Topological matter is known to exhibit unconventional surface states and anomalous transport owing to unusual bulk electronic topology. In this study, we use photoemission spectroscopy and quantum transport to elucidate the topology of the room temperature magnet Co 2 MnGa. We observe sharp bulk Weyl fermion line dispersions indicative of nontrivial topological invariants present in the magnetic phase. On the surface of the magnet, we observe electronic wave functions that take the form of drumheads, enabling us to directly visualize the crucial components of the bulk-boundary topological correspondence. By considering the Berry curvature field associated with the observed topological Weyl fermion lines, we quantitatively account for the giant anomalous Hall response observed in our samples. Our experimental results suggest a rich interplay of strongly correlated electrons and topology in this quantum magnet.The discovery of topological phases of matter has led to a new paradigm in physics, 30 which not only explores the analogs of particles relevant for high energy physics, but also 31 offers new perspectives and pathways for the application of quantum materials [1][2][3][4][5][6][7][8][9][10]. To 32 date, most topological phases have been discovered in non-magnetic materials [6][7][8], which 33 severely limits their magnetic field tunability and electronic/magnetic functionality. Iden-34 tifying and understanding electronic topology in magnetic materials will not only provide 35 indispensable information to make their existing magnetic properties more robust, but also 36 has the potential to lead to the discovery of novel magnetic response that can be used to ex-37 plore future spintronics technology. Recently, several magnets were found to exhibit a large 38 anomalous Hall response in transport, which has been linked to a large Berry curvature in 39 their electronic structures [11][12][13][14][15]. However, it is largely unclear in experiment whether the 40 Berry curvature originates from a topological band structure, such as Dirac/Weyl point or 41 line nodes, due to the lack of spectroscopic investigation. In particular, there is no direct vi-42 sualization of a topological magnetic phase demonstrating a bulk-boundary correspondence 43 with associated anomalous transport. 44Here we use angle-resolved photoemission spectroscopy (ARPES), ab initio calculation 45 and transport to explore the electronic topological phase of the ferromagnet Co 2 MnGa [10]. 46In our ARPES spectra we discover a line node in the bulk of the sample. Taken together with 47 our ab initio calculations, we conclude that we observe Weyl lines protected by crystalline 48 mirror symmetry and requiring magnetic order. In ARPES we further observe drumhead 49 surface states connecting the bulk Weyl lines, revealing a bulk-boundary correspondence in a 50 magnet. Combining our ARPES and ab initio calculation results with transport, we further 51 find that Berry curvature concentrated by the Weyl lines accounts for the giant intrinsic 52 anomal...

Topological semimetals can be classified by the connectivity and dimensionality of the band crossing in momentum space. The band crossings of a Dirac, Weyl, or an unconventional fermion semimetal are zero-dimensional (0D) points, whereas the band crossings of a nodal-line semimetal are one-dimensional (1D) closed loops. Here we propose that the presence of perpendicular crystalline mirror planes can protect three-dimensional (3D) band crossings characterized by nontrivial links such as a Hopf link or a coupled-chain, giving rise to a variety of new types of topological semimetals. We show that the nontrivial winding number protects topological surface states distinct from those in previously known topological semimetals with a vanishing spin-orbit interaction. We also show that these nontrivial links can be engineered by tuning the mirror eigenvalues associated with the perpendicular mirror planes. Using first-principles band structure calculations, we predict the ferromagnetic full Heusler compound Co2MnGa as a candidate. Both Hopf link and chain-like bulk band crossings and unconventional topological surface states are identified.Since the discovery of Dirac and Weyl semimetals [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], topological semimetals have emerged as an active frontier in condensed matter physics. Their unique topological properties are predicted to give rise to a wide range of exotic transport and optical phenomena [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. By considering various rotational and mirror symmetries in both symmorphic and non-symmorphic contexts, researchers have predicted nodal-line semimetals [38] [48][49][50]. Despite this diversity, topological semimetals can be further classified and characterized by the dimensionality of their band crossings in the bulk Brillouin zone (BZ). In a Dirac/Weyl semimetal or an unconventional (higher-fold degenerate) fermion semimetal [41,[43][44][45][46], the conduction and valence bands cross at discrete points in the BZ. Therefore, the dimension of their band crossings is 0D. In a nodal-line semimetal [38], the conduction and valence bands touch along a closed loop, thus the dimension of its band crossing is 1D. In this letter, we propose a number of previously unidentified topological semimetals and identify a candidate material class for the experimental realization. They feature 3D band crossings characterized by nontrivial links such as a Hopf link or a coupled-chain enabled by perpendicular mirror planes. The Hopf link, which consists of two rings that pass through the center of each other, represents the simplest topologically nontrivial link. While originally studied in mathematics and other areas, recently, researchers have applied this concept into topological physics in order to construct novel topological insulators and superconductors [52][53][54], although the role of Hopf link is distinctly different from what is considered here. Here we apply this idea in metals and show that the c...

