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Motivated by the experimental identification of a higher-order van Hove singularity (VHS) in AV$_3$Sb$_5$ kagome metals, we study electronic instabilities of 2D lattice models with higher-order VHS and flavor degeneracy. In contrast to conventional VHSs, the larger power-law density of states and the weaker nesting propensity of higher-order VHSs conspire together to generate distinct competing instabilities. After discussing the occurrence of higher-order VHSs on square and kagome lattice models, we perform unbiased renormalization group calculations to study competing instabilities and find a rich phase diagram containing ferromagnetism, anti-ferromagnetism, superconductivity and Pomeranchuk orders. Remarkably, there is a generic transition from superconductivity to a $d$-wave Pomeranchuk order with increasing flavor number. Implications for the intriguing quantum states of AV$_3$Sb$_5$ kagome metals are also discussed., Comment: 14 pages, 10 figures

Transition-metal-based kagome materials at van Hove filling are a rich frontier for the investigation of novel topological electronic states and correlated phenomena. To date, in the idealized two-dimensional kagome lattice, topologically Dirac surface states (TDSSs) have not been unambiguously observed, and the manipulation of TDSSs and van Hove singularities (VHSs) remains largely unexplored. Here, we reveal TDSSs originating from a ℤ

Funding: A. W. R. and A. S. G. were supported by the Engineering and Physical Sciences Research Council (grant numbers EP/P024564/1 and EP/T011130/1 respectively). This work has been supported in part by the Alexander von Humboldt Foundation. The band topology of magnetic semimetals is of interest both from the fundamental science point of view and with respect to potential spintronics and memory applications. Unfortunately, only a handful of suitable topological semimetals with magnetic order have been discovered so far. One such family that hosts these characteristics is the antiperovskites, A3BO, a family of 3D Dirac semimetals. The A=Eu2+ compounds magnetically order with multiple phases as a function of applied magnetic field. Here, by combining band structure calculations with neutron diffraction and magnetic measurements, we establish the antiperovskite Eu3PbO as a new topological magnetic semimetal. This topological material exhibits a multitude of different topological phases with ordered Eu moments which can be easily controlled by an external magnetic field. The topological phase diagram of Eu3PbO includes an antiferromagnetic Dirac phase, as well as ferro- and ferrimagnetic phases with both Weyl points and nodal lines. For each of these phases, we determine the bulk band dispersions, the surface states, and the topological invariants by means of ab initio and tight-binding calculations. Our discovery of these topological phases introduces Eu3PbO as a new platform to study and manipulate the interplay of band topology, magnetism, and transport. Publisher PDF

Here, we report on a new kind of compound, X

Transition-metal-based kagome materials at van Hove filling are a rich frontier for the investigation of novel topological electronic states and correlated phenomena. To date, in the idealized two-dimensional kagome lattice, topologically Dirac surface states (TDSSs) have not been unambiguously observed, and the manipulation of TDSSs and van Hove singularities (VHSs) remains largely unexplored. Here, we reveal TDSSs originating from a ℤ 2 bulk topology and identify multiple VHSs near the Fermi level ( E F ) in magnetic kagome material GdV 6 Sn 6 . Using in situ surface potassium deposition, we successfully realize manipulation of the TDSSs and VHSs. The Dirac point of the TDSSs can be tuned from above to below E F , which reverses the chirality of the spin texture at the Fermi surface. These results establish GdV 6 Sn 6 as a fascinating platform for studying the nontrivial topology, magnetism, and correlation effects native to kagome lattices. They also suggest potential application of spintronic devices based on kagome materials.

