Study On Topological Phase Transition And Phase Diagrams In A Coupled Kitaev Chains System

Topological insulators and topological superconductors,as the novel quantum states of matter,are hot spots in the field of condensed matter physics.According to the band theory,traditional solid materials can be divided into insulators,conductors,and semi-conductors.With the introduction of the concept "topology" and further classification according to the different topological properties of electronic states,topological insulator and topological superconductor are divided from traditional insulators and superconduc-tors.Different from the traditional insulator,the bulk of topological insulator is the insulating state while its surface or interface supports the conducting boundary states.These boundary states are immune to local perturbation and disorder due to the protection by energy gap.Soon after the discovery of topological insulators,the study of them was generalized naturally to topological superconductors.There is a direct analogy between topological insulators and topological superconductors due to similar Hamiltonian and classification.In recent years,Kitaev model,the simplest typical one-dimensional spinless p-wave topological superconductor,has attracted the interest of many researchers.The model has abundant topological phases characterized by the Majorana zero energy edge mode.The Majorana zero energy edge modes not only obey non-abelian statistics,but also are not affected by local impurities and disorder,which provides a possible platform for topological quantum fault-tolerant computing and quantum information processing.In this thesis,based on the standard Kitaev model,we propose a two-leg Kitaev ladder coupled system and study the topological phase transition and phase diagrams of the system.The detailed contents are as follows:We propose a two-leg Kitaev ladder coupled system composed of two identical or non-identical Kitaev chains,and study the effects of interchain hopping amplitude and interchain pairing strengh on the topological properties of the system.We find that one part of the energy spectrum moves to the left and the other to the right with the increase of the interchain hopping amplitude in the case of two identical Kitaev chains,where a topologically nontrivial phase is induced.However,the interchain pairing strength only induces a topological phase transition without the topologically nontrivial phase appearing.At the same time,we also find that the winding number always is quantitatively equal to half of the zero energy edge modes in the system.For the situation that the two-leg Kitaev ladder coupled system is comprised of two non-identical Kitaev chains,we find that one part of the energy spectrum moves inward and the other moves outward when the interchain hopping amplitude increases gradually Meanwhile,a pair of degenerate non-zero energy edge modes respectively appear in the upper and lower band gaps of the energy spectrum of the system when the interchain hopping amplitude exceeds a certain critical value.On the other hand,the interchain pairing strength not only can change the energy gap of the system,but also induce a pair of degenerate non-zero energy edge modes appearing in the upper and lower band gaps of the system,respectively.In addition,it is found that the phase diagram can only predict the zero energy edge modes rather than the nonzero energy edge modes.