Geliang Yu

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, 2, 3, 4, 5, 6, 7, 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.

Commensurate-incommensurate transition in graphene on hexagonal boron nitride

When a crystal is subjected to a periodic potential, under certain circumstances it can adjust itself to follow the periodicity of the potential, resulting in a commensurate state. Of particular interest are topological defects between the two commensurate phases, such as solitons and domain walls. Here we report a commensurate-incommensurate transition for graphene on top of hexagonal boron nitride (hBN). Depending on the rotation angle between the lattices of the two crystals, graphene can either stretch to adapt to a slightly different hBN periodicity (for small angles, resulting in a commensurate state) or exhibit little adjustment (the incommensurate state). In the commensurate state, areas with matching lattice constants are separated by domain walls that accumulate the generated strain. Such soliton-like objects are not only of significant fundamental interest, but their presence could also explain recent experiments where electronic and optical properties of graphene-hBN heterostructures were observed to be considerably altered.

Detecting topological currents in graphene superlattices.

Making use of graphenes valleys Graphene has two distinct valleys in its electronic structure, in which the electrons have the same energy. Theorists have predicted that creating an asymmetry between the two valleys will coax graphene into exhibiting the so-called valley Hall effect (VHE). In this effect, electrons from the two valleys move across the sample in opposite directions when the experimenters run current along the sample. Gorbachev et al. achieved this asymmetry by aligning graphene with an underlying layer of hexagonalboron nitride (hBN) (see the Perspective by Lundeberg and Folk). The authors measured the transport characteristics of the sample, which were consistent with the theoretical predictions for the VHE. The method may in the future lead to information processing using graphenes valleys. Science, this issue p. 448; see also p. 422 Graphene is aligned with a layer of hexagonal boron nitride to achieve the valley Hall effect. [Also see Perspective by Lundeberg and Folk] 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.

Electronic Properties of Graphene Encapsulated with Different Two-Dimensional Atomic Crystals

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.

Quality Heterostructures from Two-Dimensional Crystals Unstable in Air by Their Assembly in Inert Atmosphere

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.

Interaction phenomena in graphene seen through quantum capacitance

Capacitance measurements provide a powerful means of probing the density of states. The technique has proved particularly successful in studying 2D electron systems, revealing a number of interesting many-body effects. Here, we use large-area high-quality graphene capacitors to study behavior of the density of states in this material in zero and high magnetic fields. Clear renormalization of the linear spectrum due to electron–electron interactions is observed in zero field. Quantizing fields lead to splitting of the spin- and valley-degenerate Landau levels into quartets separated by interaction-enhanced energy gaps. These many-body states exhibit negative compressibility but the compressibility returns to positive in ultrahigh B. The reentrant behavior is attributed to a competition between field-enhanced interactions and nascent fractional states.

Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices

Graphene on boron nitride gives rise to a moire superlattice displaying the Hofstadter butterfly: a fractal dependence of energy bands on external magnetic fields. Now, by means of capacitance spectroscopy, further aspects of this system are revealed—most notably, suppression of quantum Hall antiferromagnetism at particular commensurate magnetic fluxes.

Raman Fingerprint of Aligned Graphene/h-BN Superlattices

Graphene placed on hexagonal-boron nitride (h-BN) experiences a superlattice (Moiré) potential, which leads to a strong reconstruction of graphenes electronic spectrum with new Dirac points emerging at sub-eV energies. Here we study the effect of such superlattices on graphenes Raman spectrum. In particular, the 2D Raman peak is found to be exquisitely sensitive to the misalignment between graphene and h-BN lattices, probably due to the presence of a strain distribution with the same periodicity of the Moiré potential. This feature can be used to identify graphene superlattices with a misalignment angle smaller than 2°.

Edge currents shunt the insulating bulk in gapped graphene

An energy gap can be opened in the spectrum of graphene reaching values as large as 0.2 eV in the case of bilayers. However, such gaps rarely lead to the highly insulating state expected at low temperatures. This long-standing puzzle is usually explained by charge inhomogeneity. Here we revisit the issue by investigating proximity-induced superconductivity in gapped graphene and comparing normal-state measurements in the Hall bar and Corbino geometries. We find that the supercurrent at the charge neutrality point in gapped graphene propagates along narrow channels near the edges. This observation is corroborated by using the edgeless Corbino geometry in which case resistivity at the neutrality point increases exponentially with increasing the gap, as expected for an ordinary semiconductor. In contrast, resistivity in the Hall bar geometry saturates to values of about a few resistance quanta. We attribute the metallic-like edge conductance to a nontrivial topology of gapped Dirac spectra.

Quantum capacitance measurements of electron-hole asymmetry and next-nearest-neighbor hopping in graphene

the highest theoretical values. Here, we report dedicated measurements of the density of states in graphene by using high-quality capacitance devices. The density of states exhibits a pronounced electron-hole asymmetry that increases linearly with energy. This behavior yields t � ≈− 0.3 eV ±15%, in agreement with the high end of