Here we report on a new kind of compound, X{\delta}Ir4X12-{\delta} (X = P, As), the first hole-doped skutterudites superconductor. We provide atomic resolution images of the caging As atoms using scanning transmission electron microscopy (STEM). By inserting As atoms into the caged structure under a high pressure, superconductivity emerges with a maximum transition temperature (Tc) of 4.4 K (4.8 K) in IrAs3 (IrP3). In contrast to all of the electron-doped skutterudites, the electronic states around the Fermi level in X{\delta}Ir4X12-{\delta} are dominated by the caged X atom, which can be described by a simple body-centered tight-binding model, implying a distinct paring mechanism. Our density functional theory (DFT) calculations reveal an intimate relationship between the pressure-dependent local-phonon mode and the enhancement of Tc. The discovery of X{\delta}Ir4X12-{\delta} provides an arena to investigate the uncharted territory of hole-doped skutterudites, and the method proposed here represents a new strategy of carrier doping in caged structures, without introducing extra elements., Comment: 14 pages, 4 figures, 1 table

The recently discovered layered kagome metals AV

The recent discovery of $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A=\mathrm{K},\mathrm{Rb},\mathrm{Cs}$) has uncovered an intriguing arena for exotic Fermi surface instabilities in a kagome metal. Among them, superconductivity is found in the vicinity of multiple van Hove singularities, exhibiting indications of unconventional pairing. We show that the sublattice interference mechanism is central to understanding the formation of superconductivity in a kagome metal. Starting from an appropriately chosen minimal tight-binding model with multiple van Hove singularities close to the Fermi level for $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$, we provide a random phase approximation analysis of superconducting instabilities. Nonlocal Coulomb repulsion, the sublattice profile of the van Hove bands, and the interaction strength turn out to be the crucial parameters to determine the preferred pairing symmetry. Implications for potentially topological surface states are discussed, along with a proposal for additional measurements to pin down the nature of superconductivity in $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$.

We identify all symmetry-enforced band crossings in nonmagnetic orthorhombic crystals with and without spin-orbit coupling and discuss their topological properties. We find that orthorhombic crystals can host a large number of different band degeneracies, including movable Weyl and Dirac points with hourglass dispersions, fourfold double Weyl points, Weyl and Dirac nodal lines, almost movable nodal lines, nodal chains, and topological nodal planes. Interestingly, spin-orbit coupled materials in the space groups 18, 36, 44, 45, and 46 can have band pairs with only two Weyl points in the entire Brillouin zone. This results in a simpler connectivity of the Fermi arcs and more pronounced topological responses than in materials with four or more Weyl points. In addition, we show that the symmetries of the space groups 56, 61, and 62 enforce nontrivial weak $\mathbb{Z}_2$ topology in materials with strong spin-orbit coupling, leading to helical surface states. With these classification results in hand, we perform extensive database searches for orthorhombic materials crystallizing in the relevant space groups. We find that Sr$_2$Bi$_3$ and Ir$_2$Si have bands crossing the Fermi energy with a symmetry-enforced nontrivial $\mathbb{Z}_2$ invariant, CuIrB possesses nodal chains near the Fermi energy, Pd$_7$Se$_4$ and Ag$_2$Se exhibit fourfold double Weyl points, the latter one even in the absence of spin-orbit coupling, whereas the fourfold degeneracies in AuTlSb are made up from intersecting nodal lines. For each of these examples we compute the ab-initio band structures, discuss their topologies, and for some cases also calculate the surface states., 26 pages, 14 figures, supplemental material

Recent findings of new Higgs modes in unconventional superconductors require a classification and characterization of the modes allowed by nontrivial gap symmetry. Here we develop a theory for a tailored nonequilibrium quantum quench to excite all possible oscillation symmetries of a superconducting condensate. We show that both a finite momentum transfer and quench symmetry allow for an identification of the resulting Higgs oscillations. These serve as a fingerprint for the ground state gap symmetry. We provide a classification scheme of these oscillations and the quench symmetry based on group theory for the underlying lattice point group. For characterization, analytic calculations as well as full scale numeric simulations of the transient optical response resulting from an excitation by a realistic laser pulse are performed. Our classification of Higgs oscillations allows us to distinguish between different symmetries of the superconducting condensate., 12+6 pages

