Matthew Yankowitz

Massive Dirac Fermions and Hofstadter Butterfly in a van der Waals Heterostructure

Graphene, Gapped and Butterflied The remarkable transport properties of graphene, such as the high electron mobility, make it a promising material for electronics. However, unlike semiconductors such as silicon, graphenes electronic structure lacks a band gap, and a transistor made out of graphene would not have an “off” state. Hunt et al. (p. 1427, published online 16 May; see the Perspective by Fuhrer) modulated the electronic properties of graphene by building a heterostructure consisting of a graphene flake resting on hexagonal boron nitride (hBN), which has the same honeycomb structure as graphene, but consists of alternating boron and nitrogen atoms instead of carbons. The natural mismatch between the graphene and hBN lattices led to a moire pattern with a large wavelength, causing the opening of a band gap, the formation of an elusive fractional quantum Hall state, and, at high magnetic fields, a fractal phenomenon in the electronic structure called the Hofstadter butterfly. A band gap is observed in a monolayer graphene–hexagonal boron nitride heterostructure. [Also see Perspective by Fuhrer] van der Waals heterostructures constitute a new class of artificial materials formed by stacking atomically thin planar crystals. We demonstrated band structure engineering in a van der Waals heterostructure composed of a monolayer graphene flake coupled to a rotationally aligned hexagonal boron nitride substrate. The spatially varying interlayer atomic registry results in both a local breaking of the carbon sublattice symmetry and a long-range moiré superlattice potential in the graphene. In our samples, this interplay between short- and long-wavelength effects resulted in a band structure described by isolated superlattice minibands and an unexpectedly large band gap at charge neutrality. This picture is confirmed by our observation of fractional quantum Hall states at ±53 filling and features associated with the Hofstadter butterfly at ultrahigh magnetic fields.

Emergence of superlattice Dirac points in graphene on hexagonal boron nitride

It is well known that graphene deposited on hexagonal boron nitride produces moire patterns in scanning tunnelling microscopy images. The interaction that produces this pattern also produces a commensurate periodic potential that generates a set of Dirac points that are different from those of the graphene lattice itself.

Graphene on hexagonal boron nitride.

The field of graphene research has developed rapidly since its first isolation by mechanical exfoliation in 2004. Due to the relativistic Dirac nature of its charge carriers, graphene is both a promising material for next-generation electronic devices and a convenient low-energy testbed for intrinsically high-energy physical phenomena. Both of these research branches require the facile fabrication of clean graphene devices so as not to obscure its intrinsic physical properties. Hexagonal boron nitride has emerged as a promising substrate for graphene devices as it is insulating, atomically flat and provides a clean charge environment for the graphene. Additionally, the interaction between graphene and boron nitride provides a path for the study of new physical phenomena not present in bare graphene devices. This review focuses on recent advancements in the study of graphene on hexagonal boron nitride devices from the perspective of scanning tunneling microscopy with highlights of some important results from electrical transport measurements.

Tunneling spectroscopy of graphene-boron-nitride heterostructures

We report on the fabrication and measurement of a graphene tunnel junction using hexagonal-boron nitride as a tunnel barrier between graphene and a metal gate. The tunneling behavior into graphene is altered by the interactions with phonons and the presence of disorder. We extract prop- erties of graphene and observe multiple phonon-enhanced tunneling thresholds. Finally, differences in the measured properties of two devices are used to shed light on mutually-contrasting previous results of scanning tunneling microscopy in graphene.

van der Waals Heterostructures with High Accuracy Rotational Alignment

We describe the realization of van der Waals (vdW) heterostructures with accurate rotational alignment of individual layer crystal axes. We illustrate the approach by demonstrating a Bernal-stacked bilayer graphene formed using successive transfers of monolayer graphene flakes. The Raman spectra of this artificial bilayer graphene possess a wide 2D band, which is best fit by four Lorentzians, consistent with Bernal stacking. Scanning tunneling microscopy reveals no moiré pattern on the artificial bilayer graphene, and tunneling spectroscopy as a function of gate voltage reveals a constant density of states, also in agreement with Bernal stacking. In addition, electron transport probed in dual-gated samples reveals a band gap opening as a function of transverse electric field. To illustrate the applicability of this technique to realize vdW heterostructuctures in which the functionality is critically dependent on rotational alignment, we demonstrate resonant tunneling double bilayer graphene heterostructures separated by hexagonal boron-nitride dielectric.

