Double Moiré with a Twist: Supermoiré in Encapsulated Graphene

A periodic spatial modulation, as created by a moiré pattern, has been extensively studied with the view to engineer and tune the properties of graphene. Graphene encapsulated by hexagonal boron nitride (hBN) when slightly misaligned with the top and bottom hBN layers experiences two interfering moiré patterns, resulting in a so-called supermoiré (SM). This leads to a lattice and electronic spectrum reconstruction. A geometrical construction of the nonrelaxed SM patterns allows us to indicate qualitatively the induced changes in the electronic properties and to locate the SM features in the density of states and in the conductivity. To emphasize the effect of lattice relaxation, we report band gaps at all Dirac-like points in the hole doped part of the reconstructed spectrum, which are expected to be enhanced when including interaction effects. Our result is able to distinguish effects due to lattice relaxation and due to the interfering SM and provides a clear picture on the origin of recently experimentally observed effects in such trilayer heterostuctures.

Interlayer Repulsion of Retinal Ganglion Cell Mosaics Regulates Spatial Organization of Functional Maps in the Visual Cortex

In higher mammals, orientation tuning of neurons is organized into a quasi-periodic pattern in the primary visual cortex. Our previous model studies suggested that the topography of cortical orientation maps may originate from moiré interference of ON and OFF retinal ganglion cell (RGC) mosaics, but did not account for how the consistent spatial period of maps could be achieved. Here we address this issue with two crucial findings on the development of RGC mosaics: first, homotypic local repulsion between RGCs can develop a long-range hexagonal periodicity. Second, heterotypic interaction restrains the alignment of ON and OFF mosaics, and generates a periodic interference pattern map with consistent spatial frequency. To validate our model, we quantitatively analyzed the RGC mosaics in cat data, and confirmed that the observed retinal mosaics showed evidence of heterotypic interactions, contrary to the previous view that ON and OFF mosaics are developed independently.SIGNIFICANCE STATEMENT Orientation map is one of the most studied functional maps in the brain, but it has remained unanswered how the consistent spatial periodicity of maps could be developed. In the current study, we address this issue with our developmental model for the retinal origin of orientation map. We showed that local repulsive interactions between retinal ganglion cells (RGCs) can develop a hexagonal periodicity in the RGC mosaics and restrict the alignment between ON and OFF mosaics, so that they generate a periodic pattern with consistent spatial frequency for both the RGC mosaics and the cortical orientation maps. Our results demonstrate that the organization of functional maps in visual cortex, including its structural consistency, may be constrained by a retinal blueprint.