A decade of intense research on two-dimensional (2D) atomic crystals has revealed that their properties can differ greatly from those of the parent compound. These differences are governed by changes in the band structure due to quantum confinement and are most profound if the underlying lattice symmetry changes. Here we report a high-quality 2D electron gas in few-layer InSe encapsulated in hexagonal boron nitride under an inert atmosphere. Carrier mobilities are found to exceed 10 cm V s and 10 cm V s at room and liquid-helium temperatures, respectively, allowing the observation of the fully developed quantum Hall effect. The conduction electrons occupy a single 2D subband and have a small effective mass. Photoluminescence spectroscopy reveals that the bandgap increases by more than 0.5 eV with decreasing the thickness from bulk to bilayer InSe. The band-edge optical response vanishes in monolayer InSe, which is attributed to the monolayer's mirror-plane symmetry. Encapsulated 2D InSe expands the family of graphene-like semiconductors and, in terms of quality, is competitive with atomically thin dichalcogenides and black phosphorus.

Topological materials may exhibit Hall-like currents flowing transversely to the applied electric field even in the absence of a magnetic field. In graphene superlattices, which have broken inversion symmetry, topological currents originating from graphene's two valleys are predicted to flow in opposite directions and combine to produce long-range charge neutral flow. We observed this effect as a nonlocal voltage at zero magnetic field in a narrow energy range near Dirac points at distances as large as several micrometers away from the nominal current path. Locally, topological currents are comparable in strength with the applied current, indicating large valley-Hall angles. The long-range character of topological currents and their transistor-like control by means of gate voltage can be exploited for information processing based on valley degrees of freedom.

Many layered materials can be cleaved down to individual atomic planes, similar to graphene, but only a small minority of them are stable under ambient conditions. The rest react and decompose in air, which has severely hindered their investigation and potential applications. Here we introduce a remedial approach based on cleavage, transfer, alignment, and encapsulation of air-sensitive crystals, all inside a controlled inert atmosphere. To illustrate the technology, we choose two archetypal two-dimensional crystals that are of intense scientific interest but are unstable in air: black phosphorus and niobium diselenide. Our field-effect devices made from their monolayers are conductive and fully stable under ambient conditions, which is in contrast to the counterparts processed in air. NbSe2 remains superconducting down to the monolayer thickness. Starting with a trilayer, phosphorene devices reach sufficiently high mobilities to exhibit Landau quantization. The approach offers a venue to significantly expand the range of experimentally accessible two-dimensional crystals and their heterostructures.

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.

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...