SOLID STATE CHEMISTRY Exceptional transport properties of topological semimetals and metals Chandra Shekhar # , Claudia Felser, Satya N. Guin, Nitesh Kumar, Kaustuv Manna, Marcus Schmidt, Vicky Sü Topological materials (TMs) represent a family of new quantum materials, and the quantum Hall effect is the first realized topological phenomenon in condensed-matter physics. Band inversion occurs in topological insulators, and symmetry allows the bulk gap to fully reopen. At the surface of the three dimensional topological insulator, bands cross linearly (Dirac cone) and the crossing point is protected by time reversal symmetry. In contrast to Weyl and Dirac semimetals, the Dirac cone forms in the bulk, wherein the nodal points are two- and four-fold degenerate, respectively. Quasiparticles residing at these nodal points are equivalent of Dirac and Weyl fermions in particle physics. Recently, many other topological materials like nodal line semimetals, double Weyl semimetals, triple point Fermion metals, etc. have also been discovered. Topology in the band structure makes these materials interesting by imparting many exotic physical characteristics. Our group is involved in crystal growth and transport property measurements at very low temperatures and high magnetic fields to understand the effect of topology in materials. Among the first verified Weyl semimetals, NbP shows ultrahigh mobility of 5,000,000 cm 2 V -1 s - 1 , low effective mass, and extremely large magnetoresistance (MR). We find both extremely large MR (200 million % in 63 T at 2.5 K) and ultralow resistivity (3 n· cm at 2 K) simultaneously in the Weyl semimetal. In the Heusler family, the Weyl semimetal GdPtBi is significant because it exhibits a chiral anomaly, anomalous Hall conductivity (60  -1 cm -1 ) with a large anomalous Hall angle (23%), planar Hall effect, and linear optical conductivity in a large energy range well above the transition temperature. Triple point fermionic MoP behaves like an ultra-pure metal, wherein the long-lived electrons in MoP flow collectively like a liquid. The topological semimetal LaBi exhibits quasi-two-dimensional electron transport, and the nodal-line semimetal HfSiS exhibits a non-trivial -Berry phase. These unusual transport properties hint at the existence of fermions as a quasiparticle in condensed matter systems. Materials are conventionally divided into metals, semiconductors, and insulators. Through the lens of topology, materials can be reclassified as either topologically trivial or non-trivial. Depending on the inherent symmetry and touching point of bands in a particular compound, two- and four-fold degenerate points are classified as Weyl and Dirac types, respec- tively, which are equivalent to Dirac and Weyl fermions in particle physics. Materials possessing such fermions as quasiparticles are known as Dirac semimetal (DSM) and Weyl semimetal (WSM). In solid-state band structures, Weyl fermions exist as low-energy excitations of the Weyl semimetal, in which bands disperse linearly in three-dimensional (3D) momentum space through a node termed a Weyl point. Weyl points act as monopoles in momentum space with a fixed chirality that behave as a source (“+” chirality) or a sink (“–” chirality); a non-vanishing Berry curvature exists between them. The Berry curvature is a quantity that can be used to characterise topological entanglement between the conduction and valence bands, which is equivalent to a magnetic field in momentum space. Due to the topology of the bulk bands, topological surface states appear on the surface and form exotic Fermi arcs in WSM. All bands in a DSM are doubly degenerate, while the degeneracy is lifted due to breaking of inversion symmetry, breaking of time- reversal symmetry, or both in the WSM. In a type-I WSM, the Fermi surface (FS) shrinks to zero at the Weyl points when the Fermi energy is sufficiently close to the Weyl points, while the Weyl point acts as the touching point between electron and hole pockets in the FS due to the strong tilting of the Weyl cones in a type-II WSM. In condensed matter systems such as non-trivial semimetals and metals exhibit novel, low- energy fermionic excitations which are associated with bands that are linearly dispersed around a crossing point. Pnictide TaAs-family of Weyl semimetals At the beginning of this decade, the WSM was predicted to be a class of time reversal symmetry breaking (magnetism) compounds, including pyro- chlore iridates (such as Y2Ir2O7) and HgCr2Se4. These compounds, however, have not been confirmed experimentally. A Major breakthrough came in early 2015 when a WSM was predicted in the transition metal pnictides NbP, TaP, NbAs, and TaAs (TaAs-family). These compounds have non-centrosymmetric tetragonal crystal structure with I41md space group (no. 109) that breaks inversion symmetry. Each of them show twelve pairs of Weyl points throughout the Brillouin zone (BZ).