This volume contains the proceedings of the NATO Advanced Research Workshop on Band Structure Engineering in Semiconductor Microstructures held at Il Ciocco, Castelvecchio Pascali in Tuscany between 10th and 15th April 1988. Research on semiconductor microstructures has expanded rapidly in recent years as a result of developments in the semiconductor growth and device fabrication technologies. The emergence of new semiconductor structures has facilitated a number of approaches to producing systems with certain features in their electronic structure which can lead to useful or interesting properties. The interest in band structure engineering has stimd ated a variety of physical investigations and nove 1 device concepts and the field now exhibits a fascinating interplay betwepn pure physics and device technology. Devices based on microstruc tures are useful vehicles for fundamental studies but also new device ideas require a thorough understanding of the basic physics. Around forty researchers gathered at I1 Ciocco in the Spring of 1988 to discuss band structure engineering in semiconductor microstructures.

The monograph reviews various aspects of electronic properties of Dirac and Weyl semimetals. After a brief discussion of 2D Dirac semimetals, a comprehensive review of 3D materials is given. The description starts from an overview of the topological properties and symmetries of Dirac and Weyl semimetals. In addition, several low-energy models of Dirac and Weyl quasiparticles are presented. The key ab initio approaches and material realizations are given. The monograph includes detailed discussions of the surface Fermi arcs, anomalous transport properties, and collective modes of Dirac and Weyl semimetals. Superconductivity in these materials is briefly addressed.

Much fundamental research in condensed matter physics has been driven by the tremendous influence of high-energy physics. In 1928, Paul Dirac laid a strong foundation in the unification of quantum mechanics and relativistic physics in explaining the nature of the electron. The key idea of Dirac's equation was to describe relativistic particles like Dirac and Weyl fermions in high-energy physics. After the discovery of topological insulators (ordinary insulators in the bulk state but allowing charge to flow on their surfaces) in the early 1980s, the search for new topological semimetals such as Dirac and Weyl mushroomed over the recent decades in condensed matter physics. Dirac and Weyl semimetals host Dirac and Weyl fermions respectively in the form of low-energy excitations and are characterized by band-touching points with linear dispersion similar to massless relativistic particles predicted in high-energy physics.The smallest feature size of current silicon-based advanced microelectronic devices is around 4 nm and the rate of development of current microelectronics has slowed down as silicon appears to have reached its physical limit. Industries are looking for alternatives to silicon-based technology. The discovery of Dirac and Weyl semimetals paves the way for developing new forms of microelectronics. These materials offer nearly dissipationless current and that could dramatically speed up the performance and efficiency of modern electronic devices. Weyl semimetals are also known for exhibiting exotic low energy physics such as Fermi arcs on the surface, distinct magneto-transport properties, and chiral anomaly-induced quantum transport. Such exotic properties of Weyl semimetals are useful for making new types of electronic devices such as broadband photodetectors, light-emitting diodes, biosensors, and superfast quantum computers capable of parsing multi-state superposition. While the promise of Dirac and Weyl semimetal is clear, the practical integration of such systems into everyday devices depends on a thorough understanding of the materials at the nanoscale. In my dissertation research, I have grown nanofilms of three different systems - LaAlGe, MoTe2, and FeSn, of which the former two are examples of Weyl semimetal and later is a Dirac semimetal. For the first time, high-quality thin films for LaAlGe and FeSn have been grown using the ultra-high vacuum molecular beam epitaxy method. I have shown that these systems can be grown on silicon substrates, which can be directly used for multifunctional device applications. I have systematically investigated the electrical transport and magneto-transport properties of these systems to understand the underlying physics, especially non-saturating magnetoresistance due to perfect electron and hole carrier balance up to a very high magnetic field. Not only are these new systems extremely important for our understanding of fundamental quantum phenomena, but also, they exhibit completely different transport phenomena from ordinary materials. Dirac semimetals also exhibit non-saturating extremely large magnetoresistance as a consequence of their robust electronic bands being protected by time-reversal symmetry. These open undeniably new possibilities for materials engineering and applications including quantum computing.