Topological Effects in Two-Dimensional Systems

Two-dimensional (2D) systems are the hatcheries of novel phenomena in condensed matter physics. For example, in graphene and transition metal dichalcogenides, the<br>electronic behavior near the Fermi level is described by a 2D Dirac fermion model, which is the origin of many interesting Berry phase effects; recent studies for 2D ferromagnetic insulators such as CrI₃ revealed a series of novel optical and transport phenomena. The excitations in 2D systems manifest completely different properties compared to unconstrained free excitations in three-dimensional systems. The excitations of interest in this thesis include electrons, excitons, phonons and magnons. We explain the nontrivial properties of these excitations in 2D systems<br>from a topological point of view. We first show that we can construct electronic Chern insulators using graphene-hexagonal Boron Nitride superlattices. An eective<br>mass theory for the conduction band electrons is derived using the Foldy-Wouthuysen (FW) transformation, the band projection method and the wave packet theory. This<br>effective mass theory demonstrates how the Berry curvature distinguishes 2D Bloch band systems from free electron systems. Secondly, we show that the interaction<br>between magnons and phonons can generate Berry curvatures, which can lead to the thermal Hall effect for magnon-phonon hybrid excitations even when the isolated<br>magnon and phonon systems do not show thermal Hall effect separately. We also provide an analytical expression for the thermal Hall conductance as a function of the Berry curvature using the wave packet theory which is confirmed by the linear response theory. Finally, we unveil the importance of another topological number, the winding number. We found that the angular momenta of the bright exciton states in chiral fermion systems are determined by the winding number and the crystal symmetry. Based on our theory, we propose two chiral fermion systems capable<br>of hosting dark s-like excitons: gapped surface states of a topological crystalline insulator with C₄ rotational symmetry and biased 3R-stacked MoS₂ bilayers. <br>