Research On The Electronic Properties Of Graphene Nanoribbons Based On The Ssh Model

In traditional physics, We usually only need to research the infinite crystal. Therefore, we can directly use Bloch theorem to solve the crystal form of electronic state. However, for solid state physics, how to solve the electronic state of the crystals whose size are limited is also a basic research problem. Using the tight-binding approximation with hard-wall boundary conditions,the discrete form of the Bloch theorem or low energy approximation of the Dirac equation, we can get the electronic spectrum of armchair type and zigzag type graphene nanoribbons analytically. We use SSH model to research the energy dispersion relation of zigzag type graphene nanoribbons in this paper.we propose a discrete system method of the Bloch theorem to calculate analytically the electronic state of limited graphene lattice model which is based on the tight-binding approximation in the second chapter. we first apply Bloch theorem to the infinite direction of the lattice model of ZGNRs and turn it into a solution of a super original cell, and then bring the original cell into two polymerization atomic chain model, where the Bloch theorem method of the discrete system is used again to get the electronic spectrum of graphene nanoribbons with zigzag edges. We think this method is universal.we mainly use the SSH model theory in the third chapter. In the method, the single Polyacetylene chain is taken as quasi one-dimensional system and the coupling between chain and chain is supposed to be weaker than the coupling within the chains. Also, the CH group is taken as a whole and the mass of the atomic lattices are much greater than that of the electrons, so that the quantum effects of electrons can be ignored and the classical movement method can be used to deal with the movement of the atomic lattices. For trans-polyacetylene chain, if we ignore the coupling between chain and chain, it will be a quasi one-dimensional structure, but the weak coupling between chain and chain will produce certain physical effect. For a system composed of two chains, considering the coupling between chain and chain, which can be divided into two kinds of structure with bond-bond parallel and non-parallel. We can know from Electronic energy spectrum that both the spectra are related to the coupling intensity, but the effect of the bond-bond parallel structure on the spectrum is obvious compared to the non-parallel, the itinerant of electrons increase with the increase of the hopping Coupling integral. Whether we can give the electronic spectrum of graphene nanoribbons analytically based on SSH model? There is periodic structure in one direction on the graphene nanoribbons, especially the graphene nanoribbons with zigzag edges, which can be regarded to be formed by the coupling of homogeneous polyacetylene chains with bond-bond non-parallel. To get the accurate electronic spectrum, the appropriate unit cell is only needed. It can be derived from the electronic spectrum that the extended states of electrons increased with the increase of the hopping coupling integral, but the energy gap still can not be opened. Adjust the numerical value of coupling integral chain and chain until it is equal to the coupling integral within the chain and then the carbon atoms own hexagonal structure, whose electronic spectrum reflects the normal band of graphene nanoribbons. The results show that the energy dispersion relations are consistent with the conclusion reached by applying the discrete form of Bloch theorem in the second chapter.