Non-Hermitian Phenomena in the Trimer Su-Schrieffer-Heeger Model

Sammanfattning

The trimer Su-Schrieffer-Heeger (SSH3) model extends the traditional Su-Schrieffer-Heeger model by incorporating an additional lattice site per unit cell. Although it lacks chiral symmetry, the SSH3 model exhibits bulk-boundary correspondence (BBC) with topologically protected, localized edge states under open boundary conditions. This thesis investigates non-Hermitian phenomena in the anisotropic SSH3 model. Introducing anisotropy in the hopping amplitudes breaks the BBC, leading to the emergence of the non-Hermitian skin effect and exceptional points. Through a unitary transformation, the SSH3 model is mapped to a model with reciprocal hopping amplitudes and on-site dissipation, where the non-Hermitian skin effect nevertheless remains. An extensive analysis of exceptional points of order n (EPns) in the SSH3 model uncovers the existence of EP2s and EP3s, with EP2 lines connecting EP3s under chiral and particle-hole symmetry. EP3s are shown to occur only in the presence of chiral or sublattice symmetry. Additionally, analytical solutions for the boundary states are derived, and the biorthogonal framework is employed to examine the model's topological properties. The biorthogonal polarization is identified as a topological invariant that accurately predicts the localization of boundary states.