Exact Solution for Bulk-Edge Coupling in the Non-Abelian ν=5/2\nu=5/2 Quantum Hall Interferometer

It has been predicted that the phase sensitive part of the current through a non-abelian $\nu = 5/2$ quantum Hall Fabry-Perot interferometer will depend on the number of localized charged $e/4$ quasiparticles (QPs) inside the interferometer cell. In the limit where all QPs are far from the edge, the leading contribution to the interference current is predicted to be absent if the number of enclosed QPs is odd and present otherwise, as a consequence of the non-abelian QP statistics. The situation is more complicated, however, if a localized QP is close enough to the boundary so that it can exchange a Majorana fermion with the edge via a tunneling process. Here, we derive an exact solution for the dependence of the interference current on the coupling strength for this tunneling process, and confirm a previous prediction that for sufficiently strong coupling, the localized QP is effectively incorporated in the edge and no longer affects the interference pattern. We confirm that the dimensionless coupling strength can be tuned by the source-drain voltage, and we find that not only does the magnitude of the even-odd effect change with the strength of bulk-edge coupling, but in addition, there is a universal shift in the interference phase as a function of coupling strength. Some implications for experiments are discussed at the end.Comment: 12 pages, 3 figure

The non-Abelian Interferometer

We consider the tunneling current through a double point-contact Fabry-Perot interferometer such as used in recent experimental studies of the fractional quantum Hall plateau at filling fraction nu=5/2. We compare the predictions of several different models of the state of the electrons at this plateau: the Moore-Read, anti-Pfaffian, SU(2)_2 NAF, K=8 strong pairing, and (3,3,1) states. All of these predict the existence of charge e/4 quasiparticles, but the first three are non-Abelian while the last two are Abelian. We give explicit formulas for the scaling of charge e/2 and charge e/4 quasiparticle contributions to the current as a function of temperature, gate voltage and distance between the two point contacts for all three models. Based on these, we analyze several possible explanations of two phenomena reported for recent experiments by Willett et al., namely halving of the period of the observed resistance oscillations with rising temperature and alternation between the same two observed periods at low temperatures as the area of the interference loop is varied with a side gate. We conclude that the most likely explanation is that the observed alternation is due to switching between even and odd numbers of charge e/4 quasiparticles enclosed within the loop as a function of side gate voltage, which is a clear signature of the presence of non-Abelian anyons. However, there are important features of the data which do not have a simple explanation within this picture. We suggest further experiments which could help rule out some possible scenarios. We make the corresponding predictions for future tunneling and interference experiments at the other observed second Landau level fractional quantum Hall states.Comment: 15 pages, 1 figure; v2: additional discussions and references added; v3: clarifications and references updated; Appendix C has been removed and incorporated in arXiv:0909.1056; this paper has been given the more clear, accurate, and informative title "Interferometric signature of non-Abelian anyons" in PRB by its editor

Exotic resonant level models in non-Abelian quantum Hall states coupled to quantum dots

In this paper we study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state. We assume the dot is small enough that its level spacing is large compared to both the temperature and the coupling to the spatially proximate bulk non-Abelian fractional quantum Hall state. We focus on the physics of level degeneracy with electron number on the dot. The physics of such a resonant level is governed by a $k$-channel Kondo model when the quantum Hall state is a Read-Rezayi state at filling fraction $\nu=2+k/(k+2)$ or its particle-hole conjugate at $\nu=2+2/(k+2)$. The $k$-channel Kondo model is channel symmetric even without fine tuning any couplings in the former state; in the latter, it is generically channel asymmetric. The two limits exhibit non-Fermi liquid and Fermi liquid properties, respectively, and therefore may be distinguished. By exploiting the mapping between the resonant level model and the multichannel Kondo model, we discuss the thermodynamic and transport properties of the system. In the special case of $k=2$, our results provide a novel venue to distinguish between the Pfaffian and anti-Pfaffian states at filling fraction $\nu=5/2$. We present numerical estimates for realizing this scenario in experiment.Comment: 18 pages, 2 figures. Clarified final discussio

