Topological Phases of Non-Hermitian physics

Sammanfattning: Non-Hermitian physics has introduced phenomena like the skin effect and exceptional points, challenging traditional views of topological phases. This thesis contrasts two classification frameworks for non-Hermitian systems. The first approach employs K-theory classifications based on line-gaps and point-gaps, which explain the topological origins of the skin effect but fail to adequately describe exceptional points. The second, more nuanced approach uses homotopy theory, where the braiding of complex energies around exceptional points is integral to the classification. This method provides a detailed account of the behaviour of exceptional points, such as the splitting and merging of these points. We also study systems restricted by PT-symmetry, a symmetry that ensures that each eigenvalue is real or has a complex conjugate pair, which leads to the formation of an exceptional cone in the parameter space of two-band models. This cone features prominently in the accompanying papers, especially when introducing the concept of non-defective exceptional points and in the homotopy classification of PT-symmetric models.