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) possess 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 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 that TBLG offers unprecedented access to the physics of FS nesting in 2d materials. 1 arXiv:1908.08318v1 [cond-mat.mtrl-sci] 22 Aug 2019 of the FS consists of nested sheets) and notoriously difficult to control 10,11 . In contrast, the nesting exhibited by the twist bilayer is both complete (100% nested) and, as we show, can be fully controlled by tuning of the interlayer bias.This "nesting phase" of the twist bilayer is found in a large regime of angle-field space and is, remarkably, found both for the ideal twist geometry as well as the structural dislocation network that it reconstructs to at tiny angles 12-14 . The finding of a robust moiré-induced 2d "Fermi line" analogy of the 1d "Fermi dot" topology, controllable via bias, both offers unprecedented access to the physics of FS nesting, as well as highlighting the remarkable electronic structures that can be created by moiré geometries and their structural dislocation networks in 2d materials. II. RESULTS A. ModelThe physics of the tiny angle regime of the twist bilayer is an essentially multiscale problem involving both the lattice constant of graphene -the scale at which atomic relaxation 2 FIG. 1: Fully nested Fermiology in the graphene twist bilayer and the corresponding dislocation network (θ = 0.51 • , E = 90 mV/Å). Below ∼ 1 • twist bilayer graphene relaxes into an ordered network of dislocations, with the smoothly varying stacking order of the ideal twist geometry (a) becoming series of sharp AB and BA domains (b), each separated by pure shear partial dislocations with high von Mises strain (J 2 ) (c,d). Pseudo-magnetic fields of the order of 40 T are induced in the AB and BA regions with alternating sign between the latter (e,f). In the density of states (DOS) the zero mode is substantially broadened, with the valley region shifting upwards in energy (g).However, while atomic relaxation induces dramatic changes to the Fermiology in the zero mode region (l,m), in the valley region a remarkably stable Fermi topology of fully nested Fermi lines is seen (nesting vector indicated by...

With respect to molecular switches, initializing the quadricyclane (QC) to norbornadiene (NBD) back‐reaction by light is highly desirable. Our previous publication provided a unique solution for this purpose by utilizing covalently bound C60. In this work, the fundamental processes within these hybrids has been investigated. Variation of the linker unit connecting the NBD/QC moiety with the fullerene core is used as a tool to tune the properties of the resulting hybrids. Utilizing the Prato reaction, two unprecedented NBD/QC – fullerene hybrids having a long‐rigid and a short‐rigid linker were synthesized. Molecular dynamics simulations revealed that this results in an average QC–C60 distance of up to 14.2 Å. By comparing the NBD–QC switching of these derivatives with the already established one having a flexible linker, valuable mechanistic insights were gained. Most importantly, spatial convergence of the QC moiety and the fullerene core is inevitable for an efficient back‐reaction.

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