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Topological Weyl semimetals represent a novel class of nontrivial materials, where band crossings with linear dispersions take place at generic momenta across reciprocal space. These crossings give rise to low -energy properties akin to those of Weyl fermions, and are responsible for several exotic phenomena. Up to this day, only a handful of Weyl semimetals have been discovered, and the search for new ones remains a very active area. The main challenge on the computational side arises from the fact that many of the tools used to identify the topological class of a material do not provide a complete picture in the case of Weyl semimetals. In this work, we propose an alternative and inexpensive, procedure to screen for possible Weyl fermions, starting from the analysis of the band structure along high -symmetry directions in the absence of spin -orbit coupling. We test the method by running a high -throughput screening on a set of 5455 inorganic bulk materials and identify 49 possible candidates for topological properties. A further analysis, carried out by identifying and characterizing the crossings in the Brillouin zone, shows us that three of these candidates are Weyl semimetals. Interestingly, while these three materials underwent other high -throughput screenings, none had revealed their topological behavior before.

Quantum spin Hall insulators are a class of topological materials that has been extensively studied during the past decade. One of their distinctive features is the presence of a finite band gap in the bulk and gapless, topologically protected edge states that are spin-momentum locked. These materials are characterized by a Z(2) topological order where, in the two-dimensional case, a single topological invariant can be even or odd for a trivial or a topological material, respectively. Thanks to their interesting properties, such as the realization of dissipationless spin currents, spin pumping, and spin filtering, they are of great interest in the field of electronics, spintronics, and quantum computing. In this work we perform a high-throughput screening of quantum spin Hall insulators starting from a set of 783 two-dimensional exfoliable materials, recently identified from a systematic screening of the Inorganic Crystal Structure Database, Crystallography Open Database, and Materials Platform for Data Science databases. We find four Z(2) topological insulators and seven direct gap metals that have the potential of becoming quantum spin Hall insulators under a reasonably weak external perturbation.