The recently discovered layered kagome metals AV_{3}Sb_{5} (A=K, Rb, and Cs) with vanadium kagome networks provide a novel platform to explore correlated quantum states intertwined with topological band structures. Here we report the prominent effect of hole doping on both superconductivity and charge density wave (CDW) order, achieved by selective oxidation of exfoliated thin flakes. A superconducting dome is revealed as a function of the effective doping content. The superconducting transition temperature (T_{c}) and upper critical field in thin flakes are significantly enhanced compared with the bulk, which are accompanied by the suppression of CDW. Our detailed analyses establish the pivotal role of van Hove singularities in promoting correlated quantum orders in these kagome metals. Our experiments not only demonstrate the intriguing nature of superconducting and CDW orders, but also provide a novel route to tune the carrier concentration through both selective oxidation and electric gating. This establishes CsV_{3}Sb_{5} as a tunable 2D platform for the further exploration of topology and correlation among 3d electrons in kagome lattices.

We study the occurrence of symmetry-enforced topological band crossings in tetragonal crystals with strong spin-orbit coupling. By computing the momentum dependence of the symmetry eigenvalues and the global band topology in the entire Brillouin zone, we determine all symmetry-enforced band crossings in tetragonal space groups. In particular, we classify all Dirac and Weyl degeneracies on points, lines, and planes, and find a rich variety of topological degeneracies. This includes, among others, double Weyl points, fourfold-double Weyl points, fourfold-quadruple Weyl points, Weyl and Dirac nodal lines, as well as topological nodal planes. For the space groups with symmetry-enforced Weyl points, we determine the minimal number of Weyl points for a given band pair and, remarkably, find that materials in space groups 119 and 120 can have band pairs with only two Weyl points in the entire Brillouin zone. This simplifies the topological responses, which would be useful for device applications. Using the classification of symmetry-enforced band crossings, we perform an extensive database search for candidate materials with tetragonal space groups. Notably, we find that Ba$_5$In$_4$Bi$_5$ and NaSn$_5$ exhibit twofold and fourfold Weyl nodal lines, respectively, which cross the Fermi energy. Hf$_3$Sb and Cs$_2$Tl$_3$ have band pairs with few number of Weyl points near the Fermi energy. Furthermore, we show that Ba$_3$Sn$_2$ has Weyl points with an accordion dispersion and topological nodal planes, while AuBr and Tl$_4$PbSe$_3$ possess Dirac points with hourglass dispersions. For each of these candidate materials we present the ab-initio band structures and discuss possible experimental signatures of the nontrivial band topology., 31 pages, 17 figures

Experimental control of local spin-charge interconversion is of primary interest for spintronics. Van der Waals (vdW) heterostructures combining graphene with a strongly spin-orbit coupled two-dimensional (2D) material enable such functionality by design. Electric spin valve experiments have thus far provided global information on such devices, while leaving the local interplay between symmetry breaking, charge flow across the heterointerface and aspects of topology unexplored. Here, we probe the gate-tunable local spin polarisation in current-driven graphene/WTe

We present a comprehensive study on the silver bismuthate ${\mathrm{Ag}}_{2}{\mathrm{BiO}}_{3}$, synthesized under high-pressure, high-temperature conditions, which has been the subject of recent theoretical work on topologically complex electronic states. We present x-ray photoelectron spectroscopy results showing two different bismuth states and x-ray absorption spectroscopy results on the oxygen $K$ edge showing holes in the oxygen bands. These results support a bond disproportionated state with holes on the oxygen atoms for ${\mathrm{Ag}}_{2}{\mathrm{BiO}}_{3}$. We estimate a band gap of $\ensuremath{\sim}1.25$ eV for ${\mathrm{Ag}}_{2}{\mathrm{BiO}}_{3}$ from optical conductivity measurements, which matches the band gap in density functional calculations of the electronic band structure in the nonsymmorphic space group $Pnn2$, which supports two inequivalent Bi sites. In our band structure calculations the disproportionated ${\mathrm{Ag}}_{2}{\mathrm{BiO}}_{3}$ is expected to host Weyl nodal chains, one of which is located $\ensuremath{\sim}0.5$ eV below the Fermi level. Furthermore, we highlight similarities between ${\mathrm{Ag}}_{2}{\mathrm{BiO}}_{3}$ and the well-known disproportionated bismuthate ${\mathrm{BaBiO}}_{3}$, including breathing phonon modes with similar energy. In both compounds, hybridization of Bi $6s$ and O $2p$ atomic orbitals is important in shaping the band structure, but in contrast to the Ba $5p$ bands in ${\mathrm{BaBiO}}_{3}$, the Ag $4d$ bands in ${\mathrm{Ag}}_{2}{\mathrm{BiO}}_{3}$ extend up to the Fermi level.

