We combined periodic ripples and electrostatic potentials to form curved graphene superlattices and studied the effects of space-dependent Fermi velocity induced from curvature on their electronic properties. With equal periods and symmetric potentials, the Dirac points do not move, but their locations shift under asymmetric potentials. This shift can be tuned by curvature and potentials. Tunable extra gaps in band structures can appear with unequal periods. The existence of new Dirac points is proposed, such that these new Dirac points can appear under smaller potentials with curvature, and their locations can be changed even under a fixed potential by adjusting the curvature. Our results suggest that curvature provides a new possible dimension to tune the electronic properties in graphene superlattices and a platform to more easier study physics near new Dirac points.

我们将周期性波纹和静电势结合起来形成弯曲的石墨烯超晶格，并研究了由曲率引起的空间相关费米速度对其电子特性的影响。在相等的周期和对称势下，狄拉克点不会移动，但它们的位置在不对称势下会发生变化。这种转变可以通过曲率和电位进行调整。能带结构中可调谐的额外间隙可能以不等的周期出现。提出了新狄拉克点的存在性，使得这些新狄拉克点可以出现在具有曲率的较小势能下，并且通过调整曲率，即使在固定势能下也可以改变其位置。