Mora Christophe, Regnault Nicolas, Bernevig B Andrei
Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris 75005, France.
Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev Lett. 2019 Jul 12;123(2):026402. doi: 10.1103/PhysRevLett.123.026402.
We investigate the electronic structure of a twisted multilayer graphene system forming a moiré pattern. We consider small twist angles separating the graphene sheets and develop a low-energy theory to describe the coupling of Dirac Bloch states close to the K point in each individual plane. Extending beyond the bilayer case, we show that, when the ratio of the consecutive twist angles is rational, a periodicity emerges in quasimomentum space with moiré Bloch bands even when the system does not exhibit a crystalline lattice structure in real space. For a trilayer geometry, we find flatbands in the spectrum at certain rotation angles. Performing a symmetry analysis of the band model for the trilayer, we prove that the system is a perfect metal in the sense that it is gapless at all energies. This striking result originates from the three Dirac cones which can only gap in pairs and produce bands with an infinite connectivity. It also holds quite generally for multilayer graphene with an odd number of planes under the condition of C_{2z}T symmetry.
我们研究了形成莫尔图案的扭曲多层石墨烯系统的电子结构。我们考虑了分隔石墨烯片层的小扭转角，并发展了一种低能理论来描述每个单独平面中靠近K点的狄拉克布洛赫态的耦合。超越双层情况，我们表明，当连续扭转角的比值为有理数时，即使系统在实空间中不呈现晶格结构，在准动量空间中也会出现具有莫尔布洛赫带的周期性。对于三层几何结构，我们发现在特定旋转角度下光谱中存在平带。对三层的能带模型进行对称性分析，我们证明该系统在所有能量下均无能隙的意义上是一种完美金属。这一惊人结果源于三个狄拉克锥，它们只能成对地产生能隙并产生具有无限连通性的能带。在(C_{2z}T)对称性条件下，对于奇数个平面的多层石墨烯，这一结果也普遍成立。