Full experimental control of local spin-charge interconversion is of primary interest for spintronics. Heterostructures combining graphene with a strongly spin-orbit coupled two-dimensional (2D) material enable such functionality by design. Electric spin valve experiments have provided so far global information on such devices, while leaving the local interplay between symmetry breaking, charge flow across the heterointerface and aspects of topology unexplored. Here, we utilize magneto-optical Kerr microscopy to resolve the gate-tunable, local current-induced spin polarisation in graphene/WTe$_2$ van der Waals (vdW) heterostructures. It turns out that even for a nominal in-plane transport, substantial out-of-plane spin accumulation is induced by a corresponding out-of-plane current flow. We develop a theoretical model which explains the gate- and bias-dependent onset and spatial distribution of the massive Kerr signal on the basis of interlayer tunnelling, along with the reduced point group symmetry and inherent Berry curvature of the heterostructure. Our findings unravel the potential of 2D heterostructure engineering for harnessing topological phenomena for spintronics, and constitute an important further step toward electrical spin control on the nanoscale., Comment: 6 pages, 4 figures

We report the structure and physical properties of two newly-discovered compounds AV8Sb12 and AV6Sb6 (A = Cs, Rb), which have C2 (space group: Cmmm) and C3 (space group: R-3m) symmetry, respectively. The basic V-kagome unit is present in both compounds, but stacking differently. A V2Sb2 layer is sandwiched between two V3Sb5 layers in AV8Sb12, altering the V-kagome lattice and lowering the symmetry of kagome layer from hexagonal to orthorhombic. In AV6Sb6, the building block is a more complex slab made up of two half-V3Sb5 layers that are intercalated by Cs cations along the c-axis. Transport property measurements demonstrate that both compounds are nonmagnetic metals, with carrier concentrations at around 1021cm-3. No superconductivity has been observed in CsV8Sb12 above 0.3 K under in-situ pressure up to 46 GPa. In contrast to CsV3Sb5, theoretical calculations and angle-resolved photoemission spectroscopy (ARPES) reveal a quasi-two-dimensional electronic structure in CsV8Sb12 with C2 symmetry and no van Hove singularities near the Fermi level. Our findings will stimulate more research into V-based kagome quantum materials., Comment: 11 pages 6 figures

In high-energy physics, the Higgs field couples to gauge bosons and fermions and gives mass to their elementary excitations. Experimentally, such couplings can be inferred from the decay product of the Higgs boson, i.e., the scalar (amplitude) excitation of the Higgs field. In superconductors, Cooper pairs bear a close analogy to the Higgs field. Interaction between the Cooper pairs and other degrees of freedom provides dissipation channels for the amplitude mode, which may reveal important information about the microscopic pairing mechanism. To this end, we investigate the Higgs (amplitude) mode of several cuprate thin films using phase-resolved terahertz third harmonic generation (THG). In addition to the heavily damped Higgs mode itself, we observe a universal jump in the phase of the driven Higgs oscillation as well as a non-vanishing THG above Tc. These findings indicate coupling of the Higgs mode to other collective modes and potentially a nonzero pairing amplitude above Tc., Interaction between Cooper pairs and other collective excitations may reveal important information about the pairing mechanism. Here, the authors observe a universal jump in the phase of the driven Higgs oscillations in cuprate thin films, indicating the presence of a coupled collective mode, as well as a nonvanishing Higgs-like response at high temperatures, suggesting a potential nonzero pairing amplitude above Tc.

