Session Y28: Weyl Semimetals: Theory and New Materials

Prediction of an arc-tunable Weyl Fermion metallic state in Mo$_x$W$_{1-x}$Te$_2$

A Weyl semimetal is a new state of matter that hosts Weyl fermions as emergent quasiparticles. The Weyl fermions correspond to isolated points of bulk band degeneracy, Weyl nodes, which are connected only through the crystal’s boundary by an exotic Fermi arc surface state. The length of the Fermi arc gives a measure of the topological strength, because the only way to destroy the Weyl nodes is to annihilate them in pairs in k space. To date, Weyl semimetals are only realized in the TaAs class. Here, we propose a tunable Weyl metallic state in Mo$_x$W$_{1-x}$Te$_2$ via our first-principles calculations, where the Fermi arc length can be continuously changed as a function of Mo concentration, thus tuning the topological strength of the system [1]. Our results provide an experimentally feasible route to realizing Weyl physics in the layered compound Mo$_x$W$_{1-x}$Te$_2$ where non-saturating magneto-resistance and pressure driven superconductivity have been observed. \newline [1] T.-R. Chang et al., arXiv:1508.06723.   

Nonsymmorphic topological photonic crystal with a single surface Dirac cone

We predict a realization of the nonsymmorphic topological crystalline phase: a three-dimensional (3D) photonic crystal with a single surface Dirac cone. A single Dirac cone on the surface is the hallmark of the 3D topological insulators, where the double degeneracy at the Dirac point is protected by time-reversal symmetry and the spin-splitting away from the point is provided by the spin-orbital coupling. In our 3D topological photonic crystal, the degeneracy at the Dirac point is protected by a nonsymmorphic glide reflection and the linear splitting away from it is enabled by breaking time-reversal symmetry. Such a gapless surface state is fully robust against random disorder of any type. This bosonic topological band structure is achieved by applying alternating magnetization to gap out the 3D "generalized Dirac points" discovered in the bulk of our crystal. The Z2 bulk invariant is characterized through the evolution of Wannier centers. Our proposal--readily realizable using ferrimagnetic materials at microwave frequencies--can also be regarded as the photonic analog of topological crystalline insulators, providing the first 3D bosonic symmetry-protected topological system.   

Topological semimetals with Riemann surface states

Topological semimetals have robust bulk band crossings between the conduction and the valence bands. Among them, Weyl semimetals are so far the only class having topologically protected signatures on the surface known as the ``Fermi arcs''. Here we theoretically find new classes of topological semimetals protected by nonsymmorphic glide reflection symmetries. On a symmetric surface, there are multiple Fermi arcs protected by nontrivial $Z_2$ spectral flows between two high-symmetry lines (or two segments of one line) in the surface Brillouin zone. We observe that so far topological semimetals with protected Fermi arcs have surface dispersions that can be mapped to noncompact Riemann surfaces representing simple holomorphic functions. We propose perovskite superlattice [(SrIrO$_3$)$_{2m}$, (CaIrO$_3$)$_{2n}$] as a nonsymmorphic Dirac semimetal.   

Type-II Weyl semimetals

The Dirac equation of quantum field theory gives rise to massless Weyl fermions that respect Lorentz invariance. In condensed matter these fermions are realized as low energy excitations in Weyl semimetals. In these materials a topologically protected linear crossing of two bands, called a Weyl point, occurs at the Fermi level resulting in a point-like Fermi surface. Lorentz invariance, however, can be violated in condensed matter, and here we generalize the Dirac equation accordingly to obtain a fundamentally new kind of Weyl fermions. In particular, we report on a novel type of Weyl semimetal, with a new type of Weyl point that emerges at the boundary between electron and hole pockets. This node, although still a protected crossing, has an open, not point-like, Fermi surface, resulting in physical properties very different from that of standard Weyl points. We show that an established material, WTe$_2$, is an example of this novel type of topological semimetals.   

Topological Dirac line nodes in centrosymmetric semimetals

Dirac line nodes (DLNs) are one-dimensional lines of Dirac band-touching points, characterized by linear dispersion in only a single direction in momentum space. In the presence of inversion symmetry and time-reversal symmetry, crystals with vanishing spin-orbit coupling can host topologically protected DLNs. Recently, we have proposed and characterized a novel Z2 class of DLN semimetals [1]. We present Z2 topological invariants, dictating the presence of DLNs, based on the parity eigenvalues at the time-reversal invariant crystal momenta. Our first-principles calculations show that DLNs can be realized in Cu3N in an anti-ReO3 structure via a metal-insulator electronic transition, driven by transition metal doping. We also discuss the resultant surface states and the effects of spin-orbit coupling.   

