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3D Dirac semimetals with square-net non-symmorphic symmetry, such as ternary ZrXY (X=Si, Ge; Y=S, Se, Te) compounds, have attracted significant attention owing to the presence of topological nodal lines, loops, or networks in their bulk. Orbital symmetry plays a profound role such materials as the different branches of the nodal dispersion can be distinguished by their distinct orbital symmetry eigenvalues. The presence of different eigenvalues suggests that scattering between states of different orbital symmetry may be strongly suppressed. Indeed, in ZrSiS, there has been no clear experimental evidence of quasiparticle scattering between states of different symmetry eigenvalue has been reported at small wave vector $q$. Here we show, using quasiparticle interference (QPI), that atomic step-edges in the ZrSiS surface facilitate quasiparticle scattering between states of different symmetry eigenvalues. This symmetry eigenvalue mixing quasiparticle scattering is the first to be reported for ZrSiS and contrasts quasiparticle scattering with no mixing of symmetry eigenvalues, where the latter occurs with scatterers preserving the glide mirror symmetry of the crystal lattice, e.g., native point defects in ZrSiS. Finally, we show that the electronic structure of the ZrSiS surface, including its unique floating band surface state (FBSS), can be tuned by a vertical electric field locally applied by the tip of a scanning tunneling microscope (STM), enabling control of a spin-orbit induced avoided crossing near the Fermi level by as much as 300%.

Based on first-principles calculations, we predict that nitrogen atoms can assemble into a single-layer double kagome lattice (DKL), which possesses the characteristics of an intrinsic direct band gap semiconductor, boasting a substantial band gap of 3.460 eV. The DKL structure results in a flat valence band with high effective mass and a conduction band with small effective mass comes from Dirac electrons. These distinctive band edges lead to a significant disparity in carrier mobilities, with electron mobility being four orders of magnitude higher than that of holes. The presence of flat band in DKL-nitrogene can be further discerned through the enhanced optical absorption and correlated effects as exemplified by hole-induced ferromagnetism. Interestingly, DKL-nitrogene exhibits inherent second-order topological states, confirmed by a non-trivial second Stiefel-Whitney number and the presence of 1D floating edge states and 0D corner states within the bulk band gap. Additionally, the robust N-N bonds and the lattice's bending structure ensure thermodynamic stability and mechanical stiffness. These attributes make it exceptionally stable for potential applications in nano-devices., Comment: 9 pages, 4 figures

Xenes, two-dimensional (2D) monolayers composed of a single element, with graphene as a typical representative, have attracted widespread attention. Most of the previous Xenes, X from group-IIIA to group-VIA elements have bonding characteristics of covalent bonds. In this work, we for the first time unveil the pivotal role of a halogen bond, which is a distinctive type of bonding with interaction strength between that of a covalent bond and a van der Waals interaction, in 2D group-VIIA monolayers. Combing the ingenious non-edge-to-edge tiling theory and state-of-art ab initio method with refined local density functional M06-L, we provide a precise and effective bottom-up construction of 2D iodine monolayer sheets, iodinenes, primarily governed by halogen bonds, and successfully design a category of stable iodinenes, encompassing herringbone, Pythagorean, gyrated truncated hexagonal, i.e. diatomic-kagome, and gyrated hexagonal tiling pattern. These iodinene structures exhibit a wealth of properties, such as flat bands, nontrivial topology, and fascinating optical characteristics, offering valuable insights and guidance for future experimental investigations. Our work not only unveils the unexplored halogen bonding mechanism in 2D materials but also opens a new avenue for designing other non-covalent bonding 2D materials., Comment: 6 pages, 4 figures

Employing a combination of first-principles calculations and low-energy effective models, we present a comprehensive investigation on the electronic structure of Pb$_{10}$(PO$_{4}$)$_{6}$O$_{4}$, which exhibits remarkable quasi-one-dimensional flat-band around the Fermi level that contains novel multi-dimensional fermions. These flat bands predominantly originate from $p_x/p_y$ orbital of the oxygen molecules chain at $4e$ Wyckoff positions, and thus can be well-captured by a four-band tight-binding model. Furthermore, the abundant crystal symmetry inherent to Pb$_{10}$(PO$_{4}$)$_{6}$O$_{4}$ provides an ideal platform for the emergence of various multi-dimensional fermions, including a 0D four-fold degenerated Dirac fermion with quadratic dispersion, a 1D quadratic/linear nodal-line (QNL/LNL) fermion along symmetric $k$-paths, 1D hourglass nodal-line (HNL) fermion linked to the Dirac fermion, and a 2D symmetry-enforced nodal surface (NS) found on the $k_z$=$\pi$ plane. Moreover, when considering the weak ferromagnetic order, Pb$_{10}$(PO$_{4}$)$_{6}$O$_{4}$ transforms into a rare semi-half-metal, which is characterized by the presence of Dirac fermion and HNL fermion at the Fermi level for a single spin channel exhibiting 100$\%$ spin polarization. Our findings reveal the coexistence of flat bands, diverse topological semimetal states and ferromagnetism within in Pb$_{10}$(PO$_{4}$)$_{6}$O$_{4}$, which may provide valuable insights for further exploring intriguing interplay between superconductivity and exotic electronic states., Comment: 8 pages, 4 figures

