Hexagonal boron nitride is the only substrate that has so far allowed graphene devices exhibiting micrometer-scale ballistic transport. Can other atomically flat crystals be used as substrates for making quality graphene heterostructures? Here we report on our search for alternative substrates. The devices fabricated by encapsulating graphene with molybdenum or tungsten disulfides and hBN are found to exhibit consistently high carrier mobilities of about 60 000 cm(2) V(-1) s(-1). In contrast, encapsulation with atomically flat layered oxides such as mica, bismuth strontium calcium copper oxide, and vanadium pentoxide results in exceptionally low quality of graphene devices with mobilities of ∼1000 cm(2) V(-1) s(-1). We attribute the difference mainly to self-cleansing that takes place at interfaces between graphene, hBN, and transition metal dichalcogenides. Surface contamination assembles into large pockets allowing the rest of the interface to become atomically clean. The cleansing process does not occur for graphene on atomically flat oxide substrates.

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.

In graphene placed on hexagonal boron nitride, replicas of the original Dirac spectrum appear near edges of superlattice minibands. More such replicas develop in high magnetic fields, and their quantization gives rise to a fractal pattern of Landau levels, referred to as the Hofstadter butterfly. Some evidence for the butterfly has recently been reported by using transport measurements. Here we employ capacitance spectroscopy to probe directly the density of states and energy gaps in graphene superlattices. Without magnetic field, replica spectra are seen as pronounced minima in the density of states surrounded by van Hove singularities. The Hofstadter butterfly shows up in magnetocapacitance clearer than in transport measurements and, near one flux quantum per superlattice unit cell, we observe Landau fan diagrams related to quantization of Dirac replicas in a reduced magnetic field. Electron-electron interaction strongly modifies the superlattice spectrum. In particular, we find that graphene's quantum Hall ferromagnetism, due to lifted spin and valley degeneracies, exhibits a reverse Stoner transition at commensurable fluxes and that Landau levels of Dirac replicas support their own ferromagnetic states.2 When graphene is placed on top of atomically flat hexagonal boron nitride (hBN) and their crystallographic axes are carefully aligned, graphene's electron transport properties become strongly modified by a hexagonal periodic potential induced by the hBN substrate [1][2][3][4][5][6] . Replicas of the main Dirac spectrum appear [7][8][9][10][11][12] at the edges of superlattice Brillouin zones (SBZ) and, for the lowest SBZs, the second-generation Dirac cones can be reached using electric field doping [4][5][6] . Because the superlattice period, , for aligned graphene-hBN structures is relatively large (15 nm), magnetic fields B 10 T are sufficient to provide a magnetic flux  of about one flux quantum  0 per area A = √3 2 /2 of the superlattice unit cell. The commensurability between  and the magnetic length l B gives rise to a fractal energy spectrum, the Hofstadter butterfly [4][5][6][13][14][15][16][17][18][19] . An informative way to understand its structure is to consider the butterfly as a collection of Landau levels (LLs) that originate from numerous mini-replicas of the original spectrum, which appear at all rational flux values  = 0 (p/q) where p and q are integer 4,12 . At these fluxes, the electronic spectrum can be described [12][13][14][15] in terms of Zak's minibands 14 for an extended superlattice with a unit cell q times larger than the original one. In graphene, Zak's minibands are expected to be gapped cones (thirdgeneration Dirac fermions) 12 . Away from the rational flux values, these Dirac replicas experience Landau quantization in an effective field B eff =B -B p/q where B p/q = 0 (p/q)/A.In this work, we have employed capacitance measurements to examine the electronic spectrum of graphene superlattices and its evolution into the Hofstadter butterfly. In zero B, pronounced minima...

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.

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