Huang Danhong, Iurov Andrii, Gumbs Godfrey, Zhemchuzhna Liubov
Air Force Research Laboratory, Space Vehicles Directorate, Kirtland Air Force Base, NM 87117, United States of America. Department of Electrical & Computer Engineering, University of New Mexico, Albuquerque, NM 87131, United States of America.
J Phys Condens Matter. 2019 Mar 27;31(12):125503. doi: 10.1088/1361-648X/aafd01. Epub 2019 Jan 9.
Under a magnetic field perpendicular to an monolayer graphene, the existence of a two-dimensional periodic scatter array can not only mix Landau levels of the same valley for displaying split electron-hole Hofstadter-type energy spectra, but also couple two sets of Landau subbands from different valleys in a bilayer graphene. Such a valley mixing effect with a strong scattering strength has been found observable and studied thoroughly in this paper by using a Bloch-wave expansion approach and a projected [Formula: see text] effective Hamiltonian including interlayer effective mass, interlayer coupling and asymmetrical on-site energies due to a vertically-applied electric field. For bilayer graphene, we find two important characteristics, i.e. mixing and interference of intervalley scatterings in the presence of a scatter array, as well as a perpendicular-field induced site-energy asymmetry which deforms severely or even destroys completely the Hofstadter-type band structures due to the dependence of Bloch-wave expansion coefficients on the applied electric field.
在垂直于单层石墨烯的磁场下，二维周期性散射阵列的存在不仅可以混合同一能谷的朗道能级以展现分裂的电子 - 空穴霍夫施塔特型能谱，还能耦合双层石墨烯中来自不同能谷的两组朗道子带。本文通过使用布洛赫波展开方法和一个投影的[公式：见原文]有效哈密顿量（包括层间有效质量、层间耦合以及由于垂直施加电场导致的不对称在位能），发现了这种具有强散射强度的能谷混合效应是可观测的，并对其进行了深入研究。对于双层石墨烯，我们发现了两个重要特性，即在存在散射阵列时能谷散射的混合与干涉，以及垂直场诱导的在位能不对称性，由于布洛赫波展开系数对施加电场的依赖性，这种不对称性会严重变形甚至完全破坏霍夫施塔特型能带结构。
