Abstract
Unconventional Josephson effects in quantum materials are fascinating, especially when the materials further exhibit topology or magnetism. In this thesis, we present our studies of Josephson effects on several systems: quantum Hall and quantum anomalous Hall insulators, antiferromagnetic topological insulator MnBi2Te4, magic-angle twisted bilayer graphene, and altermagnets, where the interplay of superconductivity, topology, and magnetism gives rise to novel physics. Specifically, in Chapter 2, we focus on the novel phenomena associated with the edge state-mediated supercurrent in Josephson junctions based on topological insulators. In Chapter 3, we study the Josephson diode effect in the gate-defined Josephson junctions based on magic-angle twisted bilayer graphene, and its applications in creating superconducting qubits. In chapter 4, we introduce the generic topological altermagnetic Josephson junctions by leveraging the intrinsic spin-polarized band splitting and zero net magnetization attributes of altermagnets. Our research unveils several intriguing physical properties of quantum materials through Josephson junctions and examines their potential applications in both superconducting and topological quantum computing.