Symmetry-protected ideal Weyl semimetal in HgTe-class materials

Ideal Weyl semimetals with all Weyl nodes exactly at the Fermi level and no coexisting trivial Fermi surfaces in the bulk, similar to graphene, could feature deep and novel physics such as exotic transport phenomena induced by the chiral anomaly. Here, we show that HgTe and half-Heusler compounds, under a broad range of inplane compressive strain, could be the first materials in nature realizing ideal Weyl semimetals with four pairs of Weyl nodes and topological surface Fermi arcs. Generically, we find that the HgTe-class materials with nontrivial band inversion and noncentrosymmetry provide a promising arena to realize ideal Weyl semimetals. Such ideal Weyl semimetals could further provide a unique platform to study emergent phenomena such as the interplay between ideal Weyl fermions and superconductivity in the half-Heusler compound LaPtBi.   

Spin-Orbit Nodal Semimetals in the Layer Groups

Recent interest in point and line node semimetals has lead to the proposal and discovery of these phenomena in numerous systems. Frequently, though, these nodal systems are described in terms of individual properties reliant on specific space group intricacies or band-tuning conditions. Restricting ourselves to cases with strong spin-orbit interaction, we develop a more general framework which captures existing systems and predicts new examples of nodal materials. In many previously proposed systems, the three-dimensional nature of the space group has obscured key generalities. Therefore, we show how within our framework one can predict and characterize a diverse set of nodal phenomena even in two-dimensional systems constructed of three-dimensional sites, known as the ``Layer Groups''. Introducing a set of simple models, we characterize the allowed semimetallic structures in the layer groups and draw connections to analogous three-dimensional systems.   

Scanning Tunneling Microscopy study and unusual transport properties of the topological semimetal a-Sn.

Weyl semimetals are new states of quantum matter with topological Weyl nodes near Fermi level in the bulk and Fermi arcs at the surface, which are paid a lot attention in recently years. Here£¬we report another topological semimetal a-Sn., which is double Weyl semimetal in the magnetic field and Dirac semimetal in an appropriate in-plane strain. By combing Landau level spectroscopy and quasiparticle interference, we obtain the linear dispersion near the Dirac point within strain while quadratic band dispersion near $\Gamma $point without strain. We also observe the negative longitudinal magnetoresistance (LMR) in both two system, which is caused by chiral anomaly. However ,the LMR profiles of strained a-Sn have a little rise and then descend while the unstrained one drop directly, which is due to the different type of Weyl semimetal and further confirm our prediction.   

Spinless Weyl semimetals and $Z_2$ topological crystalline insulator with glide symmetry

A topological crystalline insulator (TCI) is one of the symmetry protected topological phases protected by crystalline symmetries such as rotational symmetry, mirror symmetry etc. In recent works, a new class of three-dimensional (3D) $Z_2$ TCI with a nonsymmorphic glide plane symmetry is theoretically predicted both for spinless and spinfull systems. Our study shows that a spinless Weyl semimetal (WSM) phase always emerges between a normal insulator (NI) and TCI phases transition in general glide symmetric spinless systems. In particular, we find how the $Z_2$ topological invariant is changed by pair creations and pair annihilations of Weyl nodes in general phase transition. To confirm this scenario, we introduce a simple spinless tight-binding model on a 3D rectangular lattice with two sublattices and two orbitals with glide plane symmetry. Using this model, we show that the spinless WSM phase emerges between the NI and TCI phases, and the changing of $Z_2$ topological invariant comes from the behavior of Weyl nodes. Our numerical calculation also shows that surface Fermi arcs in the spinless WSM phase evolve into a surface Dirac cone in the TCI phase.   