Following over a decade of intense efforts to enable major progress in spintronics devices and quantum information technology by means of materials in which the electronic structure exhibits non-trivial topological properties, three key challenges are still unresolved. First, the identification of topological band degeneracies that are generically rather than accidentally located at the Fermi level. Second, the ability to easily control such topological degeneracies. And third, to identify generic topological degeneracies in large, multi-sheeted Fermi surfaces. Combining de Haas - van Alphen spectroscopy with density functional theory and band-topology calculations, we report here that the non-symmorphic symmetries in ferromagnetic MnSi generate nodal planes (NPs), which enforce topological protectorates (TPs) with substantial Berry curvatures at the intersection of the NPs with the Fermi surface (FS) regardless of the complexity of the FS. We predict that these TPs will be accompanied by sizeable Fermi arcs subject to the direction of the magnetization. Deriving the symmetry conditions underlying topological NPs, we show that the 1651 magnetic space groups comprise 7 grey groups and 26 black-and-white groups with topological NPs, including the space group of ferromagnetic MnSi. Thus, the identification of symmetry-enforced TPs on the FS of MnSi that may be controlled with a magnetic field suggests the existence of similar properties, amenable for technological exploitation, in a large number of materials., accepted version prior to processing by editorial staff

Majorana fermions feature non-Abelian exchange statistics and promise fascinating applications in topological quantum computation. Recently, second-order topological superconductors (SOTSs) have been proposed to host Majorana fermions as localized quasiparticles with zero excitation energy, pointing out a new avenue to facilitate topological quantum computation. We provide a minimal model for SOTSs and systematically analyze the features of Majorana zero modes with analytical and numerical methods. We further construct the fundamental fusion principles of zero modes stemming from a single or multiple SOTS islands. Finally, we propose concrete schemes in different setups formed by SOTSs, enabling us to exchange and fuse the zero modes for non-Abelian braiding and holonomic quantum gate operations., Improvements in the descriptions of Majorana exchanges; Appendices are included. Comments are welcome!

Weyl superconductors feature Weyl points at zero energy in the three-dimensional (3D) Brillouin zone and arc states that connect the projections of these Weyl points on the surface. We report that higher-order Weyl superconductors can be realized in odd-parity topological superconductors with time-reversal symmetry being broken by periodic driving. Different from conventional Weyl points, the higher-order Weyl points in the bulk separate 2D first- and second-order topological phases, while on the surface, their projections are connected not only by conventional surface Majorana arcs, but also by hinge Majorana arcs. We show that the Weyl-point connectivity via Majorana arcs is largely enriched by the underlying higher-order topology and becomes anisotropic with respect to surface orientations. We identify the anisotropic Weyl-point connectivity as a characteristic feature of higher-order Weyl materials. As each 2D subsystem can be singled out by fixing the periodic driving, we propose how the Majorana zero modes in the 2D higher-order topological phases can be detected and manipulated in experiments., 7 pages, 3 figures

The fermion doubling theorem plays a pivotal role in Hermitian topological materials. It states, for example, that Weyl points must come in pairs in three-dimensional semimetals. Here, we present an extension of the doubling theorem to non-Hermitian lattice Hamiltonians. We focus on two-dimensional non-Hermitian systems without any symmetry constraints, which can host two different types of topological point nodes, namely, (i) Fermi points and (ii) exceptional points. We show that these two types of protected point nodes obey doubling theorems, which require that the point nodes come in pairs. To prove the doubling theorem for exceptional points, we introduce a generalized winding number invariant, which we call the "discriminant number." Importantly, this invariant is applicable to any two-dimensional non-Hermitian Hamiltonian with exceptional points of arbitrary order and, moreover, can also be used to characterize nondefective degeneracy points. Furthermore, we show that a surface of a three-dimensional system can violate the non-Hermitian doubling theorems, which implies unusual bulk physics.

