Study On Properties Of Special Modes Induced By Inter-Chain Coupling In A Non-Hermitian System Of Coupled Su-Schrieffer-Heeger Chains

Topological insulators,as the novel states of matter,have been widely concerned and studied in the field of condensed matter physics.In contrast to insulators,there are always conductive edge states at the boundary of topological insulators,which are immune to the local perturbation and disorder as certain symmetry is preserved.The previous studies of topological insulators are concentrate on the Hermitian systems.However,the non-Hermitian systems have become a high-profie subject in recent years for the unique properties,which is significantly different from those of Hermitian systems,like the breakdown of conventional bulk-boundary correspondence,non-Hermitian effect and special spectral degeneracies.The unique properties are gradually revealed with further investigation for the non-Hermitian systems.So far,the Hermitian and non-Hermitian systems have been investigated in most of the prototypical topological systems.In these popular models,the Su-Schrieffer-Heeger(SSH)model for polyacetylene,as the simplest two-band model,provides a possible platform for the study of topological insulators and topological superconductor.SSH model shows the hopping of spinless fermions on a one-dimension(1D)lattice with staggered hopping amplitude.The topological zero energy states characterize the rich topological phase.In this thesis,based on the SSH model,we propose a non-Hermitian system of coupled SSH chains and numerically study spectra and density profiles of the system,in which the essence of the interesting phenomenon is investigated.The detailed contents are as follows:The non-Hermitian system of coupled SSH chains consists of two identical nonHermitian SSH chains with asymmetric hopping amplitude,and the inter-chain-coupling is symmetric or asymmetric.The non-Hermitian system of coupled SSH chains grantinducings special modes,the magnitude of the eigenvalues of which are equal to the interchain-coupling strength inducing the appearance of the special modes,and the eigenvalues are pure real or pure imaginary for symmetric or asymmetric inter-chain-coupling strengths.The odd and even lattice sites can affect the region of the special modes appearing in the gap.From the density profiles of the special modes,it is clear that the density profiles of all the special modes are completely identical at a same fixed parameter condition even if the inter-chain-coupling strength is added into the non-Hermitian system of coupled SSH chains in different ways for odd lattice sites.The density profiles of the special modes change due to the non-Hermitian skin effect when the parameters change,but the density profiles of all the special modes are still same as long as the parameters change the same for all symmetrical and asymmetrical inter-chain-coupling.Finally,we illustrate that the effect of different inter-chain-coupling are fundamentally equivalent to the effect of the on-site potential energy on the two non-Hermitian SSH chain.