No abstract

The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and a remarkably similar set of constraints at the surface of a 3D interacting topological insulator. This, combined with recent work on symmetry-enriched topological phases with on-site unitary symmetries, enables us to develop a framework for understanding the structure of symmetry-enriched topological phases with both translational and on-site unitary symmetries, including the effective theory of symmetry defects. This framework places stringent constraints on the possible types of symmetry fractionalization that can occur in 2D systems whose unit cell contains fractional spin, fractional charge, or a projective representation of the symmetry group. As a concrete application, we determine when a topological phase must possess a "spinon" excitation, even in cases when spin rotational invariance is broken down to a discrete subgroup by the crystal structure. We also describe the phenomena of "anyonic spin-orbit coupling," which may arise from the interplay of translational and on-site symmetries. These include the possibility of on-site symmetry defect branch lines carrying topological charge per unit length and lattice dislocations inducing degeneracies protected by onsite symmetry.

We consider a two-dimensional (p(x) + ip(y)) superconductor in the presence of multiple vortices, which support zero-energy Majorana-fermion states in their cores. Intervortex tunnelings of the Majorana fermions lift the topological state degeneracy. Using the Bogoliubov-de Gennes equation, we calculate splitting of the zero-energy modes due to these tunneling events. We also discuss superconducting fluctuations and, in particular, their effect on the energy splitting.

The lateral flow assay is one of the most convenient analytical techniques for analyzing the immune response, but its applicability to precise genetic analyses is limited by the false-positive signal and tedious and inefficient hybridization steps. Here, we introduce the CRISPR (clustered regularly interspaced short palindromic repeats) /Cas system into the lateral flow assay, termed CRISPR/Cas9-mediated lateral flow nucleic acid assay (CASLFA), to address such issues. In this study, CASLFA is utilized to identify Listeria monocytogenes, genetically modified organisms (GMOs), and African swine fever virus (ASFV) at a detection limit of hundreds of copies of genome samples with high specificity within 1 h. We further evaluated the performance of CASLFA in a nonlaboratory environment and successfully confirmed 27 ASFV-infected samples from 110 suspected swine serum samples, with an accuracy of 100% when compared to real-time PCR (RT-PCR) assay. CASLFA satisfies some of the characteristics of a next-generation molecular diagnostics tool due to its rapidity and accuracy, allowing for point-of-care use without the need for technical expertise and complex ancillary equipment. This method has great potential for gene analysis in resource-poor or nonlaboratory environments.