Strongly anisotropic media, where the principal components of the dielectric tensor have opposite signs, are called hyperbolic. Such materials exhibit unique nanophotonic properties enabled by the highly directional propagation of slow-light modes localized at deeply subdiffractional length scales. While artificial hyperbolic metamaterials have been demonstrated, they suffer from high plasmonic losses and require complex nanofabrication, which in turn induces size-dependent limitations on optical confinement. The low-loss, mid-infrared, natural hyperbolic material hexagonal boron nitride is an attractive alternative. Here we report on three-dimensionally confined 'hyperbolic polaritons' in boron nitride nanocones that support four series (up to the seventh order) modes in two spectral bands. The resonant modes obey the predicted aspect ratio dependence and exhibit high-quality factors (Q up to 283) in the strong confinement regime (up to l/86). These observations assert hexagonal boron nitride as a promising platform for studying novel regimes of light-matter interactions and nanophotonic device engineering.

When a crystal is subjected to a periodic potential, under certain circumstances (such as when the period of the potential is close to the crystal periodicity; the potential is strong enough, etc.) it might adjust itself to follow the periodicity of the potential, resulting in a, so called, commensurate state 1-3 .Such commensurate-incommensurate transitions are ubiquitous phenomena in many areas of condensed matter physics: from magnetism and dislocations in crystals, to vortices in superconductors, and atomic layers adsorbed on a crystalline surface 1 . Of particular interest might be the properties of topological defects between the two commensurate phases: solitons 2,4 , domain walls 1 , and dislocation walls 5-7 . Here we report a commensurate-incommensurate transition for graphene on top of hexagonal boron nitride (hBN) 8,9 . Depending on the rotational angle between the two hexagonal lattices, graphene can either stretch to adjust to a slightly different hBN periodicity (the commensurate state found for small rotational angles) or exhibit little adjustment (the incommensurate state). In the commensurate state, areas with matching lattice constants are separated by domain walls that accumulate the resulting strain. Such soliton-like objects present significant fundamental interest 1 , and their presence might explain recent observations when the electronic, optical, Raman and other properties of graphene-hBN heterostructures have been notably altered 10 .

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.