Cloning of Dirac fermions in graphene superlattices.

Superlattices have attracted great interest because their use may make it possible to modify the spectra of two-dimensional electron systems and, ultimately, create materials with tailored electronic properties. In previous studies (see, for example, refs 1-8), it proved difficult to realize superlattices with short periodicities and weak disorder, and most of their observed features could be explained in terms of cyclotron orbits commensurate with the superlattice. Evidence for the formation of superlattice minibands (forming a fractal spectrum known as Hofstadter's butterfly) has been limited to the observation of new low-field oscillations and an internal structure within Landau levels. Here we report transport properties of graphene placed on a boron nitride substrate and accurately aligned along its crystallographic directions. The substrate's moiré potential acts as a superlattice and leads to profound changes in the graphene's electronic spectrum. Second-generation Dirac points appear as pronounced peaks in resistivity, accompanied by reversal of the Hall effect. The latter indicates that the effective sign of the charge carriers changes within graphene's conduction and valence bands. Strong magnetic fields lead to Zak-type cloning of the third generation of Dirac points, which are observed as numerous neutrality points in fields where a unit fraction of the flux quantum pierces the superlattice unit cell. Graphene superlattices such as this one provide a way of studying the rich physics expected in incommensurable quantum systems and illustrate the possibility of controllably modifying the electronic spectra of two-dimensional atomic crystals by varying their crystallographic alignment within van der Waals heterostuctures.

Signatures of van Hove Singularities Probed by the Supercurrent in a Graphene-hBN Superlattice.

The band structure of graphene can be strongly modified if its lattice is aligned with the one of a boron nitride substrate. A moiré superlattice forms, which manifests itself by the appearance of new Dirac points, accompanied by van Hove singularities. In this work, we present supercurrent measurements in a Josephson junction made from such a graphene superlattice in the long and diffusive transport regime, where the critical current depends on the Thouless energy. We can then estimate the specific density of states of the graphene superlattice from the combined measurement of the critical current and the normal state resistance. The result matches with theoretical predictions and highlights the strong increase of the density of states at the van Hove singularities. By measuring the magnetic field dependence of the critical current, we find the presence of edge currents at these singularities. We explain it by the reduction of the Fermi velocity associated with the van Hove singularity, which suppresses the supercurrent in the bulk while the electrons at the edges remain less localized, resulting in an edge supercurrent. We attribute these different behaviors of the edges to defects or chemical doping.

Tuning the valley and chiral quantum state of Dirac electrons in van der Waals heterostructures.

Chirality is a fundamental property of electrons with the relativistic spectrum found in graphene and topological insulators. It plays a crucial role in relativistic phenomena, such as Klein tunneling, but it is difficult to visualize directly. Here, we report the direct observation and manipulation of chirality and pseudospin polarization in the tunneling of electrons between two almost perfectly aligned graphene crystals. We use a strong in-plane magnetic field as a tool to resolve the contributions of the chiral electronic states that have a phase difference between the two components of their vector wave function. Our experiments not only shed light on chirality, but also demonstrate a technique for preparing graphene's Dirac electrons in a particular quantum chiral state in a selected valley.

Twist-controlled resonant tunnelling in graphene/boron nitride/graphene heterostructures.

Recent developments in the technology of van der Waals heterostructures made from two-dimensional atomic crystals have already led to the observation of new physical phenomena, such as the metal-insulator transition and Coulomb drag, and to the realization of functional devices, such as tunnel diodes, tunnel transistors and photovoltaic sensors. An unprecedented degree of control of the electronic properties is available not only by means of the selection of materials in the stack, but also through the additional fine-tuning achievable by adjusting the built-in strain and relative orientation of the component layers. Here we demonstrate how careful alignment of the crystallographic orientation of two graphene electrodes separated by a layer of hexagonal boron nitride in a transistor device can achieve resonant tunnelling with conservation of electron energy, momentum and, potentially, chirality. We show how the resonance peak and negative differential conductance in the device characteristics induce a tunable radiofrequency oscillatory current that has potential for future high-frequency technology.