Quantum materials with strong spin-orbit coupling are partially interesting, especially when there further exhibits topology or superconductivity. In this thesis, we present our studies on several systems: noncentrosymmetric achiral materials, quantum anomalous hall and superconductor heterostructures, and the topological monolayer WTe₂, where the interplay of spin-orbit coupling, topology, and superconductivity gives rise to novel physics. Specifically, in chapter II, we show that all achiral non-centrosymmetric materials with SOC can be a new class of topological materials, which we term Kramers nodal line metals (KNLMs). In KNLMs, there always are doubly degenerate lines connecting time-reversal invariant momenta with achiral little groups. In chapter III, we demonstrate that making...[ Read more ]

Quantum materials with strong spin-orbit coupling are partially interesting, especially when there further exhibits topology or superconductivity. In this thesis, we present our studies on several systems: noncentrosymmetric achiral materials, quantum anomalous hall and superconductor heterostructures, and the topological monolayer WTe₂, where the interplay of spin-orbit coupling, topology, and superconductivity gives rise to novel physics. Specifically, in chapter II, we show that all achiral non-centrosymmetric materials with SOC can be a new class of topological materials, which we term Kramers nodal line metals (KNLMs). In KNLMs, there always are doubly degenerate lines connecting time-reversal invariant momenta with achiral little groups. In chapter III, we demonstrate that making a cut (a narrow vacuum regime) in the bulk of a quantum anomalous Hall insulator (QAHI) creates a topologically protected single helical channel with counter-propagating electron modes, and inducing superconductivity on the helical channel through proximity effects will create Majorana zero-energy modes (MZMs) at the ends of the cut. In chapter IV, we unveil some distinctive superconducting properties of centrosymmetric 1T′-WTe₂ which arise from the coupling of spin, momentum, and band parity degrees of freedom. As a result of this spin-orbit-parity coupling (SOPC), the spin susceptibility is anisotropic with respect to in-plane directions and can result in possible anisotropic and strong gate dependence B_c2 even in this centrosymmetric system. Our studies identify several interesting physical properties in both noncenstrosymmetric and centrosymmetric quantum materials with the interplay of spin-orbit coupling, topology, and superconductivity.