Lattice deformations act on the low-energy excitations of Dirac materials as effective axial vector fields. This allows to directly detect quantum anomalies of Dirac materials via the response to axial gauge fields. We investigate the parity anomaly in Dirac nodal line semimetals induced by lattice vibrations, and establish a topological piezoelectric effect; i.e., periodic lattice deformations generate topological Hall currents that are transverse to the deformation field. The currents induced by this piezoelectric effect are dissipationless and their magnitude is completely determined by the length of the nodal ring, leading to a semi-quantized transport coefficient. Our theoretical proposal can be experimentally realized in various nodal line semimetals, such as CaAgP and Ca$_{_3}$P${_2}$., 6 pages, 4 figures + Supplementary information

The pairing symmetry of the hexagonal pnictide superconductor SrPtAs is discussed with taking into account its multiband structure. The topological chiral d-wave state with time-reversal-symmetry breaking has been anticipated from the spontaneous magnetization observed by the muon-spin-relaxation experiment. We point out in this paper that the recent experimental reports on the nuclear-spin–lattice relaxation rate T−1^-1 and superfluid density ns(T), which seemingly support the conventional s-wave pairing, are also consistent with the chiral d-wave state. The compatibility of the gap and multiband structures is crucial in this argument. We propose that the measurement of the bulk quasiparticle density of states would be useful for the distinction between two pairing states., JPS Conference Proceedings, 30, Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2019), ISBN:978-4-89027-142-9

Majorana corner modes appearing in two-dimensional second-order topological superconductors have great potential applications for fault-tolerant topological quantum computations. We demonstrate that in the presence of an in-plane magentic field two-dimensional ($s+p$)-wave superconductors host Majorana corner modes, whose location can be manipulated by the direction of the magnetic field. In addition, we discuss the effects of edge imperfections on the Majorana corner modes. We describe how different edge shapes and edge disorder affect the number and controllability of the Majorana corner modes, which is of relevance for the implementation of topological quantum computations. We also discuss tunneling spectroscopy in the presence of the Majorana corner modes, where a lead-wire is attached to the corner of the noncentrosymmetric superconductor. The zero-bias differential conductance shows a distinct periodicity with respect to the direction of the magnetic field, which demonstrates the excellent controllability of the Majorana corner modes in this setup. Our results lay down the theoretical groundwork for observing and tuning Majoran corner modes in experiments on ($s+p$)-wave superconductors., Comment: 11 pages, 10 figures

Magnetic Weyl semimetals are a newly discovered class of topological materials that may serve as a platform for exotic phenomena, such as axion insulators or the quantum anomalous Hall effect. Here, we use angle-resolved photoelectron spectroscopy and ab initio calculations to discover Weyl cones in CoS2, a ferromagnet with pyrite structure that has been long studied as a candidate for half-metallicity, which makes it an attractive material for spintronic devices. We directly observe the topological Fermi arc surface states that link the Weyl nodes, which will influence the performance of CoS2 as a spin injector by modifying its spin polarization at interfaces. In addition, we directly observe a minority-spin bulk electron pocket in the corner of the Brillouin zone, which proves that CoS2 cannot be a true half-metal., This work was supported by NSF through the Princeton Center for Complex Materials, a Materials Research Science and Engineering Center DMR-1420541, by Princeton University through the Princeton Catalysis Initiative, and by the Gordon and Betty Moore Foundation through grant GBMF9064 to L.M.S. F.d.J. acknowledges funding from the Spanish MCI/AEI through grant no. PGC2018-101988-B-C21. M.G.V. and F.J. acknowledge funding from the Basque Government through grant PIBA 2019-81. M.G.V. and I.R. acknowledge the Spanish Ministerio de Ciencia e Innovacion (grant number PID2019-109905GB-C21). N.B.M.S. was supported by Microsoft. A.B. acknowledges financial support from the Spanish Ministry of Science and Innovation (PID2019-105488GB-I00). The work of S.S. was supported by the Swiss National Science Foundation under grant no. 159690. D.P. acknowledges the support from the Chinese Scholarship Council. J.A.K. acknowledges support by the Swiss National Science Foundation (SNF-Grant no. 200021_165910).

