Non-Hermitian extension of the Haldane model induced by non-reciprocal hopping

• Main Author: Law, Yi Khing
• Other Authors: Zhang Baile
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2023
• Subjects: Science::Physics
• Online Access: https://hdl.handle.net/10356/166577
• Institution: Nanyang Technological University

In this report, we present an analysis of a non-Hermitian extension of the Haldane model induced by non-reciprocal coupling. This study is novel as non- reciprocal couplings in the Haldane model have not received considerable attention. Prior to the introduction of this model, the concepts of band topology and topo- logical insulators are reviewed, with a dive into the Hermitian Haldane model as a paradigmatic example. In the Haldane model, distinct topological phases and chiral edge states associated with the nontrivial phase are studied. The complexities of the non-Hermitian regime and the new degrees of freedom it introduces in band topology are then delved into. A study on the Hatano-Nelson model is conducted to review the non-Hermitian skin effect, an elusive phenomenon that arises when non-Hermiticity is introduced. Finally, we carry out the formulation for the non- Hermitian extension of the Haldane model. The degeneracies in the non-Hermitian framework are categorized, followed by the Chern number topological phase transi- tions. In the presence of non-Hermiticity however, there is a failure of the correspon- dence between the bulk and the boundary which is attributed to the non-Hermitian skin effect. The report concludes with a depiction of the non-Hermitian skin effect in the form of a square geometry under open boundary conditions.