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.
We consider a two-orbital tight-binding model defined on a layered three-dimensional hexagonal lattice to investigate the properties of topological nodal lines and their associated drumhead surface states. We examine these surface states in centrosymmetric systems, where the bulk nodal lines are of Dirac type (i.e., four-fold degenerate), as well as in non-centrosymmetric systems with strong Rashba and/or Dresselhaus spin-orbit coupling, where the bulk nodal lines are of Weyl type (i.e., two-fold degenerate). We find that in non-centrosymmetric systems the nodal lines and their corresponding d…
Here, we systematically investigate the structure, phase stability, half-metallicity, and topological electronic structure for a new topological spintronic material NaV2O4. The material has a tetragonal structure with excellent dynamical and thermal stabilities. It shows a half-metallic ground state, where only the spin-up bands present near the Fermi level. These bands form a Weyl nodal line close to the Fermi level, locating in the kz = 0 plane. The nodal line is robust against SOC, under the protection of the mirror symmetry. The nodal line band structure is very clean, thus the drumhead su…
We study surface superconductivity involving the `drumhead' surface states of (doped) Weyl loop materials. The leading weak coupling instability in the bulk is toward a chiral superconducting order, which fully gaps the Fermi surface. In this state the surface also becomes superconducting, with $p+ip$ symmetry. We show that the surface SC state is "topological" as long as it is fully gapped, and the system traps Majoarana modes wherever a vortex line enters or exits the bulk. In contrast to true 2D $p+ip$ superconductors, these Majorana zero modes arise even in the "strong pairing" regime wher…
Nodal-line metals and semimetals, as interesting topological states of matter, have been mostly studied in nonmagnetic materials. Here, based on first-principles calculations and symmetry analysis, we predict that fully spin-polarized Weyl loops can be realized in the half metal state for the three-dimensional material Li$_3$(FeO$_3$)$_2$. We show that this material has a ferromagnetic ground state, and it is a half metal with only a single spin channel present near the Fermi level. The spin-up bands form two separate Weyl loops close to the Fermi level, which arise from band inversions and ar…
For topological materials with coexistence of Weyl nodes and nodal rings, the surface-state configuration and connection are unique yet have never been studied and discussed before. In this paper, we predict a ferromagnetic (FM) material, Cs2MoCl6, with coexistence of Weyl and nodering fermions in its spinful FM electronic band structure, which is unusual since FM materials are very rare in nature and node-ring band crossings will usually open a gap when spin-orbit coupling (SOC) is taken into consideration. We find that the surface states of Cs2MoCl6 show different properties along different …
Recently, magnetic topological semimetals have received a lot of attention due to their potential applications in the field of spintronics. By using first-principles calculations, we propose that two ferromagnetic spinel materials of X2MnO4 (X=Li, Na) have Weyl-type nodal chains around the Fermi level. Their stabilities are validated by cohesive energies, phonon dispersions, and elastic constants. The nodal chains are composed of two types of nodal loops, which are protected by the glide operation Mz, the mirror operation M101 and their equivalent. The drumhead surface states are observed on t…
We propose a correspondence between the description of emergent Lorentz symmetry in condensed-matter systems and the established general effective field theory for Lorentz violation in fundamental theories of spacetime and matter. This correspondence has potential implications in both directions. We illustrate the proposal by investigating its consequences for the spectral and transport properties of Dirac and Weyl semimetals. Particular realizations of this framework give rise to Dirac nodal spectra with nodal lines and rings. We demonstrate a bulk-boundary correspondence between bulk topolog…
We theoretically predict proximity-induced odd-frequency (odd-$ω$) pairing on the surface of a Weyl nodal loop semimetal, characterized by a nodal loop Fermi surface and drumhead-like surface states (DSSs), attached to conventional spin-singlet $s$-wave superconducting leads. Due to the complete spin polarization of the DSS, odd-$ω$ equal-spin triplet pairing is present, and we show that it gives rise to a finite Josephson current. Placing an additional ferromagnet in the junction can also generate odd-$ω$ mixed-spin triplet pairing, but the pairing and current is not affected if the magnetiza…
The effect of Anderson diagonal disorder on the topological surface (``drumhead'') states of a Weyl nodal loop semimetal is addressed. Since diagonal disorder breaks chiral symmetry, a winding number cannot be defined. Seen as a perturbation, the weak random potential mixes the clean exponentially localized drumhead states of the semimetal, thereby producing two effects: (i) the algebraic decay of the surface states into the bulk; (ii) a broadening of the low energy density of surface states of the open system due to degeneracy lifting. This behavior persists with increasing disorder, up to th…
