Topological Quantum Materials for Realizing Majorana Quasiparticles

In the past decade, basic physics, chemistry, and materials science research on topological quantum materials - and their potential use to implement reliable quantum computers - has rapidly expanded to become a major endeavor. A pivotal goal of this research has been to realize materials hosting Majorana quasiparticles, thereby making topological quantum computing a technological reality. While this goal remains elusive, recent data-mining studies, performed using topological quantum chemistry methodologies, have identified thousands of potential topological materials - some, and perhaps many, with potential for hosting Majoranas. We write this Review for advanced materials researchers who are interested in joining this expanding search, but who are not currently specialists in topology. The first half of the Review addresses, in readily understood terms, three main areas associated with topological sciences: (1) a description of topological quantum materials and how they enable quantum computing; (2) an explanation of Majorana quasiparticles, the important topologically endowed properties, and how it arises quantum mechanically; and (3) a description of the basic classes of topological materials where Majoranas might be found. The second half of the Review details selected materials systems where intense research efforts are underway to demonstrate nontrivial topological phenomena in the search for Majoranas. Specific materials reviewed include the groups II-V semiconductors (Cd3As2), the layered chalcogenides (MX2, ZrTe5), and the rare-earth pyrochlore iridates (A2Ir2O7, A = Eu, Pr). In each case, we describe crystallographic structures, bulk phase diagrams, materials synthesis methods (bulk, thin film, and/or nanowire forms), methods used to characterize topological phenomena, and potential evidence for the existence of Majorana quasiparticles.