Abstract
Topological materials have been the focus of condensed matter physics for the last two decades. The understanding of topology in quantum materials reveals numerous topological materials hosting a range of topological band crossings, from Dirac/Weyl points to nodal lines and nodal surfaces. Interestingly, fascinating physical properties are manifested by these topological fermions, including chiral anomaly, exotic surface states, and anomalous Hall effect. Here in this thesis, I carry out an exhaustive search of triply degenerate points (TPs) over 230 space groups in spinless crystalline systems. I find that the spinless TPs can exist at both high-symmetry points and high-symmetry paths with linear or quadratic dispersions. For TPs located at high-symmetry points, they all share a common minimal set of symmetries, which is the point group T. The TP protected solely by the T group is chiral and has a Chern number of ±2. By incorporating additional symmetries, this TP can evolve into chiral pseudospin-1 point, linear TP without chirality, or quadratic contact TP. For accidental TPs residing on a high-symmetry path, they are not chiral but can have either linear or quadratic dispersions in the plane normal to the path. I further construct effective k · p models and minimal lattice models for characterizing these TPs. Distinguished phenomena for the chiral TPs are discussed, including the extensive surface Fermi arcs and the chiral Landau bands. Furthermore, I investigate the behavior of triply degenerate pseudospin-1 fermions during the Andreev reflection at a normal-metal/superconductor (NS) interface. I show that distinct from the previously studied pseudospin-1/2 and two-dimensional electron gas models, the pseudospin-1 fermions exhibit a strongly enhanced Andreev reflection probability, and remarkably, can be further tuned to approach perfect Andreev reflection with unit efficiency for all incident angles, exhibiting a previously unknown super-Andreev reflection effect. The super-Andreev reflection leads to perfect transparency of the NS interface that strongly promotes charge injection into the superconductor and directly manifests as a differential conductance peak which can be readily probed in experiment. Additionally, I find that sizable longitudinal shifts exist in the normal and Andreev reflections of pseudospin-1 fermions. Distinct from the pseudospin-1/2 case, the shift is always in the forward direction in the subgap regime, regardless of whether the reflection is of retro- or specular type. In this thesis, I present the possibility of triply degenerate points in 3D spinless systems and their classification with respect to their locations, dispersions, symmetry protections, and topological charges. Meanwhile, the pseudospin-1 fermions manifest exotic properties, including chiral Landau levels, extensive Fermi arcs and super- Andreev reflection. This work promotes our understanding of novel topological fermions in solid state systems, and can be also generalized to other spinless systems, including artificial acoustic/photonic systems. It is also of interest to extend the current study to other novel fermions, looking for new physical effects. One can expect their fascinating properties in subsequent theoretical predictions and experimental measurements.