Three-dimensional nodal line semimetals (NLSMs) provide remarkable importance for both enrich topological physics and wave management. However, NLSMs realized in acoustic systems are twofold bands degenerate, which are called Weyl NLSMs. Here, we first report on the experimental observation of novel Dirac NLSMs with fourfold degenerate in sonic crystals. We reveal that the topological properties of the Dirac NLSMs are entirely different than that of the conventional Weyl NLSMs. The Berry phase related to the Dirac nodal line (DNL) is 2{\pi}, which results in the surface responses of the Dirac NLSMs with two radically different situations: a torus surface state occupying the entire surface Brillouin zone (SBZ) and without any surface state in the SBZ. We further reveal that topological surface arcs caused by DNL can change from open to closed contours. The findings of Dirac NLSMs and their unique surface response may provoke exciting frontiers for flexible manipulation of acoustic surface waves., Comment: 6 pages, 4 figures

Traditional electronic devices rely on the electron's intrinsic degrees of freedom (d.o.f.) to process information. However, additional d.o.f. like the valley, can emerge in the low-energy states of certain systems. Here, we show that the quantum dots (QDs) constructed from two-dimensional (2D) second-order topological insulators (SOTI) posses a new kind of d.o.f., namely corner freedom, related to the topological corner states that reside at different corners of the systems. Since the corner states are well separated in real space, they can be individually and intuitively manipulated, giving rise to the concept of cornertronics. Via symmetry analysis and material search, we identify the TiSiCO-family monolayers as the first prototype of cornertronics materials, where the corner states can be controlled by both electric and optical fields, due to novel corner-layer coupling (CLC) effect and corner-contrasted linear dichroism. Furthermore, we find that the band gap of the TiSiCO nanodisk lies in the terahertz region and is robust to size reduction. These results indicate that the TiSiCO nanodisks can be used to design terahertz devices with ultrasmall size and electric-field tunable band gap. Besides, the TiSiCO nanodisks are simultaneously sensitive to both the strength and polarization of the terahertz waves. Our findings not only pave the way for cornertronics, but also open a new direction for research in 2D SOTI, QD and terahertz electronics.

Recently, Heusler ferromagnets have been found to exhibit unconventional anomalous electric, thermal, and thermoelectric transport properties. In this study, we employed first-principles density functional theory calculations to systematically investigate both intrinsic and extrinsic contributions to the anomalous Hall effect (AHE), anomalous Nernst effect (ANE), and anomalous thermal Hall effect (ATHE) in two Heusler ferromagnets: Fe$_2$CoAl and Fe$_2$NiAl. Our analysis reveals that the extrinsic mechanism originating from disorder dominates the AHE and ATHE in Fe$_2$CoAl , primarily due to the steep band dispersions across the Fermi energy and corresponding high longitudinal electronic conductivity. Conversely, the intrinsic Berry phase mechanism, physically linked to nearly flat bands around the Fermi energy and gapped by spin-orbit interaction band crossings, governs the AHE and ATHE in Fe$_2$NiAl. With respect to ANE, both intrinsic and extrinsic mechanisms are competing in Fe$_2$CoAl as well as in Fe$_2$NiAl. Furthermore, Fe$_2$CoAl and Fe$_2$NiAl exhibit tunable and remarkably pronounced anomalous transport properties. For instance, the anomalous Nernst and anomalous thermal Hall conductivities in Fe$_2$NiAl attain giant values of 8.29 A/Km and 1.19 W/Km, respectively, at room temperature. To provide a useful comparison, we also thoroughly investigated the anomalous transport properties of Co$_2$MnGa. Our findings suggest that Heusler ferromagnets Fe$_2$CoAl and Fe$_2$NiAl are promising candidates for spintronics and spin-caloritronics applications., Comment: 9 pages, 5 figures

We present a systematic investigation of the magnetoresponses of the Weyl points (WPs) with a topological charge of n = 2, 3 and 4, and with both linear and quadratic energy tilt. The linear tilt always tends to squeeze the Landau levels (LLs) of both conduction and valence bands of all the WPs, and eventually leads to LL collapse in the type-II phase. However, the quadratic energy tilt has more complex influences on the LLs of the unconventional WPs. For charge-n (n = 2, 4) WP, the influence of the quadratic tilt on the LLs of conduction and valence bands are opposite, i.e. if the LLs of conduction (valence) bands are squeezed, then that of the valence (conduction) bands are broadened, and the squeezed LL spectrum will be collapsed in type-III phase. But, the LL collapse generally can not be found in the type-III charge-3 WP. Moreover, for charge-n (n = 2, 3) WP, the quadratic tilt breaks the degeneracy of the chiral LLs regardless of the direction of the magnetic field, leading to additional optical transitions and magneto-optical conductivity peaks at low frequencies. Interestingly, the four chiral LLs in charge-4 WP are always not degenerate. Hence, there inevitably exist magneto-optical conductivity peaks at low frequencies for charge-4 WP. Since the density of state of the LL spectrum is very large, one can expect that the low-frequency magneto-optical responses in unconventional WPs would be significant and may be used for developing efficient terahertz photodetectors.

