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.

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.

Exploring and expanding the menagerie of topological materials has been at the forefront of condensed matter physics for over a decade. With the discovery of each new class of materials, starting with graphene, followed by topological insulators, and continuing most recently into topological semimetals, new paradigms have been discovered that provide a platform for exploring fundamental physics as well as novel practical applications. Crucial to all these innovations has been the topologically protected edge and surface states, which in addition to their robust nature, also have strong spin or valley correlation with momentum, offering direct coupling of macroscopic electronic properties to the quantum state of electrons. The interaction between magnetism and topology has lead to novel quantum phenomena, such as the quantum anomalous Hall effect, as well as enhanced device capabilities, such as the switching of magnetic polarization via the topological surface states. In topological semimetals, it is predicted that magnetism creates a transition from a Dirac to a Weyl semimetal phase by breaking time-reversal symmetry. Experimentally realizing such a transition will provide a fundamental platform for examining the emergence of Weyl fermions, as well as a practical platform for engineering tailored Weyl semimetals, including the ideal case of two Weyl nodes which has yet to be discovered in any intrinsic Weyl semimetal. The material system explored most extensively throughout this dissertation is the transition metal dichalcogenide Dirac semimetal ZrTe2. Thus far, a few thin film studies have demonstrated the existence of a Dirac semimetal phase in this material directly through angle resolved photoemission spectroscopy (ARPES) analysis of the Dirac cone as well as through transport measurements of the chiral anomaly. Additionally, a very recent experiment demonstrates the existence of a superconducting phase in ZrTe2 that could lead to further interest if it is shown to coexist with the Dirac semimetal phase. To facilitate further research into this promising material platform, the first portion of this dissertation focuses on the the development of high quality ZrTe2 thin films on insulating substrates. This is a necessary step for characterizing the electronic states of the material as well as adapting it for spintronics. Through transmission electron microscopy, scanning tunneling microscopy, and x-ray diffraction, the lattice structure and quality are assessed. ARPES and transport measurements demonstrate hole-like carriers. While this matches theoretical predictions for this material, it is at odds with most of the current literature, which demonstrates n-type carriers due to the high defect density. To observe the Dirac cone, tellurium vacancies are intentionally introduced for ARPES measurements, although this method was not effective for transport measurements. Ultimately, this prevents the observation of many of the desirable transport phenomena expected of a Dirac semimetal. Finally, we report the presence of weak anti-localization in ZrTe2 thin films at low temperatures. After establishing the MBE growth of ZrTe2 thin films, chromium dopants are introduced into these films to form (CrxZr1-x)Te2. Structural characterization is consistent with a transition between the Dirac semimetal ZrTe2 and the recently discovered metallic 2D ferromagnet CrTe2. This makes it phenomenologically distinct from a recently reported Cr-intercalated ZrTe2, which did not demonstrate similar changes in lattice structure and demonstrates completely different ARPES and transport phenomena. The (CrxZr1-x)Te2 thin films presented in this work are demonstrated to be ferromagnetic, with a TC of ∼150 K, as revealed via the anomalous Hall effect as well as magnetometry measurements. This system could be a critical component for realizing the transition from a Dirac to a Weyl semimetal, although currently it is limited by the location of the Fermi level. Finally, the next steps to utilizing the Dirac semimetal ZrTe2 in real devices are presented. Additionally, other methods of inducing magnetism based on the foundation laid by the study of (CrxZr1-x)Te2 are explored, such as magnetic proximity effect and alternative dopants. Ultimately, this research presents an approach towards tailoring magnetism in topological semimetals that has important implications for examining the transition between Dirac and Weyl semimetals through time-reversal symmetry breaking as well as for designing functional materials for spintronics applications.

This fifteenth volume of the Poincare Seminar Series, Dirac Matter, describes the surprising resurgence, as a low-energy effective theory of conducting electrons in many condensed matter systems, including graphene and topological insulators, of the famous equation originally invented by P.A.M. Dirac for relativistic quantum mechanics. In five highly pedagogical articles, as befits their origin in lectures to a broad scientific audience, this book explains why Dirac matters. Highlights include the detailed "Graphene and Relativistic Quantum Physics", written by the experimental pioneer, Philip Kim, and devoted to graphene, a form of carbon crystallized in a two-dimensional hexagonal lattice, from its discovery in 2004-2005 by the future Nobel prize winners Kostya Novoselov and Andre Geim to the so-called relativistic quantum Hall effect; the review entitled "Dirac Fermions in Condensed Matter and Beyond", written by two prominent theoreticians, Mark Goerbig and Gilles Montambaux, who consider many other materials than graphene, collectively known as "Dirac matter", and offer a thorough description of the merging transition of Dirac cones that occurs in the energy spectrum, in various experiments involving stretching of the microscopic hexagonal lattice; the third contribution, entitled "Quantum Transport in Graphene: Impurity Scattering as a Probe of the Dirac Spectrum", given by Hélène Bouchiat, a leading experimentalist in mesoscopic physics, with Sophie Guéron and Chuan Li, shows how measuring electrical transport, in particular magneto-transport in real graphene devices - contaminated by impurities and hence exhibiting a diffusive regime - allows one to deeply probe the Dirac nature of electrons. The last two contributions focus on topological insulators; in the authoritative "Experimental Signatures of Topological Insulators", Laurent Lévy reviews recent experimental progress in the physics of mercury-telluride samples under strain, which demonstrates that the surface of a three-dimensional topological insulator hosts a two-dimensional massless Dirac metal; the illuminating final contribution by David Carpentier, entitled "Topology of Bands in Solids: From Insulators to Dirac Matter", provides a geometric description of Bloch wave functions in terms of Berry phases and parallel transport, and of their topological classification in terms of invariants such as Chern numbers, and ends with a perspective on three-dimensional semi-metals as described by the Weyl equation. This book will be of broad general interest to physicists, mathematicians, and historians of science.

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.

This book serves as a quick guide on the latest material systems including their synthesis, fabrication and characterization techniques. It discusses recent developments in different material systems and discusses their novel applications in various branches of science and engineering. The book briefs latest computational tools and techniques that are used to discover new material systems. The book also briefs applications of new emerging materials in various fields including, healthcare, sensors, opto-electronics, high power devices and nano-electronics. This book helps to create a synergy between computational and experimental research methods to better understand a particular material system.