Parallel ("nested") regions of a Fermi surface (FS) drive instabilities of the electron fluid, for example, the spin density wave in elemental chromium. In one-dimensional materials, the FS is trivially fully nested (a single nesting vector connects two "Fermi dots"), while in higher dimensions only a fraction of the FS consists of parallel sheets. We demonstrate that the tiny angle regime of twist bilayer graphene (TBLG) possesses a phase, accessible by interlayer bias, in which the FS consists entirely of nestable "Fermi lines", the first example of a completely nested FS in a two-dimensional (2D) material. This nested phase is found both in the ideal as well as relaxed structure of the twist bilayer. We demonstrate excellent agreement with recent STM images of topological states in this material and elucidate the connection between these and the underlying Fermiology. We show that the geometry of the Fermi lines network is controllable by the strength of the applied interlayer bias, and thus TBLG offers unprecedented access to the physics of FS nesting in 2D materials.

中文翻译：

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在最小扭曲的双层石墨烯中实现完美且可控的嵌套。

费米表面（FS）的平行（“嵌套”）区域驱动电子流体的不稳定性，例如元素铬中的自旋密度波。在一维材料中，FS几乎是完全嵌套的（单个嵌套向量连接两个“费米点”），而在更高尺寸的材料中，只有FS的一小部分由平行的薄片组成。我们证明了扭曲双层石墨烯（TBLG）的微小角度范围具有一个可通过层间偏置访问的相，其中FS完全由可嵌套的“费米线”组成，这是二维中完全嵌套FS的第一个示例（ 2D）材料。这种嵌套相既存在于扭曲双层的理想结构中，也存在于其松弛结构中。我们证明了与这种材料中拓扑状态的最新STM图像极为吻合，并阐明了这些与潜在的费米病学之间的联系。我们表明，费米线网络的几何形状可通过所施加的层间偏压的强度来控制，因此TBLG为2D材料中FS嵌套的物理学提供了前所未有的途径。