The observation of massless Dirac fermions in monolayer graphene has generated a new area of science and technology seeking to harness charge carriers that behave relativistically within solid-state materials. Both massless and massive Dirac fermions have been studied and proposed in a growing class of Dirac materials that includes bilayer graphene, surface states of topological insulators and iron-based high-temperature superconductors. Because the accessibility of this physics is predicated on the synthesis of new materials, the quest for Dirac quasi-particles has expanded to artificial systems such as lattices comprising ultracold atoms. Here we report the emergence of Dirac fermions in a fully tunable condensed-matter system-molecular graphene-assembled by atomic manipulation of carbon monoxide molecules over a conventional two-dimensional electron system at a copper surface. Using low-temperature scanning tunnelling microscopy and spectroscopy, we embed the symmetries underlying the two-dimensional Dirac equation into electron lattices, and then visualize and shape the resulting ground states. These experiments show the existence within the system of linearly dispersing, massless quasi-particles accompanied by a density of states characteristic of graphene. We then tune the quantum tunnelling between lattice sites locally to adjust the phase accrual of propagating electrons. Spatial texturing of lattice distortions produces atomically sharp p-n and p-n-p junction devices with two-dimensional control of Dirac fermion density and the power to endow Dirac particles with mass. Moreover, we apply scalar and vector potentials locally and globally to engender topologically distinct ground states and, ultimately, embedded gauge fields, wherein Dirac electrons react to 'pseudo' electric and magnetic fields present in their reference frame but absent from the laboratory frame. We demonstrate that Landau levels created by these gauge fields can be taken to the relativistic magnetic quantum limit, which has so far been inaccessible in natural graphene. Molecular graphene provides a versatile means of synthesizing exotic topological electronic phases in condensed matter using tailored nanostructures.

The unimolecular rectifier is a fundamental building block of molecular electronics. Rectification in single molecules can arise from electron transfer between molecular orbitals displaying asymmetric spatial charge distributions, akin to p-n junction diodes in semiconductors. Here we report a novel all-hydrocarbon molecular rectifier consisting of a diamantane-C 60 conjugate. By linking both sp 3 (diamondoid) and sp 2 (fullerene) carbon allotropes, this hybrid molecule opposingly pairs negative and positive electron affinities. The single-molecule conductances of self-assembled domains on Au(111), probed by lowtemperature scanning tunnelling microscopy and spectroscopy, reveal a large rectifying response of the molecular constructs. This specific electronic behaviour is postulated to originate from the electrostatic repulsion of diamantane-C 60 molecules due to positively charged terminal hydrogen atoms on the diamondoid interacting with the top electrode (scanning tip) at various bias voltages. Density functional theory computations scrutinize the electronic and vibrational spectroscopic fingerprints of this unique molecular structure and corroborate the unconventional rectification mechanism.

Atomic manipulation techniques have provided a bottom-up approach to investigating the unconventional properties and complex phases of strongly correlated electron materials. By engineering artificial systems containing tens to thousands of atoms with tailored electronic or magnetic properties, it has become possible to explore how quantum many-body effects emerge as the size of a system is increased from the nanoscale to the mesoscale. Here we investigate both theoretically and experimentally the quantum engineering of nanoscale Kondo lattices – Kondo droplets – exemplifying nanoscopic replicas of heavy-fermion materials. We demonstrate that by changing a droplet’s real-space geometry, we can not only create coherently coupled Kondo droplets whose properties asymptotically approach those of a quantum-coherent Kondo lattice, but also markedly increase or decrease the droplet’s Kondo temperature. Furthermore we report on the discovery of a new quantum phenomenon – the Kondo echo – a signature of droplets containing Kondo holes functioning as direct probes of spatially extended, quantum-coherent Kondo cloud correlations.