The search for artificial structure with tunable topological properties is an interesting research direction of today's topological physics. Here, we introduce a scheme to realize `topological semimetal states' with a three-dimensional periodic inductor-capacitor (LC) circuit lattice, where the topological nodal-line state and Weyl state can be achieved by tuning the parameters of inductors and capacitors. A tight-binding-like model is derived to analyze the topological properties of the LC circuit lattice. The key characters of the topological states, such as the drumhead-like surface bands f…
Young and Kane have given a great insight for 2D Dirac semimetals with nontrivial topology in the presence of nonsymmorphic crystalline symmetry. Based on one of 2D nonsymmorphic square lattice structures they proposed, we further construct a set of 3D minimal tight-binding models via vertically stacking the 2D nonsymmorphic lattice. Specifically, our model provides a platform to generate three topologically semimetallic phases such as Dirac nodal line semimetals, Weyl nodal line semimetals and Weyl semimetals. The off-centered mirror symmetry sufficiently protects nodal lines emerging within …
Recent experimental observations of Weyl fermions in materials opens a new frontier of condensed matter physics. Based on first-principles calculations, we here discover Weyl fermions in a two-dimensional layered electride material Y$_2$C. We find that the Y 4$d$ orbitals and the anionic $s$-like orbital confined in the interstitial spaces between [Y$_2$C]$^{2+}$ cationic layers are hybridized to give rise to van Have singularities near the Fermi energy $E_{\rm F}$, which induce a ferromagnetic (FM) order via the Stoner-type instability. This FM phase with broken time-reversal symmetry hosts t…
Magnetic topological quantum materials have attracted great attention due to their exotic topological quantum physics induced by the interplay among crystalology, magnetism, and topology, which is of profound importance to fundamental research and technology applications. However, limited materials are experimentally available, most of whom are realized by magnetic impurity doping or heterostructural constructions. In this work, based on the first-principles calculations, we predict that double perovskite Ba2CdReO6 is an intrinsic ferromagnetic topological semi-half-metal, while the ferrimagne…
Based on first-principles calculations, we predict that the superconducting MgB$_2$ with a AlB$_2$-type centrosymmetric lattice host the so-called phononic topological Weyl nodal lines (PTWNLs) on its bulk phonon spectrum. These PTWNLs can be viewed as countless Weyl points (WPs) closely aligned along the straight lines in the $-$H-K-H direction within the three-dimensional Brillouin zone (BZ). Their topological non-trivial natures are confirmed by the calculated Berry curvature distributions on the planes perpendicular to these lines. These lines are highly unique, because they exactly locate…
Magnetic Weyl fermions, which occur in magnets, have novel transport phenomena related to pairs of Weyl nodes, and they are, of both, scientific and technological interest, with the potential for use in high-performance electronics, spintronics and quantum computing. Although magnetic Weyl fermions have been predicted to exist in various oxides, evidence for their existence in oxide materials remains elusive. SrRuO3, a 4d ferromagnetic metal often used as an epitaxial conducting layer in oxide heterostructures, provides a promising opportunity to seek for the existence of magnetic Weyl fermion…
Composite quantum compounds (CQC) are classic example of quantum materials which host more than one apparently distinct quantum phenomenon in physics. Magnetism, topological superconductivity, Rashba physics etc. are few such quantum phenomenon which are ubiquitously observed in several functional materials and can co-exist in CQCs. In this letter, we use {\it ab-initio} calculations to predict the co-existence of two incompatible phenomena, namely topologically non-trivial Weyl semimetal and spin gapless semiconducting (SGS) behavior, in a single crystalline system. SGS belong to a special cl…
Based on the first-principles calculations, we theoretically propose topologically non-trivial states in a recently experimentally discovered superconducting material CaSn$_3$. When the spin-orbit coupling (SOC) is ignored, the material is a host to three-dimensional topological nodal-line semimetal states. Drumhead like surface states protected by the coexistence of time-reversal and mirror symmetry emerge within the two-dimensional regions of the surface Brillouin zone connecting the nodal lines. When SOC is included, unexpectedly, each nodal line evolves into two Weyl nodes (W1, W2) in this…
