A simple model based on the divide and conquer rule and tight-binding (TB) approximation is employed for studying the role of finite size effect on the electronic properties of elongated graphene nanoribbon (GNR) heterojunctions. In our model, the GNR heterojunction is divided into three parts: a left (L) part, middle (M) part, and right (R) part. The left part is a GNR of width $W_{L}$, the middle part is a GNR of width $W_{M}$, and the right part is a GNR of width $W_{R}$. We assume that the left and right parts of the GNR heterojunction interact with the middle part only. Under this approximation, the Hamiltonian of the system can be expressed as a block tridiagonal matrix. The matrix elements of the tridiagonal matrix are computed using real space nearest neighbor orthogonal TB approximation. The electronic structure of the GNR heterojunction is analyzed by computing the density of states. We demonstrate that for heterojunctions for which $W_{L} = W_{R}$, the band gap of the system can be tuned continuously by varying the length of the middle part, thus providing a new approach to band gap engineering in GNRs. Our TB results were compared with calculations employing divide and conquer rule in combination with density functional theory (DFT) and were found to agree nicely.
Synthesis of Metal-Semiconductor Heterojunctions in Single Graphene Nanoribbons
University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Kavli Energy NanoSciences Institute at the University of California Berkeley and the Lawrence Berkeley National Laboratory（加州大学伯克利分校与劳伦斯伯克利国家实验室卡弗里能源纳米科学研究所）；Department of Chemistry, Columbia University（哥伦比亚大学化学系）；Department of Physics, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校物理系）；Department of Physics, Cornell University（康奈尔大学物理系）；Department of Materials Science and Nanoengineering, Rice University（莱斯大学材料科学与纳米工程系）