Interacting weak topological insulators and their transition to Dirac semimetal phases

Topological insulators in the presence of strong Coulomb interaction constitute novel phases of matter. Transitions between these phases can be driven by single-particle or many-body effects. On the basis of {\it ab-initio} calculations, we identify a concrete material, {\it i.e.} Ca$_{2}$PtO$_{4}$, that turns out to be a hole-doped weak topological insulator. Interestingly, the Pt-$d$ orbitals in this material are relevant for the band inversion that gives rise to the topological phase. Therefore, Coulomb interaction should be of importance in Ca$_{2}$PtO$_{4}$. To study the influence of interactions on the weak topological insulating phase, we look at a toy model corresponding to a layer-stacked 3D version of the Bernevig-Hughes-Zhang model with local interactions. For small to intermediate interaction strength, we discover novel interaction-driven topological phase transitions between the weak topological insulator and two Dirac semimetal phases. The latter correspond to gapless topological phases. For strong interactions, the system eventually becomes a Mott insulator.   

Landau levels and longitudinal magnetoresistance in generalized Weyl semimetals

The notion of axial anomaly is a venerable concept in quantum field theory that has received ample attention in condensed matter physics due to the discovery of Weyl materials (WSMs). In such systems Kramers non-degenerate bands touch at isolated points in the Brillouin zone that act as (anti)monopoles of Berry flux, and the monopole number ($m$) defines the topological invariant of the system. Although so far only simple WSMs (with $m=1$) has been found in various inversion and/or time-reversal asymmetric systems, generalized Weyl semimetals with $m>1$ can also be found in nature, for example double-Weyl semimetals in HgCr$_2$Se$_4$ and SrSi$_2$ and triple-Weyl semimetals. In this work, we demonstrate the Landau level spectrum in generalized Weyl systems and its ramification on longitudinal magnetotransport measurements. We show that in the quantum limit generalized Weyl semimetals display negative longitudinal magnetoresistance due to the chiral anomaly. Moreover, the magnetoresistance has nontrivial dependence on the relative orientation of the external fields with the crystallographic axis, stemming from underlying anisotropic quasiparticle dispersion in the pristine system. Our theory can thus provide diagnostic tools to pin the quasiparticle properties in Weyl systems.   

Magnetotransport in a Weyl semimetal

We studied the magnetotransport in a Weyl semimetal having the surface boundary, to investigate the effect of the topological surface states on the chiral anomaly. We Found that the conductivity behavior becomes completely different from that of the in finite system, where the surface state plays a crucial role in the relaxation of the bulk carriers.   

Cohomological Insulators

We present a cohomological classification of insulators, in which we extend crystal symmetries by Wilson loops. Such an extended group describes generalized symmetries that combine space-time transformations with quasimomentum translations. Our extension generalizes the construction of nonsymmorphic space groups, which extend point groups by real-space translations. Here, we \emph{further} extend nonsymmorphic groups by reciprocal translations, thus placing real and quasimomentum space on equal footing. From a broader perspective, cohomology specifies not just the symmetry group, but also the quasimomentum manifold in which the symmetry acts -- both data are needed to specify the band topology. In this sense, cohomology underlies band topology.   

Hourglass Fermions

Spatial symmetries in crystals are distinguished by whether they preserve the spatial origin. We show how this basic geometric property gives rise to a new topology in band insulators. We study spatial symmetries that translate the origin by a fraction of the lattice period, and find that these nonsymmorphic symmetries protect a novel surface fermion whose dispersion is shaped like an hourglass; surface bands connect one hourglass to the next in an unbreakable zigzag pattern. These exotic fermions are materialized in the large-gap insulators: KHg$X$ ($X{=}$As,Sb,Bi), which we propose as the first material class whose topology relies on nonsymmorphic symmetries. Beside the hourglass fermion, a different surface of KHg$X$ manifests a 3D generalization of the quantum spin Hall effect. To describe the bulk topology of nonsymmorphic crystals, we propose a non-Abelian generalization of the geometric theory of polarization. Our nontrivial topology originates not from an inversion of the parity quantum numbers, but rather of the rotational quantum numbers, which we propose as a fruitful in the search for topological materials. Finally, KHg$X$ uniquely exemplifies a cohomological insulator, a concept that we will introduce in a companion work.   

Hourglass Fermions and Cohomological Insulators

We present a new fermion, the Hourglass fermions, which extends the currently known Dirac, Weyl and Majorana classification. We further present a set of materials which host this particle as a surface state. The materials already exist in nature and have a large gap. The topological index involves group cohomology, and, in our particular material example, a group-extension of an already non-symmorphic group.