy : Theory and Experiment

International audienceIsotropic single-objective (ISO) microscopy is a recently proposed imaging technique that can theoretically exhibit the same axial and transverse resolutions as 4Pi microscopy while using a classical single-objective confocal microscope. This achievement is obtained by placing the sample on a mirror and shaping the illumination beam so that the interference of the incident and mirror-reflected fields yields a quasi-spherical spot. In this work, we model the image formation in the ISO fluorescence microscope and simulate its point spread function. Then, we describe the experimental implementation and discuss its practical difficulties

Two-photon fluorescence isotropic-single-objective microscopy

International audienceTwo-photon excitation provides efficient optical sectioning in three-dimensional fluorescence microscopy, independently of a confocal detection. In two-photon laser-scanning microscopy, the image resolution is governed by the volume of the excitation light spot, which is obtained by focusing the incident laser beam through the objective lens of the microscope. The light spot being strongly elongated along the optical axis, the axial resolution is much lower than the transverse one. In this Letter we show that it is possible to strongly reduce the axial size of the excitation spot by shaping the incident beam and using a mirror in place of a standard glass slide to support the sample. Provided that the contribution of sidelobes can be removed through deconvolution procedures, this approach should allow us to achieve similar axial and lateral resolution

Random Dirac Fermions and Non-Hermitian Quantum Mechanics

We study the influence of a strong imaginary vector potential on the quantum mechanics of particles confined to a two-dimensional plane and propagating in a random impurity potential. We show that the wavefunctions of the non-Hermitian operator can be obtained as the solution to a two-dimensional Dirac equation in the presence of a random gauge field. Consequences for the localization properties and the critical nature of the states are discussed.Comment: 5 pages, Latex, 1 figure, version published in PR

Counting Majorana zero modes in superconductors

A counting formula for computing the number of (Majorana) zero modes bound to topological point defects is evaluated in a gradient expansion for systems with charge-conjugation symmetry. This semi-classical counting of zero modes is applied to some examples that include graphene and a chiral p-wave superconductor in two-dimensional space. In all cases, we explicitly relate the counting of zero modes to Chern numbers.Comment: 21 pages, 3 figure

Zero-modes in the random hopping model

If the number of lattice sites is odd, a quantum particle hopping on a bipartite lattice with random hopping between the two sublattices only is guaranteed to have an eigenstate at zero energy. We show that the localization length of this eigenstate depends strongly on the boundaries of the lattice, and can take values anywhere between the mean free path and infinity. The same dependence on boundary conditions is seen in the conductance of such a lattice if it is connected to electron reservoirs via narrow leads. For any nonzero energy, the dependence on boundary conditions is removed for sufficiently large system sizes.Comment: 12 pages, 11 figure