National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, 210093, People's Republic of China.
J Phys Condens Matter. 2013 Jun 19;25(24):245301. doi: 10.1088/0953-8984/25/24/245301. Epub 2013 May 24.
To show the specific behavior of Dirac fermions in a quasi-periodic structure, we investigate the electronic properties in a deterministic Thue-Morse graphene superlattice. Our main findings include the following. (i) Unlike conventional Schrödinger electrons, quasi-periodic features such as the striking self-similarity and trifurcation in the transmission spectrum can be manifested only at oblique incidence. (ii) In the vicinity of the usual Dirac point, extra Dirac points emerge; their locations are dependent merely on the second generation of the Thue-Morse structure and the number is double that in the periodic graphene superlattice. (iii) A classification is given about the wavefunctions in the Thue-Morse structure which are transformed from the critical states into extended ones at the Dirac points. (iv) The electrons can transmit perfectly at the extra Dirac points, and such a collimation supplies a convenient way to experimentally detect the numbers and the locations of the extra Dirac points. These exotic electronic properties in the aperiodic graphene superlattices may facilitate some applications in graphene-based electronics.
为了展示狄拉克费米子在准周期结构中的特殊行为，我们研究了确定性的狄拉克梯姆（Thue-Morse）石墨烯超晶格中的电子性质。我们的主要发现包括：（i）与传统的薛定谔电子不同，只有在倾斜入射时才能表现出传输谱中明显的自相似性和三分叉等准周期特征；（ii）在通常的狄拉克点附近，会出现额外的狄拉克点；它们的位置仅取决于梯姆结构的第二代，且数量是周期性石墨烯超晶格的两倍；（iii）对梯姆结构中的波函数进行了分类，这些波函数从临界态转变为狄拉克点处的扩展态；（iv）电子可以在额外的狄拉克点处完全传输，这种准直提供了一种方便的实验检测额外狄拉克点数量和位置的方法。这些在非周期性石墨烯超晶格中的奇异电子性质可能会促进基于石墨烯的电子学的一些应用。