Electric field control of soliton motion and stacking in trilayer graphene

The crystal structure of a material plays an important role in determining its electronic properties. Changing from one crystal structure to another involves a phase transition that is usually controlled by a state variable such as temperature or pressure. In the case of trilayer graphene, there are two common stacking configurations (Bernal and rhombohedral) that exhibit very different electronic properties. In graphene flakes with both stacking configurations, the region between them consists of a localized strain soliton where the carbon atoms of one graphene layer shift by the carbon-carbon bond distance. Here we show the ability to move this strain soliton with a perpendicular electric field and hence control the stacking configuration of trilayer graphene with only an external voltage. Moreover, we find that the free-energy difference between the two stacking configurations scales quadratically with electric field, and thus rhombohedral stacking is favoured as the electric field increases. This ability to control the stacking order in graphene opens the way to new devices that combine structural and electrical properties.

Intrinsic disorder in graphene on transition metal dichalcogenide heterostructures

Semiconducting transition metal dichalchogenides (TMDs) are a family of van der Waals bonded materials that have recently received interest as alternative substrates to hexagonal boron nitride (hBN) for graphene, as well as for components in novel graphene-based device heterostructures. We elucidate the local structural and electronic properties of graphene on TMD heterostructures through scanning tunneling microscopy and spectroscopy measurements. We find that crystalline defects intrinsic to TMDs induce substantial electronic scattering and charge carrier density fluctuations in the graphene. These signatures of local disorder explain the significant degradation of graphene device mobilities using TMD substrates, particularly compared to similar graphene on hBN devices.

Local spectroscopy of the electrically tunable band gap in trilayer graphene

The stacking order degree of freedom in trilayer graphene plays a critical role in determining the existence of an electric field tunable band gap. We present spatially-resolved tunneling spectroscopy measurements of dual gated Bernal (ABA) and rhombohedral (ABC) stacked trilayer graphene devices. We demonstrate that while ABA trilayer graphene remains metallic, ABC trilayer graphene exhibits a widely tunable band gap as a function of electric field. However, we find that charged impurities in the underlying substrate cause substantial spatial fluctuation of the gap size. Our work elucidates the microscopic behavior of trilayer graphene and its consequences for macroscopic devices.

Pressure-induced commensurate stacking of graphene on boron nitride

Combining atomically-thin van der Waals materials into heterostructures provides a powerful path towards the creation of designer electronic devices. The interaction strength between neighbouring layers, most easily controlled through their interlayer separation, can have significant influence on the electronic properties of these composite materials. Here, we demonstrate unprecedented control over interlayer interactions by locally modifying the interlayer separation between graphene and boron nitride, which we achieve by applying pressure with a scanning tunnelling microscopy tip. For the special case of aligned or nearly-aligned graphene on boron nitride, the graphene lattice can stretch and compress locally to compensate for the slight lattice mismatch between the two materials. We find that modifying the interlayer separation directly tunes the lattice strain and induces commensurate stacking underneath the tip. Our results motivate future studies tailoring the electronic properties of van der Waals heterostructures by controlling the interlayer separation of the entire device using hydrostatic pressure.

Local Spectroscopic Characterization of Spin and Layer Polarization in WSe_{2}.

We report scanning tunneling microscopy and scanning tunneling spectroscopy (STS) measurements of monolayer and bilayer WSe_{2}. We measure a band gap of 2.21±0.08  eV in monolayer WSe_{2}, which is much larger than the energy of the photoluminescence peak, indicating a large excitonic binding energy. We additionally observe significant electronic scattering arising from atomic-scale defects. Using Fourier transform STS, we map the energy versus momentum dispersion relations for monolayer and bilayer WSe_{2}. Further, by tracking allowed and forbidden scattering channels as a function of energy we infer the spin texture of both the conduction and valence bands. We observe a large spin-splitting of the valence band due to strong spin-orbit coupling, and additionally observe spin-valley-layer coupling in the conduction band of bilayer WSe_{2}.