Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene

Two monolayers of graphene twisted by a small `magic' angle exhibit nearly flat bands leading to correlated electronic states and superconductivity, whose precise nature including possible broken symmetries, remain under debate. Here we theoretically study a related but different system with reduced symmetry - twisted {\em double} bilayer graphene (TDBLG), consisting of {\em two} Bernal stacked bilayer graphene sheets, twisted with respect to one another. Unlike the monolayer case, we show that isolated flat bands only appear on application of a vertical displacement field $D$. We construct a phase diagram as a function of twist angle and $D$, incorporating interactions via a Hartree-Fock approximation. At half filling, ferromagnetic insulators are stabilized, typically with valley Chern number $C_v=2$. Ferromagnetic fluctuations in the metallic state are argued to lead to spin triplet superconductivity from pairing between electrons in opposite valleys. Response of these states to a magnetic field applied either perpendicular or parallel to the graphene sheets is obtained, and found to compare favorably with a recent experiment. We highlight a novel orbital effect arising from in-plane fields that can exceed the Zeeman effect and plays an important role in interpreting experiments.Comment: main 15 pages, appendix 11 page

Interlayer fractional quantum Hall effect in a coupled graphene double-layer

In two-dimensional (2D) electron systems under strong magnetic fields, interactions can cause fractional quantum Hall (FQH) effects. Bringing two 2D conductors to proximity, a new set of correlated states can emerge due to interactions between electrons in the same and opposite layers. Here we report interlayer correlated FQH states in a system of two parallel graphene layers separated by a thin insulator. Current flow in one layer generates different quantized Hall signals in the two layers. This result is interpreted by composite fermion (CF) theory with different intralayer and interlayer Chern-Simons gauge-field coupling. We observe FQH states corresponding to integer values of CF Landau level (LL) filling in both layers, as well as "semi-quantized" states, where a full CF LL couples to a continuously varying partially filled CF LL. Remarkably, we also recognize a quantized state between two coupled half-filled CF LLs, attributable to an interlayer CF exciton condensate.Comment: 14 pages, 3 figures, one table and supplementary informatio

Twisted Courant algebroids and coisotropic Cartan geometries

In this paper, we show that associated to any coisotropic Cartan geometry there is a twisted Courant algebroid. This includes in particular parabolic geometries. Using this twisted Courant structure, we give some new results about the Cartan curvature and the Weyl structure of a parabolic geometry. As more direct applications, we have Lie 2-algebra and 3D AKSZ sigma model with background associated to any coisotropic Cartan geometry

Genome-wide comparison of microRNAs and their targeted transcripts among leaf, flower and fruit of sweet orange

BACKGROUND: In plants, microRNAs (miRNAs) regulate gene expression mainly at the post-transcriptional level. Previous studies have demonstrated that miRNA-mediated gene silencing pathways play vital roles in plant development. Here, we used a high-throughput sequencing approach to characterize the miRNAs and their targeted transcripts in the leaf, flower and fruit of sweet orange. RESULTS: A total of 183 known miRNAs and 38 novel miRNAs were identified. An in-house script was used to identify all potential secondary siRNAs derived from miRNA-targeted transcripts using sRNA and degradome sequencing data. Genome mapping revealed that these miRNAs were evenly distributed across the genome with several small clusters, and 69 pre-miRNAs were co-localized with simple sequence repeats (SSRs). Noticeably, the loop size of pre-miR396c was influenced by the repeat number of CUU unit. The expression pattern of miRNAs among different tissues and developmental stages were further investigated by both qRT-PCR and RNA gel blotting. Interestingly, Csi-miR164 was highly expressed in fruit ripening stage, and was validated to target a NAC transcription factor. This study depicts a global picture of miRNAs and their target genes in the genome of sweet orange, and focused on the comparison among leaf, flower and fruit tissues. CONCLUSIONS: This study provides a global view of miRNAs and their target genes in different tissue of sweet orange, and focused on the identification of miRNA involved in the regulation of fruit ripening. The results of this study lay a foundation for unraveling key regulators of orange fruit development and ripening on post-transcriptional level. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/1471-2164-15-695) contains supplementary material, which is available to authorized users

Spectrally Resolved Extreme Ultraviolet Lensless Imaging With High Order Harmonic Generation Sources

High harmonic generation (HHG) serves as a transformative gateway to the quantum dynamics of electrons, offering a unique perspective on the ultrafast processes that govern chemical and physical transformations at the atomic scale. By focusing intense laser pulses into a noble gas, we can coerce the gas's electrons into a nonlinear dance—where they absorb multiple photons, tunnel through their atomic potentials, and re-emit this energy as they snap back to lower energy states, producing bursts of extreme ultraviolet (EUV) and soft X-ray radiation. Combining HHG with lensless imaging paves the way for revolutionary technological advancements in imaging and diagnostics, probing dynamics previously veiled by the limits of temporal resolution. The focus of the second chapter is the application of HHG in coherent diffractive imaging (CDI), where the coherence and extreme ultraviolet wavelengths of HHG sources allow for imaging with high spatial resolution and chemical sensitivity. CDI, a lensless imaging technique, circumvents the resolution limits imposed by lens-based systems, exploiting the phase retrieval from diffraction patterns to reconstruct images of nanostructures and biological specimens. The unique properties of HHG-enhanced CDI lie in its ability to spectrally reconstruct the image of the object, providing a powerful tool for understanding the 3D structure of the object and its chemical composition. This chapter paves the way towards spectrally resolved ptychography. In the third chapter, we propose the concept of spatial entropy minimization as a computational design principle for both mono- and polychromatic focusing optics. We show that spatial entropy minimization yields conventional ZPs for monochromatic radiation. For polychromatic radiation, we observe a previously unexplored class of diffractive optical elements (DOEs), allowing for balanced spectral efficiency. We apply the proposed approach to the design of a binary ZP, tailored to multispectral focusing of extreme ultraviolet (EUV) radiation from a high-harmonic table top source. The polychromatic focusing properties of these ZPs are experimentally confirmed using ptychography. This work provides a new route towards polychromatic wavefront engineering at EUV and soft-X-ray wavelengths. The fourth chapter focus on the technical challenges and solutions associated with measuring and manipulating the wavefronts of high-order harmonic beams. Here we present a wavefront sensing solution based on multiplexed ptychography, with which we show spectrally-resolved, high-resolution beam reconstructions.using these high fidelity quantitative wavefront measurements, we investigate aberration transfer mechanisms in the high harmonic generation process, where we present and explain harmonic-order dependent astigmatism inheritance from the fundamental wavefront. This ptychographic wavefront sensing concept thus enables detailed studies of the high-harmonic generation process, such as spatiotemporal effects in attosecond pulse formation. The final chapter consolidates the chromatic aberrations inherent in the HHG process, highlighting their impact on the focusability and quality of generated beams across different harmonic orders. By systematically varying the generation conditions and employing sophisticated wavefront characterization techniques, we uncover the wavelength-dependent focusing properties of HHG beams. The insights gained from these studies are crucial for optimizing the generation and application of high harmonics in various scientific and technological arenas