Competing orders in a magnetic field: spin and charge order in the cuprate superconductors

We describe two-dimensional quantum spin fluctuations in a superconducting Abrikosov flux lattice induced by a magnetic field applied to a doped Mott insulator. Complete numerical solutions of a self-consistent large N theory provide detailed information on the phase diagram and on the spatial structure of the dynamic spin spectrum. Our results apply to phases with and without long-range spin density wave order and to the magnetic quantum critical point separating these phases. We discuss the relationship of our results to a number of recent neutron scattering measurements on the cuprate superconductors in the presence of an applied field. We compute the pinning of static charge order by the vortex cores in the `spin gap' phase where the spin order remains dynamically fluctuating, and argue that these results apply to recent scanning tunnelling microscopy (STM) measurements. We show that with a single typical set of values for the coupling constants, our model describes the field dependence of the elastic neutron scattering intensities, the absence of satellite Bragg peaks associated with the vortex lattice in existing neutron scattering observations, and the spatial extent of charge order in STM observations. We mention implications of our theory for NMR experiments. We also present a theoretical discussion of more exotic states that can be built out of the spin and charge order parameters, including spin nematics and phases with `exciton fractionalization'.Comment: 36 pages, 33 figures; for a popular introduction, see http://onsager.physics.yale.edu/superflow.html; (v2) Added reference to new work of Chen and Ting; (v3) reorganized presentation for improved clarity, and added new appendix on microscopic origin; (v4) final published version with minor change

Application of biotechnology in breeding lentil for resistance to biotic and abiotic stress

Lentil is a self-pollinating diploid (2n = 14 chromosomes) annual cool season legume crop that is produced throughout the world and is highly valued as a high protein food. Several abiotic stresses are important to lentil yields world wide and include drought, heat, salt susceptibility and iron deficiency. The biotic stresses are numerous and include: susceptibility to Ascochyta blight, caused by Ascochyta lentis; Anthracnose, caused by Colletotrichum truncatum; Fusarium wilt, caused by Fusarium oxysporum; Sclerotinia white mold, caused by Sclerotinia sclerotiorum; rust, caused by Uromyces fabae; and numerous aphid transmitted viruses. Lentil is also highly susceptible to several species of Orabanche prevalent in the Mediterranean region, for which there does not appear to be much resistance in the germplasm. Plant breeders and geneticists have addressed these stresses by identifying resistant/tolerant germplasm, determining the genetics involved and the genetic map positions of the resistant genes. To this end progress has been made in mapping the lentil genome and several genetic maps are available that eventually will lead to the development of a consensus map for lentil. Marker density has been limited in the published genetic maps and there is a distinct lack of co-dominant markers that would facilitate comparisons of the available genetic maps and efficient identification of markers closely linked to genes of interest. Molecular breeding of lentil for disease resistance genes using marker assisted selection, particularly for resistance to Ascochyta blight and Anthracnose, is underway in Australia and Canada and promising results have been obtained. Comparative genomics and synteny analyses with closely related legumes promises to further advance the knowledge of the lentil genome and provide lentil breeders with additional genes and selectable markers for use in marker assisted selection. Genomic tools such as macro and micro arrays, reverse genetics and genetic transformation are emerging technologies that may eventually be available for use in lentil crop improvement