# Spatially resolved electronic structure of twisted graphene

## TL;DR

This study uses scanning tunneling microscopy and spectroscopy to analyze the spatial electronic structure of twisted graphene layers, revealing moire patterns, Van Hove singularities, and sub-lattice structures that depend on twist angle and energy.

## Contribution

It provides detailed experimental and theoretical insights into the spatially resolved electronic properties of twisted graphene, including the development of sub-lattice structures and their energy dependence.

## Key findings

- Identification of moire patterns with large periodicity.
- Observation of Van Hove singularities at small twist angles.
- Spatial maps showing honeycomb sub-lattice structures near the Fermi level.

## Abstract

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 with a periodicity that is substantially larger than the periodicity of a single layer graphene. The twisted graphene layer has electronic properties that are distinctly different from that of a single layer graphene due to the nonzero interlayer coupling. For small twist angles (about 1-3.5 degree) the integrated differential conductivity spectrum exhibits two well-defined Van Hove singularities. Spatial maps of the differential conductivity that are recorded at energies near the Fermi level exhibit a honeycomb structure that is comprised of two inequivalent hexagonal sub-lattices. For energies |E-E_F|>0.3 eV the hexagonal structure in the differential conductivity maps vanishes. We have performed tight-binding calculations of the twisted graphene system using the propagation method, in which a third graphene layer is added to mimic the substrate. This third layer lowers the symmetry and explains the development of the two hexagonal sub-lattices in the moire pattern. Our experimental results are in excellent agreement with the tight-binding calculations.

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Source: https://tomesphere.com/paper/1705.09083