IntroductionColorectal cancer (CRC) is the fourth most common cause of cancer-related mortality worldwide. The tumor, node, metastasis (TNM) stage remains the standard for CRC prognostication. Identification of meaningful microRNA (miRNA) and gene modules or representative biomarkers related to the pathological stage of colon cancer helps to predict prognosis and reveal the mechanisms behind cancer progression.Materials and methodsWe applied a systems biology approach by combining differential expression analysis and weighted gene co-expression network analysis (WGCNA) to detect the pathological stage-related miRNA and gene modules and construct a miRNA–gene network. The Cancer Genome Atlas (TCGA) colon adenocarcinoma (CAC) RNA-sequencing data and miRNA-sequencing data were subjected to WGCNA analysis, and the GSE29623, GSE35602 and GSE39396 were utilized to validate and characterize the results of WGCNA.ResultsTwo gene modules (Gmagenta and Ggreen) and one miRNA module were associated with the pathological stage. Six hub genes (COL1A2, THBS2, BGN, COL1A1, TAGLN and DACT3) were related to prognosis and validated to be associated with the pathological stage. Five hub miRNAs were identified to be related to prognosis (hsa-miR-125b-5p, hsa-miR-145-5p, hsa-let-7c-5p, hsa-miR-218-5p and hsa-miR-125b-2-3p). A total of 18 hub genes and seven hub miRNAs were predominantly expressed in tumor stroma. Proteoglycans in cancer, focal adhesion, extracellular matrix (ECM)–receptor interaction and so on were common pathways of the three modules. Hsa-let-7c-5p was located at the core of miRNA–gene network.ConclusionThese findings help to advance the understanding of tumor stroma in the progression of CAC and provide prognostic biomarkers as well as therapeutic targets.

We study the quasiparticle interference (QPI) patterns caused by scattering off nonmagnetic, magnetic point impurities, and edge impurities, separately, in a two dimensional helical liquid, which describes the surface states of a topological insulator. The unique features associated with hexagonal warping effects are identified in the QPI patterns of charge density with nonmagnetic impurities and spin density with magnetic impurities. The symmetry properties of the QPI patterns can be used to determine the symmetry of microscopic models. The Friedel oscillation is calculated for edge impurities and the decay of the oscillation is not universal, strongly depending on Fermi energy. Some discrepancies between our theoretical results and current experimental observations are discussed.

Bismuth-based materials have been instrumental in the development of topological physics, even though bulk bismuth itself has been long thought to be topologically trivial. A recent study has, however, shown that bismuth is in fact a higher-order topological insulator featuring one-dimensional (1D) topological hinge states protected by threefold rotational and inversion symmetries. In this paper, we uncover another hidden facet of the band topology of bismuth by showing that bismuth is also a first-order topological crystalline insulator protected by a twofold rotational symmetry. As a result, its (11¯0) surface exhibits a pair of gapless Dirac surface states. Remarkably, these surface Dirac cones are “unpinned” in the sense that they are not restricted to locate at specific k points in the (11¯0) surface Brillouin zone. These unpinned 2D Dirac surface states could be probed directly via various spectroscopic techniques. Our analysis also reveals the presence of a distinct, previously uncharacterized set of 1D topological hinge states protected by the twofold rotational symmetry. Our study thus provides a comprehensive understanding of the topological band structure of bismuth.