Weyl fermions can be created in materials with both time reversal and inversion symmetry by applying a magnetic field, as evidenced by recent measurements of anomalous negative magnetoresistance. Here, we do a thorough analysis of the Weyl points in these materials: by enforcing crystal symmetries, we classify the location and monopole charges of Weyl points created by fields aligned with high-symmetry axes. The analysis applies generally to materials with band inversion in the $T_d$, $D_{4h}$ and $D_{6h}$ point groups. For the $T_d$ point group, we find that Weyl nodes persist for all directi…
Topological phases of matter have established a new paradigm in physics, bringing quantum phenomena to the macroscopic scale and hosting exotic emergent quasiparticles. In this thesis, I theoretically and experimentally demonstrate with my collaborators the first Weyl semimetal, TaAs, using angle-resolved photoemission spectroscopy (ARPES), directly observing its emergent Weyl fermions and topological Fermi arc surface states [Science 349, 6248 (2015); Nat. Commun. 6, 7373 (2015); PRL 116, 066802 (2016)]. Next, I discover high-degeneracy topological chiral fermions in the chiral crystals RhSi …
Weyl fermions, which are fermions with definite chiralities, can give rise to anomalous breaking of the symmetry of the physical system which they are a part of. In their (3+1)-dimensional realizations in condensed matter systems, i.e., the so-called Weyl semimetals, this anomaly gives rise to topological electromagnetic response of magnetic fluctuations, which takes the form of non-local interaction between magnetic fluctuations and electromagnetic fields. We study the physical consequences of this non-local interaction, including electric field assisted magnetization dynamics, an extra gaple…
Weyl fermions have recently been observed in several time-reversal-invariant semimetals and photonics materials with broken inversion symmetry. These systems are expected to have exotic transport properties such as the chiral anomaly. However, most discovered Weyl materials possess a substantial number of Weyl nodes close to the Fermi level that give rise to complicated transport properties. Here we predict, for the first time, a new family of Weyl systems defined by broken time-reversal symmetry, namely, Co-based magnetic Heusler materials XCo2Z (X = IVB or VB; Z = IVA or IIIA). To search for…
Chiral magnetic effect is a quantum phenomenon that is breaking of chiral symmetry of relativistic Weyl fermions by quantum fluctuation under paralleled electric field E and magnetic field B. Intuitively, Weyl fermions with different chirality, under stimulus of paralleled E and B, will have different chemical potential that gives rise to an extra current, whose role likes a chiral battery in solids. However, up to now, the experimental evidence for chiral magnetic effect is the negative longitudinal magnetoresistance rather than a chiral electric source. Here, totally different from previous …
We predict a large anomalous Nernst effect in the inverse Heusler compensated ferrimagnets Ti$_2$Mn$X$ ($X$=Al,Ga,In) with vanishing net magnetic moments. Though the net magnetic moment is zero, the Weyl points in these systems lead to a large anomalous Nernst conductivity (ANC) due to the lack of a magnetic sublattice that inverses the sign of the Berry curvature. In comparison to the noncollinear antiferromagnets Mn$_3$Sn and Mn$_3$Ge, the high ANC stems almost entirely from the Weyl points in this class of compounds, and thus, it is topologically protected. This work shows for the first tim…
We predict a magnetic Weyl semimetal in the inverse Heusler Ti2MnAl, a compensated ferrimagnet with a vanishing net magnetic moment and a Curie temperature of over 650 K. Despite the vanishing net magnetic moment, we calculate a large intrinsic anomalous Hall effect (AHE) of about 300 S/cm. It derives from the Berry curvature distribution of the Weyl points, which are only 14 meV away from the Fermi level and isolated from trivial bands. Different from antiferromagnets Mn3X (X= Ge, Sn, Ga, Ir, Rh, and Pt), where the AHE originates from the non-collinear magnetic structure, the AHE in Ti2MnAl s…
Topological materials with extremely large magnetoresistance exhibit a prognostic feature of resistivity turn-on behaviour. This occurs when the temperature dependence of resistivity changes from metallic to semiconducting characteristics on application of external magnetic field above a threshold value. Here, we study the magneto-transport properties of type-II Weyl Semimetal WP2. We find that semi-classical theories of magnetoresistance are consistent with our data without the need to invoke topological surface states. Our findings in this work provides an alternative basis to understand the…
In band theory of solids, degeneracies manifest themselves as point, line, and surface objects. The topological nature of band degeneracies has recently been appreciated since the recognition of gapless topological quantum phases of matter. Based on first-principles calculations, we report the topological semimetal phase in osmium oxyhalide OsOF$_5$ that exhibits zero-dimensional Weyl points, one-dimensional nodal lines, and two-dimensional nodal surfaces. The semimetal phase is ensured by the electron filling constraint while band degeneracies of various dimensionalities are protected by the …
