Preceded by the discovery of topological insulators, Dirac and Weyl semimetals have become a pivotal direction of research in contemporary condensed matter physics. While a detailed accessible conception exists from a theoretical viewpoint, these topological semimetals pose a serious challenge in terms of experimental synthesis and analysis to allow for their unambiguous identification. In this work, we report on detailed transport experiments on compressively strained HgTe. Due to the superior sample quality in comparison to other topological semimetallic materials, this enables us to resolve the interplay of topological surface states and semimetallic bulk states to an unprecedented degree of precision and complexity. As our gate design allows us to precisely tune the Fermi level at the Weyl and Dirac points, we identify a magnetotransport regime dominated by Weyl/Dirac bulk state conduction for small carrier densities and by topological surface state conduction for larger carrier densities. As such, similar to topological insulators, HgTe provides the archetypical reference for the experimental investigation of topological semimetals.The discovery of topological insulators has inspired a remarkably broad interest in materials whose band structures exhibit relativistic properties. The effects of a linear dispersion in one-dimensional edge channels of quantum spin Hall insulators [1], as well as in twodimensional surface states of three-dimensional topological insulators [2,3], have already been extensively studied. The implications of a linear band dispersion in threedimensional conductors, however, have only recently begun to be explored. Such materials, dubbed Dirac or Weyl semimetals, represent a condensed matter realization of the Weyl/Dirac equations, and may provide an environment for studying the properties of quasiparticles which have been postulated, but not yet unambiguously demonstrated, to exist in nature.In many of these materials [4], the Weyl or Dirac band crossing is caused by a band inversion, and is intimately connected to the point group symmetry of the crystal lattice. This lends similarities to the prototypical setup of topological insulators. In fact, both in the alkali pnictide (AB 3 , where A=(Na,K,Rb), B=(As,Sb,Bi)) and Cd 2 As 3 families that boast a number of important Weyl/Dirac compounds, the inversion occurs between metallic s-like and chalcogenic p-like orbitals, a situation very similar to that found in HgTe. The correspondence in terms of band structure between these compounds and HgTe has indeed been known since the 1970's [5]. The common motif is that, for the alkali pnictides and Cd 2 As 3 , the p-like j = 3/2 bands (Γ 8 in the T d point group) cross and yield Dirac (or Weyl) points, while in HgTe the Γ 8 bands just touch, derives from the higher (zincblende) point group symmetry of the HgTe crystal. Small crystal distortions from the zincblende symmetry, as present in Weyl/Dirac semimetals, are sufficient to crucially modify the electronic structure at low energies.In the 19...

We theoretically demonstrate that the chiral structure of the nodes of nodal semimetals is responsible for the existence and universal local properties of the edge states in the vicinity of the nodes. We perform a general analysis of the edge states for an isolated node of a 2D semimetal, protected by chiral symmetry and characterized by the topological winding number N. We derive the asymptotic chiral-symmetric boundary conditions and find that there are N+1 universal classes of them. The class determines the numbers of flatband edge states on either side off the node in the 1D spectrum and the winding number N gives the total number of edge states. We then show that the edge states of chiral nodal semimetals are robust: they persist in a finite-size stability region of parameters of chiral-asymmetric terms. This significantly extends the notion of 2D and 3D topological nodal semimetals. We demonstrate that the Luttinger model with a quadratic node for j=3/2 electrons is a 3D topological semimetal in this new sense and predict that α-Sn, HgTe, possibly Pr_{2}Ir_{2}O_{7}, and many other semimetals described by it are topological and exhibit surface states.

The survival of the quantum spin Hall edge channels in presence of an external magnetic field has been a subject of experimental and theoretical research. The inversion of Landau levels that accommodates the quantum spin Hall effect is destroyed at a critical magnetic field, and a trivial insulating gap appears in the spectrum for stronger fields. In this work, we report the absence of this transport gap in disordered two dimensional topological insulators in perpendicular magnetic fields of up to 16 T. Instead, we observe that a topological edge channel (from band inversion) coexists with a counterpropagating quantum Hall edge channel for magnetic fields at which the transition to the insulating regime is expected. For larger fields, we observe only the quantum Hall edge channel with transverse resistance close to h/e2. By tuning the disorder using different fabrication processes, we find evidence that this unexpected ν = 1 plateau originates from extended quantum Hall edge channels along a continuous network of charge puddles at the edges of the device.

No abstract