Abstract: The discovery of topological properties in condensed matter started a new era of physics. Many fermionic particles and phenomena predicted in high-energy physics are now experimentally observed in topological materials such as Dirac, Weyl, and Majorana particles. Their nontrivial topology gives rise to exotic physical properties, opening a door to future electronics with low power consumption. The nontrivial topology results from crossings of conduction and valence bands. Depending on crystal symmetry, such crossings can result in degeneracy (g) with g = 2, 3, 4, 6, and 8. It is known that g = 2 corresponds to Weyl fermions and g = 4 corresponds to Dirac fermions. These fermions have been extensively studied both in condensed matter physics and high energy physics. The cases of g = 3, 6, and 8 are of particularly interesting as they can only be found in condensed matter systems, having no high-energy analogues as constrained by Poincare symmetry. Since the fermions in condensed matter systems are not constrained by Poincare symmetry but are instead required to respect the crystal symmetry, it is possible to realize these ​“unconventional fermions” (with g = 3, 6, and 8, which fall beyond Dirac and Weyl semimetals paradigm) in conventional crystals.

Based on the density functional theory, Pyrite-type cubic PdSb₂ is predicted to have g = 6 while trigonal PtBi₂ with g = 3. By growing high-quality single-crystal samples of these compelling materials, we have explored their physical properties under a variety of stimuli (e.g., temperature, magnetic field, and quasi-hydrostatic pressure). In this talk, for the most part, I will present our experimental investigation on the six-fold degenerate PdSb₂. By analyzing both the de Haas-van Alphen and Shubnikov-de Haas oscillations observed in this compound, we obtain the topological properties of the respective bands. The implications of these findings will be discussed.