The co-occurrence of phase transitions with local and global order parameters, such as the entangled magnetization and topological invariant, is attractive but has been seldom realized experimentally. Here, by using high-pressure in-situ X-ray diffraction, high-pressure electric transport measurements and high-pressure first-principles calculations, we report a magneto-topological phase transition, i.e., the phenomenon of magnetic materials undergoing different magnetic and topological phases during the process of pressure loading, in a recently discovered magnetic Weyl semimetal Co3Sn2S2. By …
The studies of topological insulators and topological semimetals have been at frontiers of condensed matter physics and material science. Both classes of materials are characterized by robust surface states created by the topology of the bulk band structures and exhibit exotic transport properties. When magnetism is present in topological materials and breaks the time-reversal symmetry, more exotic quantum phenomena can be generated, e.g. quantum anomalous Hall effect, axion insulator, large intrinsic anomalous Hall effect, etc. In this research update, we briefly summarize the recent research…
Based on the first-principles study, we report a new set of topological semimetals (TiS, TiSe, TiTe, HfS, HfSe, HfTe and ZrS) which show the co-existence of a nodal-ring and triply-degenerate points. The two-fold degenerate one-dimensional nodal ring structure in the bulk Brillouin zone exhibits the characteristic drumhead surface states. In addition to this, a peculiar band crossing along the $k_z$ direction takes place consisting of a point-crossing with three-fold band degeneracy. These triply-degenerate points give rise to "nexus" fermions as quasiparticles having no analogous elementary p…
The ferromagnetic phase of the cubic antiperovskite Mn$_3$ZnC is suggested from first-principles calculation to be a nodal line Weyl semimetal. Features in the electronic structure that are the hallmark of a nodal line Weyl state, a large density of linear band crossings near the Fermi level, can also be interpreted as signatures of a structural and/or magnetic instability. Indeed, it is known that Mn$_3$ZnC undergoes transitions upon cooling from a paramagnetic to a cubic ferromagnetic state under ambient conditions and then further into a non-collinear ferrimagnetic tetragonal phase at a tem…
Weyl fermions are expected to exhibit exotic physical properties such as the chiral anomaly, large negative magnetoresistance or Fermi arcs. Recently a new platform to realize these fermions has been introduced based on the appearance of a three-fold band crossing at high symmetry points of certain space groups. These band crossings are composed of two linearly dispersed bands that are topologically protected by a Chern number, and a at band with no topological charge. In this paper we present a new way of inducing two kinds of Weyl fermions, based on two- and three-fold band crossings, in the…
Based on $k\cdot p$ analysis and realistic tight-binding calculations, we find that time-reversal-breaking Weyl semimetals can be realized in magnetically-doped (Mn, Eu, Cr etc.) Sn$_{1-x}$Pb$_x$(Te,Se) class of topological crystalline insulators. All the Weyl points are well separated in momentum space and possess nearly the same energy due to high crystalline symmetry. Moreover, both the Weyl points and Fermi arcs are highly tunable by varying Pb/Sn composition, pressure, magnetization, temperature, surface potential etc., opening up the possibility of manipulating Weyl points and rewiring t…
Research on topological physics of phonons has attracted enormous interest but demands appropriate model materials. Our {\it ab initio} calculations identify silicon as an ideal candidate material containing extraordinarily rich topological phonon states. In silicon, we identify various topological nodal lines protected by glide mirror or mirror symmetries and characterized by quantized Berry phase $π$, which gives drumhead surface states observable from any surface orientations. Remarkably, a novel type of topological nexus phonon is discovered, which is featured by double Fermi-arc-like surf…
Three-dimensional (3D) topological nodal points, such as Weyl and Dirac nodes have attracted wide-spread interest across multiple disciplines and diverse material systems. Unlike nodal points that contain little structural variations, nodal lines can have numerous topological configurations in the momentum space, forming nodal rings, nodal chains and potentially nodal links and nodal knots. However, nodal lines have much less development for the lack of ideal material platforms. In condensed matter for example, nodal lines are often fragile to spin-orbit-coupling, locating off the Fermi level,…
Weyl semimetals are topological materials that provide a condensed-matter realization of the chiral anomaly. A positive longitudinal magnetoconductance quadratic in magnetic field has been promoted as a diagnostic for this anomaly. By solving the Boltzmann equation analytically, we show that the magnetoconductance can become negative in the experimentally relevant semiclassical regime of weak magnetic fields. This effect is due to the simultaneous presence of the Berry phase and the orbital magnetic moment of carriers and occurs for sufficiently strong intervalley scattering.
