Department of Theoretical Physics, V E Lashkaryov Institute of Semiconductor Physics, Kyiv 03028, Ukraine.
J Phys Condens Matter. 2012 May 23;24(20):205302. doi: 10.1088/0953-8984/24/20/205302. Epub 2012 Apr 24.
Based on the symmetry properties of the graphene lattice, we derive the effective Hamiltonian of graphene under spatially nonuniform acoustic and optical strains. Comparison with the published results of the first-principles calculations allows us to determine the values of some Hamiltonian parameters, and suggests the validity of the derived Hamiltonian for acoustical strain up to 10%. The results are generalized for the case of graphene with broken plane reflection symmetry, which corresponds, for example, to the case of graphene placed on a substrate. Here, essential modifications to the Hamiltonian give rise, in particular, to the gap opening in the spectrum in the presence of the out-of-plane component of optical strain, which is shown to be due to the lifting of the sublattice symmetry. The developed effective Hamiltonian can be used as a convenient tool for analysis of a variety of strain-related effects, including electron-phonon interaction or pseudo-magnetic fields induced by the nonuniform strain.
基于石墨烯晶格的对称性质，我们推导出了在空间非均匀声子和光学应变下的石墨烯有效哈密顿量。与第一性原理计算的已发表结果进行比较，使我们能够确定一些哈密顿量参数的值，并表明所推导的哈密顿量对于声子应变高达 10%是有效的。我们将结果推广到具有平面反射对称破缺的石墨烯情况，例如，石墨烯置于衬底上的情况。在这里，哈密顿量的重要修正导致了在光学应变的离面分量存在时，能谱中出现能隙，这归因于子晶格对称性的破坏。所开发的有效哈密顿量可以用作分析各种应变相关效应的便利工具，包括电子-声子相互作用或由非均匀应变引起的赝磁场。