Parity-time ($\mathcal{PT}$) symmetry plays an important role both in non-Hermitian and topological systems. In non-Hermitian systems, $\mathcal{PT}$ symmetry can lead to an entirely real-energy spectrum, while in topological systems, $\mathcal{PT}$ symmetry gives rise to stable and protected Dirac points. Here, we study a $\mathcal{PT}$-symmetric system which is both non-Hermitian and topological, namely, a $\mathcal{PT}$-symmetric Dirac semimetal with non-Hermitian perturbations in three dimensions. We find that, in general, there are only two types of symmetry-allowed non-Hermitian perturbations, namely, non-Hermitian kinetic potentials and non-Hermitian anticommuting potentials. For both of these non-Hermitian potentials, we investigate the band topology for open and periodic boundary conditions, determine the exceptional points, and compute the surface states. We find that with periodic boundary conditions, the non-Hermitian kinetic potential leads to exceptional rings, while the non-Hermitian anticommuting potential generates exceptional spheres, which separate regions with broken $\mathcal{PT}$ symmetry from regions with unbroken $\mathcal{PT}$ symmetry. With open boundary conditions, the non-Hermitian kinetic potential induces a non-Hermitian skin effect, which is localized on both sides of the sample due to symmetry, while the non-Hermitian anticommuting potential leads to Fermi ribbon surface states.

Nonsymmoprhic symmetries, such as screw rotations or glide reflections, can enforce band crossings within high-symmetry lines or planes of the Brillouin zone. When these band degeneracies are close to the Fermi energy, they can give rise to a number of unusual phenomena: e.g., anomalous magnetoelectric responses, transverse Hall currents, and exotic surface states. In this paper, we present a comprehensive classification of such nonsymmorphic band crossings in trigonal materials with strong spin-orbit coupling. We find that in trigonal systems there are two different types of nonsymmorphic band degeneracies: (i) Weyl points protected by screw rotations with an accordion-like dispersion, and (ii) Weyl nodal lines protected by glide reflections. We report a number of existing materials, where these band crossings are realized near the Fermi energy. This includes Cu2SrSnS4 and elemental tellurium (Te), which exhibit accordion Weyl points; and the tellurium-silicon clathrate Te16Si38, which shows Weyl nodal lines. The ab-initio band structures and surface states of these materials are studied in detail, and implications for experiments are briefly discussed., 13 pages, 11 figures, 4 tables

Topological quantum paramagnets are exotic states of matter, whose magnetic excitations have a topological band structure, while the ground state is topologically trivial. Here we show that a simple model of quantum spins on a honeycomb bilayer hosts a time-reversal-symmetry protected ${\mathbb{Z}}_{2}$ topological quantum paramagnet (topological triplon insulator) in the presence of spin-orbit coupling. The excitation spectrum of this quantum paramagnet consists of three triplon bands, two of which carry a nontrivial ${\mathbb{Z}}_{2}$ index. As a consequence, there appear two counterpropagating triplon excitation modes at the edge of the system. We compute the triplon edge state spectrum and the ${\mathbb{Z}}_{2}$ index for various parameter choices. We further show that upon making one of the Heisenberg couplings stronger, the system undergoes a topological quantum phase transition, where the ${\mathbb{Z}}_{2}$ index vanishes, to a different topological quantum paramagnet. In this case the counterpopagating triplon edge modes are disconnected from the bulk excitations and are protected by a chiral and a unitary symmetry. We discuss possible realizations of our model in real materials, in particular ${d}^{4}$ Mott insulators, and their potential applications.

