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Topology is familiar mostly from mathematics, but also natural sciences have found its concepts useful. Those concepts have been used to explain several natural phenomena in biology and physics, and they are particularly relevant for the electronic structure description of topological insulators and graphene systems. Here, we introduce topologically distinct graphene forms - graphene spirals - and employ density-functional theory to investigate their geometric and electronic properties. We found that the spiral topology gives rise to an intrinsic Rashba spin-orbit splitting. Through a Hamiltonian constrained by space curvature, graphene spirals have topologically protected states due to time-reversal symmetry. In addition, we argue that the synthesis of such graphene spirals is feasible and can be achieved through advanced bottom-up experimental routes that we indicate in this work.
Wrinkling is a ubiquitous phenomenon in two-dimensional membranes. In particular, in the large-scale growth of graphene on metallic substrates, high densities of wrinkles are commonly observed. Despite their prevalence and potential impact on large-s
Multilayer graphene with rhombohedral and Bernal stacking are supposed to be metallic, as predicted by density functional theory calculations using semi-local functionals. However recent angular resolved photoemission and transport data have question
We have used scanning tunneling microscopy and spectroscopy to resolve the spatial variation of the density of states of twisted graphene layers on top of a highly oriented pyrolytic graphite substrate. Owing to the twist a moire pattern develops wit
We explore a network of electronic quantum valley Hall (QVH) states in the moire crystal of minimally twisted bilayer graphene. In our transport measurements we observe Fabry-Perot and Aharanov-Bohm oscillations which are robust in magnetic fields ra
The function of nano-scale devices critically depends on the choice of materials. For electron transport junctions it is natural to characterize the materials by their conductance length dependence, $beta$. Theoretical estimations of $beta$ are made