Using both two orbital and five orbital models, we investigate the quasiparticle interference ͑QPI͒ patterns in the superconducting ͑SC͒ state of iron-based superconductors. We compare the results for nonmagnetic and magnetic impurities in sign-changed s-wave cos͑k x ͒ · cos͑k y ͒ and sign-unchanged ͉cos͑k x ͒ · cos͑k y ͉͒ SC states. While the patterns strongly depend on the chosen band structure details, the sensitivity of peaks around ͑Ϯ ,0͒ and ͑0, Ϯ ͒ wave vectors on magnetic or nonmagnetic impurities, and on sign-changed or signunchanged SC orders is a common feature. Our results suggest that the QPI can provide evidence of the pairing symmetry in the SC states.

In this work we theoretically study, using Floquet-Bloch theory, the influence of circularly and linearly polarized light on two-dimensional band structures with Dirac and quadratic band touching points, and flat bands, taking the nearest neighbor hopping model on the kagome lattice as an example. We find circularly polarized light can invert the ordering of this three band model, while leaving the flat-band dispersionless. We find a small gap is also opened at the quadratic band touching point by 2-photon and higher order processes. By contrast, linearly polarized light splits the quadratic band touching point (into two Dirac points) by an amount that depends only on the amplitude and polarization direction of the light, independent of the frequency, and generally renders dispersion to the flat band. The splitting is perpendicular to the direction of the polarization of the light. We derive an effective low-energy theory that captures these key results. Finally, we compute the frequency dependence of the optical conductivity for this 3-band model and analyze the various interband contributions of the Floquet modes. Our results suggest strategies for optically controlling band structure and interaction strength in real systems.

Background/Aims: Increasing evidences indicated the important roles of alternative splicing in the progression and prognosis of bladder urothelial carcinoma (BLCA). However, most previous research has focused on one or several alternative splicing events, without a comprehensive evaluation of the prognostic value of splicing events in BLCA. In this study, we aimed to determine risk scores for predicting prognosis of BLCA patients based on splicing events. Methods: RNA-sequencing data and clinical information of BLCA patients were downloaded from The Cancer Genome Atlas, and data of splicing events were obtained from the SpliceSeq database. Univariate and multivariate Cox regression analyses were employed to identify survival-associated alternative spicing events (SASEs) and to calculate risk scores. Protein-protein interaction analysis of genes of the SASEs was performed using STRING, a database of known and predicted protein-protein interactions, and pathway enrichment analysis of the genes was implemented using the Database for Annotation, Visualization and Integrated Discovery (version 6.8). Receiver operating characteristic (ROC) curves and Kaplan-Meier analysis were used to evaluate the clinical significance of genes from the SASEs for building a risk score in BLCA. Correlation between splicing events of splicing factors and non-splicing factors were analyzed with Pearson correlation coefficient. A potential regulatory network was then built using Cytoscape 3.5. Results: In total, 39,508 alternative splicing events in 317 patients with BLCA were analyzed, including 4,632 SASEs. The area under the curve of the ROC of risk score (all) was 0.748 for predicting survival status of BLCA patients. Low- and high-risk score groups classified using the median “risk score (all)” value displayed remarkably different survival time (Low vs. High = 3304.841±239.758 vs 1198.614±152.460 days). The potential regulatory network with SASEs of splicing factors and other genes was constructed, which might be part of the biological mechanisms associated with prognosis of BLCA patients. Conclusions: In this study, prognostic signatures constructed using splicing events could be used for predicting the prognosis of BLCA patients.