Session K3: Weyl Topological Semimetals: Theory and Experiment

Weyl semimetals and topological phase transitions

Weyl semimetals are semimetals with nondegenerate 3D Dirac cones in the bulk. We showed that in a transition between different $Z_2$ topological phases, i.e. between the normal insulator (NI) and topological insulator (TI), the Weyl semimetal phase necessarily appears when inversion symmetry is broken. In the presentation we show that this scenario holds for materials with any space groups without inversion symmetry. Namely, let us take any band insulator without inversion symmetry, and assume that the gap is closed by a change of an external parameter. In such cases we found that the system runs either into (i) a Weyl semimetal or (ii) a nodal-line semimetal, but no insulator-to-insulator transition happens. This is confirmed by classifying the gap closing in terms of the space groups and the wavevector. In the case (i), the number of Weyl nodes produced at the gap closing ranges from 2 to 12 depending on the symmetry. In (ii) the nodal line is protected by mirror symmetry. In the presentation, we explain some Weyl semimetal and nodal-line semimetals which we find by using this classification. As an example, we explain our result on ab initio calculation on tellurium (Te). Tellurium consists of helical chains, and therefore lacks inversion and mirror symmetries. At high pressure the band gap of Te decreases and finally it runs into a Weyl semimetal phase, as confirmed by our ab initio calculation. In such chiral systems as tellurium, we also theoretically propose chiral transport in systems with such helical structures; namely, an orbital magnetization is induced by a current along the chiral axis, in analogy with a solenoid. [1] S. Murakami, New J. Phys. 9, 356 (2007). [2] S. Murakami and S. Kuga, Phys. Rev. B 78, 165313 (2008). [3] R. Okugawa, and S. Murakami, Phys. Rev. B 89, 235315 (2014). [4] M. Hirayama, R. Okugawa, S. Ishibashi, S. Murakami, and T. Miyake, Phys. Rev. Lett. 114, 206401 (2015). [5] T. Yoda, T. Yokoyama, S. Murakami, Sci. Rep. 5, 12024 (2015).   

Topological insulator route to Weyl fermions

I will describe one of the possible routes to realizing Weyl fermions in condensed matter, which is based on violating either time reversal or spatial inversion symmetry in a system, tuned near a quantum phase transition between a topological and an ordinary insulator. This route is particularly attractive, since it may lead to the simplest possible realization of a Weyl semimetal, with only two opposite-chirality Weyl nodes in the first Brillouin zone, which is yet to be found experimentally. I will describe some of the most important physical properties of such an elemental Weyl semimetal, in particular a negative longitudinal magnetoresistance due to the chiral anomaly and possible exotic superconducting states.   

Discovery of Weyl fermion semimetal and topological Fermi arc quasiparticles in TaAs, NbAs, NbP, TaP and related materials

Topological matter can host Dirac, Majorana and Weyl fermions as quasiparticle modes on their boundaries. First, I briefly mention the basic theoretical concepts defining insulators and superconductors where topological surface state modes are robust only in the presence of a gap (Hasan {\&} Kane; Rev. of Mod. Phys. 82, 3045 (2010)). In these systems topological protection is lost once the gap is closed turning the system into a trivial metal. A Weyl semimetal is the rare exception in this scheme which is a topologically robust metal (semimetal) whose low energy emergent excitations are Weyl fermions. In a Weyl fermion semimetal, the chiralities associated with the Weyl nodes can be understood as topological charges, leading to split monopoles and anti-monopoles of Berry curvature in momentum space. This gives a measure of the topological strength of the system. Due to this topology a Weyl semimetal is expected to exhibit 2D Fermi arc quasiparticles on its surface (Wan et.al., 2011). These arcs (``fractional'' Fermi surfaces) are discontinuous or disjoint segments of a two dimensional Fermi contour, which are terminated onto the projections of the Weyl fermion nodes on the surface we have observed experimentally in TaAs, NbAs, NbP class of materials (Xu, Belopolski et.al., Science 349, 613 (2015); Xu, Alidoust et.al., Nature Phys. (2015); Xu, Belopolski et.al., Science Adv. (2015), Belopolski, Xu et.al., arXiv (2015)) following our theoretical predictions (Huang, Xu, Belopolski et.al., Nature Commun. 6:7373 (2015), submitted in November 2014). Our theoretical predictions (Nature Commun. 2015) and experimental demonstrations (Science 2015, Nature Physics 2015, Science Advances 2015) reveal that these Fermi arc quasiparticles can only live on the boundary of a 3D crystal which collectively represents the realization of a new state of quantum matter beyond our earlier work on Fermi arcs in topological materials (Xu, Liu, Kushwaha et.al., Science 347, 294 (2015), adv.online (2014)). This work is in collaboration with Su-Yang Xu, Ilya Belopolski, Nasser Alidoust, Madhab Neupane, Chenglong Zhang, Raman Sankar, Shin-Ming Huang, Chi-Cheng Lee, Guoqing Chang, BaoKai Wang, Guang Bian, Hao Zheng, Daniel S. Sanchez, Fangcheng Chou, Hsin Lin, Shuang Jia, Titus Neupert. This work is supported by GBMF and U.S. DOE.   

Observation of Weyl fermions in condensed matter

In 1929, a German mathematician and physicist Hermann Weyl proposed that a massless solution of the Dirac equation represents a pair of new type of particles, the so-called Weyl fermions. However, their existence in particle physics remains elusive after more than eight decades, e.g., neutrino has been regarded as a Weyl fermion in the Standard Model until it was found to have mass. Recently, significant advances in topological materials have provided an alternative way to realize Weyl fermions in condensed matter as an emergent phenomenon. Weyl semimetals are predicted as a class of topological materials that can be regarded as three-dimensional analogs of graphene breaking time reversal or inversion symmetry. Electrons in a Weyl semimetal behave exactly as Weyl fermions, which have many exotic properties, such as chiral anomaly, magnetic monopoles in the crystal momentum space, and open Fermi arcs on the surface. In this talk I will report our experimental discovery of a Weyl semimetal in TaAs by observing Fermi arcs with a characteristic spin texture in the surface states and Weyl nodes in the bulk states using angle-resolved photoemission spectroscopy.