Higher-order topological insulators (HOTIs) are described by symmetric exponentially decayed Wannier functions at some $necessary$ unoccupied Wyckoff positions and classified as obstructed atomic insulators (OAIs) in the topological quantum chemistry (TQC) theory. The boundary states in HOTIs reported so far are often fragile, manifested as strongly depending on crystalline symmetries and cleavage terminations in the disk or cylinder geometry. Here, using the TQC theory, we present an intuitive argument about the connection between the obstructed Wannier charge centers of OAIs and the emergence of robust corner states in two-dimensional systems. Based on first-principles calculations and Real Space Invariant theory, we extend the concept of OAIs to phonon systems and thereby predict that the robust corner states can be realized in the phonon spectra of $MX_3$ ($M$=Bi, Sb, As, Sc, Y; $X$=I, Br, Cl) monolayers. The phonon corner modes in different shapes of nano-disks are investigated, and their robustness facilitates the detection in experiments and further applications. This work suggests a promising avenue to explore more attractive features of higher-order band topology.

Anomalous Hall effect (AHE), a protocol of various low-power dissipation quantum phenomena and a fundamental precursor of intriguing topological phases of matter, is usually observed in ferromagnetic materials with orthogonal configuration between the electric field, magnetization and the Hall current. Here, based on the symmetry analysis, we find an unconventional AHE induced by the in-plane magnetic field (IPAHE) via spin-canting effect in $\mathcal{PT}$ symmetric antiferromagnetic (AFM) systems, featuring a linear dependence of magnetic field and 2$\pi$ angle periodicity with a comparable magnitude as conventional AHE. We demonstrate the key findings in the known AFM Dirac semimetal CuMnAs and a new kind of AFM heterodimensional VS$_2$-VS superlattice with a nodal-line Fermi surface and also briefly discuss the experimental detection. Our work provides an efficient pathway to search and/or design realistic materials for novel IPAHE that could greatly facilitate their application in AFM spintronic devices., Comment: 6 pages, 4 figures, 1 table

In electronics systems, the Weyl points can be classified into three types based on the geometry of the Fermi surface, and each type exhibits various unique and intriguing phenomena. While the type-I and type-II Weyl points have been achieved in both spinful and spinless systems, the realization of type-III Weyl points remains challenging, and has not been reported in artificial periodic systems. Here, we for the first time report the experimental observation of the type-III Weyl points in a sonic crystal. Remarkably, a single pair of type-III Weyl points are observed as the only band crossings in a frequency range, experimentally disproving a common belief in the field, namely, the minimal number of Weyl points in nonmagnetic systems is four. The consistency between experimental results and theoretical predictions confirms the existence of type-III Weyl points, noncontractible Fermi arc surface states, and chiral edge states. Our work not only fill the gap of the type-III Weyl point in sonic crystal but also stimulate related researches in other systems, such as photonic, mechanical and cold atom systems.

Novel fermions with relativistic linear dispersion can emerge as low-energy excitations in topological semimetal materials. Here, we show that the orbital moment contribution in the circular photomagnetic effect for these topological semimetals exhibit an unconventional $\omega^{-1}$ frequency scaling, leading to significantly enhanced response in the low frequency window, which can be orders of magnitude larger than previous observations on conventional materials. Furthermore, the response tensor is directly connected to the Chern numbers of the emergent fermions, manifesting their topological character. Our work reveals a new signature of topological semimetals and suggests them as promising platforms for optoelectronics and spintronics applications., Comment: 6 pages, 3 figures, 1 table

Recently discovered high-quality nodal chain spin-gapless semimetals $M$F$_3$ ($M$ = Pd, Mn) feature an ultra-clean nodal chain in the spin up channel residing right at the Fermi level and displaying a large spin gap leading to a 100\% spin-polarization of transport properties. Here, we investigate both intrinsic and extrinsic contributions to anomalous and spin transport in this class of materials. The dominant intrinsic origin is found to originate entirely from the gapped nodal chains without the entanglement of any other trivial bands. The side-jump mechanism is predicted to be negligibly small, but intrinsic skew-scattering enhances the intrinsic Hall and Nernst signals significantly, leading to large values of respective conductivities. Our findings open a new material platform for exploring strong anomalous and spin transport properties in magnetic topological semimetals., Comment: 7 pages, 4 figures