Weyl semimetals are crystalline solids that host emergent relativistic Weyl fermions and have characteristic surface Fermi-arcs in their electronic structure. Weyl semimetals with broken time reversal symmetry are difficult to identify unambiguously. In this work, using angle-resolved photoemission spectroscopy, we visualized the electronic structure of the ferromagnetic crystal Co3Sn2S2 and discovered its characteristic surface Fermi-arcs and linear bulk band dispersions across the Weyl points. These results establish Co3Sn2S2 as a magnetic Weyl semimetal that may serve as a platform for real…
In this letter, we report the presence of novel type of plasmon Weyl points in a naturally existing material - magnetized plasma. In such a medium, conventional, purely longitudinal bulk plasma oscillations exists only along the direction of applied magnetic field (z direction). With strong enough magnetic field, there exist helical propagating modes along z direction with circular polarizations. The orthogonality between the longitudinal bulk plasmon mode and the transverse helical propagating modes guarantees their crossing at the bulk plasmon frequency. These crossing points, embedded in th…
We propose a torsional response raised by lattice dislocation in Weyl semimetals akin to chiral magnetic effect; i.e. a fictitious magnetic field arising from screw or edge dislocation induces charge current. We demonstrate that, in sharp contrast to the usual chiral magnetic effect which vanishes in real solid state materials, the torsional chiral magnetic effect exists even for realistic lattice models, which implies the experimental detection of the effect via SQUID or nonlocal resistivity measurements in Weyl semimetal materials.
Berry curvature in Weyl semimetals results in very intriguing magneto-electric and magneto-thermal transport properties. In this paper, we explore the impact of the tilting of the Weyl nodes, which breaks the time-reversal symmetry, on the magneto-electric conductivity of type-I and type-II Weyl semimetals. Using the Berry curvature connected Boltzmann transport formalism, we find that in addition to the quadratic-B corrections induced by the tilt, there are also anisotropic and B-linear corrections in several elements of the conductivity matrix. For the case of magnetic field applied perpendi…
We study the transport properties of junctions of normal and superconducting Weyl semi-metal with tilted dispersion, in the presence of magnetization induced by magnetic strips. The sub gap tunnelling conductance shows robust signatures in the presence of different orientation and strength of magnetization of the magnetic strips. We obtain the analytical results for the normal-magnetic-superconducting junction in the thin barrier limit and demonstrate that these results have no analogues to their conventional counterparts and junctions with Dirac electrons in two-dimensions. We discuss possibl…
We realized highly tunable Weyl semimetal-bands and subsequently emulated the topological chiral magnetic effects in superconducting quantum circuits. Driving the superconducting quantum circuits with elaborately designed microwave fields, we mapped the momentum space of a lattice to the parameter space, realizing the Hamiltonian of a Weyl semimetal. By measuring the energy spectrum, we directly imaged the Weyl points of cubic lattices, whose topological winding numbers were further determined from the Berry curvature measurement. In particular, we used an additional microwave field to produce…
