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.

Gate dependent Raman spectroscopy of graphene on hexagonal boron nitride.

Raman spectroscopy, a fast and nondestructive imaging method, can be used to monitor the doping level in graphene devices. We fabricated chemical vapor deposition (CVD) grown graphene on atomically flat hexagonal boron nitride (hBN) flakes and SiO2 substrates. We compared their Raman response as a function of charge carrier density using an ion gel as a top gate. The G peak position, the 2D peak position, the 2D peak width and the ratio of the 2D peak area to the G peak area show a dependence on carrier density that differs for hBN compared to SiO2. Histograms of two-dimensional mapping are used to compare the fluctuations in the Raman peak properties between the two substrates. The hBN substrate has been found to produce fewer fluctuations at the same charge density owing to its atomically flat surface and reduced charged impurities.

Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure.

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 ± 5/3 filling and features associated with the Hofstadter butterfly at ultrahigh magnetic fields.

Thermal averages in a quantum point contact with a single coherent wave packet.

A novel formal equivalence between thermal averages of coherent properties (e.g., conductance) and time averages of a single wave packet arises for Fermi gases and certain geometries. In the case of one open channel in a quantum point contact (QPC), only one wave packet history, with the wave packet width equal to the thermal length, completely determines the thermally averaged conductance. The formal equivalence moreover allows very simple physical interpretations of interference features surviving under thermal averaging. Simply put, pieces of the thermal wave packet returning to the QPC along independent paths must arrive at the same time in order to interfere. Remarkably, one immediate result of this approach is that higher temperature leads to narrower wave packets and therefore better resolution of events in the time domain. In effect, experiments at 4.2 K are performing time-gated experiments at better than a gigahertz. Experiments involving thermally averaged ballistic conductance in 2DEGS are presented as an application of this picture.

Imaging electron interferometer.

An imaging interferometer was created in a two-dimensional electron gas by reflecting electron waves emitted from a quantum point contact with a circular mirror. Images of electron flow obtained with a scanning probe microscope at liquid He temperatures show interference fringes when the mirror is energized. A quantum phase shifter was created by moving the mirror via its gate voltage, and an interferometric spectrometer can be formed by sweeping the tip over many wavelengths. Experiments and theory demonstrate that the interference signal is robust against thermal averaging.

Electrical generation and absorption of phonons in carbon nanotubes.

The interplay between discrete vibrational and electronic degrees of freedom directly influences the chemical and physical properties of molecular systems. This coupling is typically studied through optical methods such as fluorescence, absorption and Raman spectroscopy. Molecular electronic devices provide new opportunities for exploring vibration-electronic interactions at the single molecule level. For example, electrons injected from a scanning tunnelling microscope tip into a metal can excite vibrational excitations of a molecule situated in the gap between tip and metal. Here we show how current directly injected into a freely suspended individual single-wall carbon nanotube can be used to excite, detect and control a specific vibrational mode of the molecule. Electrons tunnelling inelastically into the nanotube cause a non-equilibrium occupation of the radial breathing mode, leading to both stimulated emission and absorption of phonons by successive electron tunnelling events. We exploit this effect to measure a phonon lifetime of the order of 10 ns, corresponding to a quality factor of well over 10,000 for this nanomechanical oscillator.

Coherent branched flow in a two-dimensional electron gas.

Semiconductor nanostructures based on two-dimensional electron gases (2DEGs) could form the basis of future devices for sensing, information processing and quantum computation. Although electron transport in 2DEG nanostructures has been well studied, and many remarkable phenomena have already been discovered (for example, weak localization, quantum chaos, universal conductance fluctuations), fundamental aspects of the electron flow through these structures have so far not been clarified. However, it has recently become possible to image current directly through 2DEG devices using scanning probe microscope techniques. Here, we use such a technique to observe electron flow through a narrow constriction in a 2DEG-a quantum point contact. The images show that the electron flow from the point contact forms narrow, branching strands instead of smoothly spreading fans. Our theoretical study of this flow indicates that this branching of current flux is due to focusing of the electron paths by ripples in the background potential. The strands are decorated by interference fringes separated by half the Fermi wavelength, indicating the persistence of quantum mechanical phase coherence in the electron flow. These findings may have important implications for a better understanding of electron transport in 2DEGs and for the design of future nanostructure devices.