Time-reversal symmetric hierarchy of fractional incompressible liquids

We provide an effective description of fractional topological insulators that include the fractional quantum spin Hall effect by considering the time-reversal symmetric pendant to the topological quantum field theories that encode the Abelian fractional quantum Hall liquids. We explain the hierarchical construction of such a theory and establish for it a bulk-edge correspondence by deriving the equivalent edge theory for chiral bosonic fields. Further, we compute the Fermi-Bose correlation functions of the edge theory and provide representative ground state wave functions for systems described by the bulk theory.Comment: 14 page

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.

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

Deconfined fractional electric charges in graphene at high magnetic fields

The resistance at the charge neutral (Dirac) point was shown by Checkelsky et al in Phys. Rev. B 79, 115434 (2009) to diverge upon the application of a strong magnetic field normal to graphene. We argue that this divergence is the signature for a Kekule instability of graphene, which is induced by the magnetic field. We show that the strong magnetic field does not remove the zero modes that bind a fraction of the electron around vortices in the Kekule dimerization pattern, and that quenched disorder present in the system makes it energetically possible to separate the fractional charges. These findings, altogether, indicate that graphene can sustain deconfined fractionalized electrons.Comment: 11 pages, 2 figure

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

Crossover of conductance and local density of states in a single-channel disordered quantum wire

The probability distribution of the mesoscopic local density of states (LDOS) for a single-channel disordered quantum wire with chiral symmetry is computed in two different geometries. An approximate ansatz is proposed to describe the crossover of the probability distributions for the conductance and LDOS between the chiral and standard symmetry classes of a single-channel disordered quantum wire. The accuracy of this ansatz is discussed by comparison with a large-deviation ansatz introduced by Schomerus and Titov in Phys. Rev. B \textbf{67}, 100201(R) (2003).Comment: 19 pages, 5 eps figure

Apport de la géologie, de l’hydrogéologie et des isotopes de l’environnement à la connaissance des «nappes en creux» du Grand Yaéré (Nord Cameroun)

La carte piézométrique de la nappe du Logone-Chari-Tchad met en évidence des anomalies piézométriques interprétées comme des « nappes en creux ». Les informations de l’hydrogéologie et des isotopes de l’environnement conduisent à remettre en question les grandes profondeurs des niveaux statiques observées par certains auteurs dans ces dépressions piézométriques. Les données hydrogéologiques démontrent que dans la zone déprimée de la surface piézométrique, l’aquifère est de type bicouche. Par ailleurs, la distribution des teneurs en isotopes stables (oxygène-18 et deutérium) et en tritium confirme le cloisonnement des aquifères :La relation δ 2H vs. δ 18O montre que les effets d’enrichissement par évaporation lors de la recharge des nappes ne sont très marqués que dans les eaux des nappes superficielles dont les niveaux statiques ne dépassent pas 20 m de profondeur. Les dépressions fermées dont les points les plus bas atteignent 60 m sous la surface du sol s’interprètent difficilement dans l’hypothèse d’une reprise évaporatoire.Il résulte de cette étude que l’absence de dépendance nette entre les niveaux piézométriques superficiels et les niveaux profonds place le problème des anomalies piézométriques du Grand Yaéré dans un contexte totalement différent de celui des anciennes interprétations qui s’appuyaient sur l’hypothèse d’une nappe libre généralisée monocouche. À l’avenir, la construction de la carte piézométrique de la nappe du Logone-Chari-Tchad devra tenir compte de la structure des deux nappes superposées.Piezometric depressions, common in sub-Saharan Africa, are major hydrogeological anomalies manifested by closed curves, pronounced hollows and dips attaining several tens of meters below the regional water table level. The Logone-Chari-Chad piezometric map reveals piezometric anomalies that have been interpreted as depressed aquifers. The depth of the water table is 60 m in the Tagawa-Am Talia axis, 40 m between Louba-Louba and Andirni and 30 m around Yagoua. Factors linked to evaporation are generally thought to be responsible for these depressed zones.The objective of this study (based on the saturated zone) was: 1) to place the Logone-Chari-Chad piezometric anomalies in their hydrogeological settings, and 2) to evaluate the use of environmental isotopes to explain their formation processes. To achieve our goal, 27 water supply points (8 boreholes and 19 wells) were selected from the borders and centre of the Logone-Chari-Chad depression. Samples were collected between 1989 and 1991. Measurements performed in the field involved static water levels, whereas the laboratory analyses 18O, 2H and 3H were performed at the International Atomic Energy Agency (IAEA) laboratory in Vienna, within the framework of the project RAF/8/012 funded by IAEA.The new geological and hydrogeological data demonstrate that in the depressed zone of the piezometric surface, the aquifer has two layers. In contrast, the Logone-Chari-Chad piezometric map was previously drawn considering the aquifer as a single-layer. From a hydrochemical point of view, the groundwater in the Logone-Chari-Chad aquifer is stratified: calcium bicarbonate type water was found at the surface (shallow groundwater), whereas sodium carbonate type water was found at depth (deeper groundwater).Seasonal piezometric fluctuations of 1.5 to 3 m have been observed in the shallow groundwater. In the deeper groundwater, they range from 0.20 to 0.30 m. The difference in the values of water table fluctuation leads not only to variations in the mode of groundwater circulation, but also to variations in the hydrodynamic properties of aquifers, such as transmissivity.The distribution in stable isotope contents (18O, 2H and 3H) confirmed the compartmentalization of aquifers. The correlation between 3H and 18O showed that there are two water types, with different recharge modes and episodes. On the border of the depression, shallow groundwater pinches out on the semi-permeable substratum, resulting in a tritium content greater than 4 UT. In the depression axis, there is deeper groundwater with a tritium content below 4 UT.The relationship between 2H and 18O shows that the enrichment effects of evaporation at the time of recharge are very pronounced only in the shallow groundwater, where the static level does not exceed 20 m below the soil surface. The closed piezometric depressions, whose deepest point attains 60 m below the soil surface, cannot be explained by the presence of intense evaporation. The variation in tritium content with respect to the static level shows that in the depressed zone, the first 20 m are characterized by a tritium content greater than 4 UT, whereas at depths of 30 m or more, tritium contents are lower than 4 UT.The absence of dependence between shallow and deep piezometric levels invalidates the interpretation of great water depths proposed in previous studies of the piezometric depression of the Logone-Chari-Chad water table. Thus, the hypothesis that the Logone-Chari-Chad is a single-layer system should be abandoned. The future construction of the piezometric map of the Logone-Chari-Chad water table should take into account the structure and lithology of the two superimposed layers

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