Nanofaceting as a stamp for periodic graphene charge carrier modulations

Graphene, a simple two-dimensional honeycomb arrangement of sp2-hybridised carbon atoms, is hailed for its exceptional electronic environment, forcing charge carriers to propagate analogous to relativistic massless particles1. Its potential to revolutionize standard silicon-based electronics is widely recognised, provided that material properties like local defects, honeycomb rotational order or electronic doping can be controlled and engineered at hand down to the nanometer scale, i.e. at or beyond the limits of standard top-down state-of-the-art nanofabrication techniques. Immense progress was achieved in recent years on fabricating high-quality homogeneous graphene sheets with small defect densities, reaching high carrier mobilities up to several 100,000 cm2/Vs. However, the crucial step towards a targeted realisation of heterogeneous graphene properties, mostly relying on lithography techniques, systematically faces spurious degradation of the structure and performance of devices. Yet, heterogeneous properties majorly widen the options for electronics and for experiments on exciting fundamental physics: 1D grain boundaries between different honeycomb lattice orientations can be exploited to achieve variable bandgaps for optoelectronics in otherwise semi-metallic graphene2, to tune carrier mobilities3, or to introduce spin degrees of freedom4. Local control over graphene electronic doping is of particular interest, since it allows to induce p−n junctions as a basis for transistor functionality5,6. Moreover, when reduced to a small scale, such junctions should bring to life very fundamental prospects of relativistic quantum mechanics such as the so-called Dirac-fermion optics7, where refraction of electron and hole waves at p−n transitions is governed by doping levels and their spatial abruptness8,9,10,11. A hallmark in this field is the Klein tunneling effect12. Supporting metallic surfaces are rich playgrounds for these concepts, moreover offering the prospect of large scale production of high-quality graphene via chemical vapor deposition (CVD). Indeed, metals may exhibit coexisting surface terminations with different interaction potentials and the potential to trigger variations in graphene doping13. They allow the formation of graphene with different crystallographic orientations14, different kinds of grain boundaries between domains, and domains with various doping levels15,16. In this article we report an unprecedented 1D quasiperiodic modulation of graphene electron doping, probed by spatial mapping of the electronic band structure in wave-vector-resolved photoemission microscopy (k-PEEM). Sampling local topography and diffraction, we show that a nanometer-scale periodic structuration and electronic doping of several 1013 carriers per cm2 can be achieved straightforwardly in graphene, as-grown by CVD on high-index vicinal copper. The pattern consists of a roof-top-like alternation of Cu facets of distinctive symmetries, formed by surface energy minimization at the atomic scale, which drives copper and carbon mass-transfers during high-temperature CVD. The general concept of this work, which avoids any lithography processing steps, can be extended towards other chemical vapor deposited 2D systems of current interest such as semiconducting transition metal dichalcogenides, e.g. MoS2, insulating hexagonal boron nitride (h-BN) monolayers, and respective hybrid structures.