扶手椅型单轴应变石墨烯中的光谱蝴蝶、混合Dirac-Schrödinger费米子行为和拓扑态
Spectral butterfly, mixed Dirac-Schrödinger fermion behavior and topological states in armchair uniaxial strained graphene
摘要：
本文提出了一种将任意扶手椅单轴应变下石墨烯纳米取向的紧束缚哈密顿量精确映射到有效的一维系统的方法。作为一个应用，对于周期性调制，我们发现在费米能级处有一个能隙开口，并有一个复杂的分形谱，类似于哈珀模型产生的霍夫施塔特蝴蝶。后者可以解释为所产生的有效电位的可解释性或不可解释性的性质。当与锯齿形单轴周期应变相比时，谱显示出更大的间隙，尽管一般来说状态具有更扩展的性质。当应变幅值和波长达到某一特定的临界值时，会出现一个缺口。在这个临界点，电子在一个方向上表现为相对论性狄拉克费米子，而在另一个方向上，观察到非相对论性薛定谔行为。另外，我们还观察到了一些拓扑态，它们具有不完全边缘态的特殊性，因为它们在体中呈现出一定的振幅。然而，由于通过解耦降低了维度，这些是有效系统的边缘状态。这些状态也提出了最近在准周期系统中观察到的分形Chern beating。
英文摘要：
An exact mapping of the tight-binding Hamiltonian for a graphene's nanoribbon under any armchair uniaxial strain into an effective one-dimensional system is presented. As an application, for a periodic modulation we have found a gap opening at the Fermi level and a complex fractal spectrum, akin to the Hofstadter butterfly resulting from the Harper model. The latter can be explained by the commensurability or incommensurability nature of the resulting effective potential. When compared with the zig-zag uniaxial periodic strain, the spectrum shows much bigger gaps, although in general the states have a more extended nature. For a special critical value of the strain amplitude and wavelength, a gap is open. At this critical point, the electrons behave as relativistic Dirac femions in one direction, while in the other, a non-relativistic Schrödinger behavior is observed. Also, some topological states were observed which have the particularity of not being completly edge states since they present some amplitude in the bulk. However, these are edge states of the effective system due to a reduced dimensionality through decoupling. These states also present the fractal Chern beating observed recently in quasiperiodic systems.
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