Phylogenetic Inference From Single-cell RNA-seq Data

Tumors are comprised of subpopulations of cancer cells that harbor distinct genetic profiles and phenotypes that evolve over time and during treatment. By reconstructing the course of cancer evolution, we can understand the acquisition of the malignant properties that drive tumor progression. Unfortunately, recovering the evolutionary relationships of individual cancer cells linked to their phenotypes remains a difficult challenge. To address this need, we have developed PhylinSic, a method that reconstructs the phylogenetic relationships among cells linked to their gene expression profiles from single cell RNA-sequencing (scRNA-Seq) data. This method calls nucleotide bases using a probabilistic smoothing approach and then estimates a phylogenetic tree using a Bayesian modeling algorithm. We showed that PhylinSic identified evolutionary relationships underpinning drug selection and metastasis and was sensitive enough to identify subclones from genetic drift. We found that breast cancer tumors resistant to chemotherapies harbored multiple genetic lineages that independently acquired high K-Ras and β-catenin, suggesting that therapeutic strategies may need to control multiple lineages to be durable. These results demonstrated that PhylinSic can reconstruct evolution and link the genotypes and phenotypes of cells across monophyletic tumors using scRNA-Seq

Local Charge of the nu=5/2 Fractional Quantum Hall State

Electrons in two dimensions and strong magnetic fields effectively lose their kinetic energy and display exotic behavior dominated by Coulomb forces. When the ratio of electrons to magnetic flux quanta in the system is near 5/2, the unique correlated phase that emerges is predicted to be gapped with fractionally charged quasiparticles and a ground state degeneracy that grows exponentially as these quasiparticles are introduced. Interestingly, the only way to transform between the many ground states would be to braid the fractional excitations around each other, a property with applications in quantum information processing. Here we present the first observation of localized quasiparticles at nu=5/2, confined to puddles by disorder. Using a local electrometer to compare how quasiparticles at nu=5/2 and nu=7/3 charge these puddles, we are able to extract the ratio of local charges for these states. Averaged over several disorder configurations and samples, we find the ratio to be 4/3, suggesting that the local charges are e/3 at seven thirds and e/4 at five halves, in agreement with theoretical predictions. This confirmation of localized e/4 quasiparticles is necessary for proposed interferometry experiments to test statistics and computational ability of the state at nu=5/2.Comment: 6 pages, 4 figures corrected titl

Screening and breeding for insect resistance in pea, lentil, faba bean and chickpea

Although grain legumes are considered to be particularly susceptible to insect damage, few studies have quantified these losses in farmers’ fields. Insecticides can protect each of the; legumes from pest damage, but plant resistance appears to be an attractive alternative, particularly for developing countries. Large differences in susceptibility to the major insect pests have been detected in the germplasm of each of pea, faba bean, lentil and chickpea, but there are no reports of successful exploitation of genotypes bred for resistance. Methods of screening and breeding for resistance are described, with particular reference to Heliothis armigera on chickpea. The dangers of breeding crops under protected conditions, for subsequent use in farmers’ fields where protection is not afforded, are emphasized

RBM6 splicing factor promotes homologous recombination repair of double-strand breaks and modulates sensitivity to chemotherapeutic drugs

RNA-binding proteins regulate mRNA processing and translation and are often aberrantly expressed in cancer. The RNA-binding motif protein 6, RBM6, is a known alternative splicing factor that harbors tumor suppressor activity and is frequently mutated in human cancer. Here, we identify RBM6 as a novel regulator of homologous recombination (HR) repair of DNA double-strand breaks (DSBs). Mechanistically, we show that RBM6 regulates alternative splicing-coupled nonstop-decay of a positive HR regulator, Fe65/APBB1. RBM6 knockdown leads to a severe reduction in Fe65 protein levels and consequently impairs HR of DSBs. Accordingly, RBM6-deficient cancer cells are vulnerable to ATM and PARP inhibition and show remarkable sensitivity to cisplatin. Concordantly, cisplatin administration inhibits the growth of breast tumor devoid of RBM6 in mouse xenograft model. Furthermore, we observe that RBM6 protein is significantly lost in metastatic breast tumors compared with primary tumors, thus suggesting RBM6 as a potential therapeutic target of advanced breast cancer. Collectively, our results elucidate the link between the multifaceted roles of RBM6 in regulating alternative splicing and HR of DSBs that may contribute to tumorigenesis, and pave the way for new avenues of therapy for RBM6-deficient tumors

Quasi-Particle Tunneling in Anti-Pfaffian Quantum Hall State

We study tunneling phenomena at the edge of the anti-Pfaffian quantum Hall state at the filling factor $\nu=5/2$. The edge current in a single point-contact is considered. We focus on nonlinear behavior of two-terminal conductance with the increase in negative split-gate voltage. Expecting the appearance of the intermediate conductance plateau we calculate the value of its conductance by using the renormalization group (RG) analysis. Further, we show that non-perturbative quasi-particle tunneling is effectively described as perturbative electron tunneling by the instanton method. The two-terminals conductance is written as a function of the gate voltage. The obtained results enable us to distinguish the anti-Pfaffian state from the Pfaffian state experimentally.Comment: 5 pages, 4 figure