Intense research enthusiasm toward the topological properties of condensed matters has been ignited since the discovery of topological insulators in the first decades of the new millennium, which are characterized by the insulting bulk with a full gap, and gapless surface or edge states that are topologically protected. It was realized shortly afterward that an insulating gap is not a necessary requirement for the nontrivial topology, as a number of gapless systems join the family of topological materials, such as the Dirac and Weyl semimetals. In this thesis, we explore the nontrivial topology in various gapless systems with the interplay of symmetry, magnetism and superconductivity, and expand the category of the gapless topological materials by introducing new types of topological c...[ Read more ]

Intense research enthusiasm toward the topological properties of condensed matters has been ignited since the discovery of topological insulators in the first decades of the new millennium, which are characterized by the insulting bulk with a full gap, and gapless surface or edge states that are topologically protected. It was realized shortly afterward that an insulating gap is not a necessary requirement for the nontrivial topology, as a number of gapless systems join the family of topological materials, such as the Dirac and Weyl semimetals. In this thesis, we explore the nontrivial topology in various gapless systems with the interplay of symmetry, magnetism and superconductivity, and expand the category of the gapless topological materials by introducing new types of topological crossings.

Specifically, in Chapter 2, we show the existence of doubly degenerate lines connecting time-reversal-invariant momenta (TRIMs) in nonmagnetic noncentrosymmetric achiral crystals with the inclusion of spin-orbit coupling (SOC). The topology of degenerate lines, which we called Kramers nodal lines, is characterized by the π winding phase, and the corresponding materials are named Kramers nodal line metals (KNLMs). We further find the existence of topologically protected Fermi-arc-like surface states on particular surfaces of a KNLM. Interestingly, these Fermi-arc-like surface states of a KNLM can be continuously transformed to the Fermi arc states of the Kramers Weyl semimetal when a strain that breaks the achiral symmetry is gradually applied.

In Chapter 3, we point out the existence of a new type of Weyl fermions in the inadmissible chiral antiferromagnets, which are stabilized and pinned at points of symmetry by the Heesch group. We therefore name them the Heesch Weyl fermions (HWFs). The origin of HWFs is fundamentally different from that of Kramers Weyl fermions, as the emergence of the HWFs does not rely on any anti-unitary symmetry A that satisfies A² = −1. Through group theory analysis, we classify all the magnetic little co-groups of momenta where Heesch Weyl nodes are enforced by symmetry. With the guidance of the classification and first-principles calculation, the antiferromagnetic (AFM) perovskite YMnO₃ is identified as a candidate host of the AFM-order-induced HWFs.

In Chapter 4, the novel topological superconductivity with the interplay of multifold fermions is studied. We take superconducting Li₂Pd₃B and Li₂Pt₃B as examples, whose normal phase hosts various types of unconventional multifold fermions near the Fermi energy, such as double spin-1, spin-3/2 and double Weyl fermions. Importantly, it has been shown experimentally that Li₂Pd₃B and Li₂Pt₃B are fully gapped and gapless superconductors, respectively. By analyzing the possible pairing symmetries, we suggest the possibility that Li₂Pd₃B is a DIII class topological superconductor with Majorana surface states, while Li₂Pt₃B is a nodal topological superconductor with dispersionless surface Majorana modes.