Topological insulators and frustrated spin systems

Topological insulators and frustrated spin systems are new classes of materials that has exotic properties and they attract a lot of attention in recent years. In this thesis, we study impurity scattering and dissipative Josephson junction in topological insulators and spin wave modeling for a frustrated magnet ZnxCo4--x (OD)6Cl2 with x = 0 and 1.;Time-reversal delta-impurity scattering effects and formation in-gap bound states in the bulk of topological insulators (TI) in two and three dimensions is studied theoretically. Specifically we consider how impurity scattering strength is affected by the bulk band structure of topological insulators. A band inversion effect associated with the change of the system from ordinary to topological insulator is pointed out. Experimental consequences of our findings are discussed.;A SNS Josephson junction formed on the gapless surface state of a three-dimensional TI is theoretically shown to host the exotic Majorana fermions and many experimental efforts have been made to fabricate such a system. Here we study theoretically the effect of dissipation in such a SNS Josephson junction (JJ), which is compared against a two-dimensional quadratic band metal. It is known that dissipation in JJ can drive the system through a superconductor-insulator transition. We compare and discuss our results with recent experimental findings.;Theoretical modeling is done for the neutron scattering experiment on powder sample of a frustrated magnet Co4(OD)6Cl 2. We model the system with alternating layers of triangular and kagome lattice, coupling with ferromagnetic interactions, and the spins on the kagome plane with antiferromagnetic interactions and possible single ion crystal field anisotropy and Dzyaloshinskii-Moriya interaction. By fitting the data with the model, we found that the spins suffer from a strong crystal field anisotropy. This implies the possible physical model that describes the close relative ZnCo3(OD)6Cl2, which has a disordered ground state and is suggested to be a spin liquid candidate.