Recently, there has been a lot of activity in the research field of topological non-Hermitian physics, partly driven by fundamental interests and partly driven by applications in photonics. However, despite these activities, a general classification and characterization of non-Hermitian Dirac models that describe the experimental systems is missing. Here, we present a systematic investigation of massive Dirac models on periodic lattices, perturbed by general non-Hermitian terms. We find that there are three different types of non-Hermitian terms. For each case we determine the bulk exceptional points, the boundary modes, and the band topology. Our findings serve as guiding principles for the design of applications, for example, in photonic lattices. For instance, periodic Dirac systems with non-Hermitian mass terms can be used as topological lasers. Periodic Dirac systems with non-Hermitian anti-commuting terms, on the other hand, exhibit exceptional points at the surface, whose non-trivial topology could be utilized for optical devices., 6 pages, 2 figures + 4 pages of supplemental material

The proximity effect from a spin-triplet $p_x$-wave superconductor to a dirty normal-metal has been shown to result in various unusual electromagnetic properties, reflecting a cooperative relation between topologically protected zero-energy quasiparticles and odd-frequency Cooper pairs. However, because of a lack of candidate materials for spin-triplet $p_x$-wave superconductors, observing this effect has been difficult. In this paper, we demonstrate that the anomalous proximity effect, which is essentially equivalent to that of a spin-triplet $p_x$-wave superconductor, can occur in a semiconductor/high-$T_c$ cuprate superconductor hybrid device in which two potentials coexist: a spin-singlet $d$-wave pair potential and a spin--orbit coupling potential sustaining the persistent spin-helix state. As a result, we propose an alternative and promising route to observe the anomalous proximity effect related to the profound nature of topologically protected quasiparticles and odd-frequency Cooper pairs., Comment: 6 pages, 4 figures

Collective excitation modes are a characteristic feature of symmetry-broken phases of matter. For example, superconductors exhibit an amplitude Higgs mode and a phase mode, which are the radial and angular excitations in the Mexican-hat potential of the free energy. In two-band superconductors there exists in addition a Leggett phase mode, which corresponds to collective fluctuations of the interband phase difference. In equilibrium systems amplitude and phase modes are decoupled, since they are mutually orthogonal excitations. The direct detection of Higgs and Leggett modes by linear-response measurements is challenging, because they are often overdamped and do not couple directly to the electromagnetic field. In this work, using numerical exact simulations we show for the case of two-gap superconductors, that optical pump-probe experiments excite both Higgs and Leggett modes out of equilibrium. We find that this non-adiabatic excitation process introduces a strong interaction between the collective modes. Moreover, we predict that the coupled Higgs and Leggett modes are clearly visible in the pump-probe absorption spectra as oscillations at their respective frequencies., 8 pages, 6 figures

According to the mathematical classification of topological band structures, there exist a number of fascinating topological states in dimensions larger than three with exotic boundary phenomena and interesting topological responses. While these topological states are not accessible in condensed matter systems, recent works have shown that synthetic systems, such as photonic crystals or electric circuits, can realize higher-dimensional band structures. Here, we argue that, because of its symmetry properties, the 4D spinless topological insulator is particularly well suited for implementation in these synthetic systems. We explicitly construct a 2D electric circuit lattice, whose resonance frequency spectrum simulates the 4D spinless topological insulator. We perform detailed numerical calculations of the circuit lattice and show that the resonance frequency spectrum exhibits pairs of 3D Weyl boundary states, a hallmark of the nontrivial topology. These pairs of 3D Weyl states with the same chirality are protected by classical time-reversal symmetry that squares to +1, which is inherent in the proposed circuit lattice. We also discuss how the simulated 4D topological band structure can be observed in experiments., A 4D topological insulator is simulated on a 2D board of electric circuits, where the intrinsic classical time-reversal symmetry protects two Weyl modes with the same chirality on each boundary.