Eva Y. Andrei

Approaching ballistic transport in suspended graphene

The discovery of graphene raises the prospect of a new class of nanoelectronic devices based on the extraordinary physical properties of this one-atom-thick layer of carbon. Unlike two-dimensional electron layers in semiconductors, where the charge carriers become immobile at low densities, the carrier mobility in graphene can remain high, even when their density vanishes at the Dirac point. However, when the graphene sample is supported on an insulating substrate, potential fluctuations induce charge puddles that obscure the Dirac point physics. Here we show that the fluctuations are significantly reduced in suspended graphene samples and we report low-temperature mobility approaching 200,000 cm2 V-1 s-1 for carrier densities below 5 x 109 cm-2. Such values cannot be attained in semiconductors or non-suspended graphene. Moreover, unlike graphene samples supported by a substrate, the conductivity of suspended graphene at the Dirac point is strongly dependent on temperature and approaches ballistic values at liquid helium temperatures. At higher temperatures, above 100 K, we observe the onset of thermally induced long-range scattering.The recent discovery of methods to isolate graphene, a one-atom-thick layer of crystalline carbon, has raised the possibility of a new class of nano-electronics devices based on the extraordinary electrical transport and unusual physical properties of this material. However, the experimental realization of devices displaying these properties was, until now, hampered by the influence of the ambient environment, primarily the substrate. Here we report on the fabrication of Suspended Graphene devices and on studies of their electrical transport properties. In these devices, environmental disturbances were minimized allowing unprecedented access to the intrinsic properties of graphene close to the Dirac Point (DP) where the energy dispersion of the carriers and their density-of-states vanish linearly giving rise to a range of exotic physical properties. We show that charge inhomogeneity is reduced by almost one order of magnitude compared to that in Non-Suspended Graphene devices. Moreover, near the DP, the mobility exceeds 100,000 cm2/Vs, approaching theoretical predictions for evanescent transport in the ballistic model.

Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene.

In graphene, which is an atomic layer of crystalline carbon, two of the distinguishing properties of the material are the charge carriers’ two-dimensional and relativistic character. The first experimental evidence of the two-dimensional nature of graphene came from the observation of a sequence of plateaus in measurements of its transport properties in the presence of an applied magnetic field. These are signatures of the so-called integer quantum Hall effect. However, as a consequence of the relativistic character of the charge carriers, the integer quantum Hall effect observed in graphene is qualitatively different from its semiconductor analogue. As a third distinguishing feature of graphene, it has been conjectured that interactions and correlations should be important in this material, but surprisingly, evidence of collective behaviour in graphene is lacking. In particular, the quintessential collective quantum behaviour in two dimensions, the fractional quantum Hall effect (FQHE), has so far resisted observation in graphene despite intense efforts and theoretical predictions of its existence. Here we report the observation of the FQHE in graphene. Our observations are made possible by using suspended graphene devices probed by two-terminal charge transport measurements. This allows us to isolate the sample from substrate-induced perturbations that usually obscure the effects of interactions in this system and to avoid effects of finite geometry. At low carrier density, we find a field-induced transition to an insulator that competes with the FQHE, allowing its observation only in the highest quality samples. We believe that these results will open the door to the physics of FQHE and other collective behaviour in graphene.

Observation of Van Hove singularities in twisted graphene layers

When a Van Hove singularity exists near the Fermi energy of a solid’s density of states, it can cause a variety of exotic phenomena to emerge. Scanning tunnelling microscope measurements indicate that when graphite’s graphene sheets are rotated out of their usual alignment, it can generate low-energy Van Hove singularities for which the position is controlled by the angle of rotation.

Single-Layer Behavior and Its Breakdown in Twisted Graphene Layers

We report high magnetic field scanning tunneling microscopy and Landau level spectroscopy of twisted graphene layers grown by chemical vapor deposition. For twist angles exceeding ~3° the low energy carriers exhibit Landau level spectra characteristic of massless Dirac fermions. Above 20° the layers effectively decouple and the electronic properties are indistinguishable from those in single-layer graphene, while for smaller angles we observe a slowdown of the carrier velocity which is strongly angle dependent. At the smallest angles the spectra are dominated by twist-induced van Hove singularities and the Dirac fermions eventually become localized. An unexpected electron-hole asymmetry is observed which is substantially larger than the asymmetry in either single or untwisted bilayer graphene.

Scanning tunneling spectroscopy of graphene on graphite.

We report low temperature high magnetic field scanning tunneling microscopy and spectroscopy of graphene flakes on graphite that exhibit the structural and electronic properties of graphene decoupled from the substrate. Pronounced peaks in the tunneling spectra develop with increasing field revealing a Landau level sequence that provides a direct way to identify graphene and to determine the degree of its coupling to the substrate. The Fermi velocity and quasiparticle lifetime, obtained from the positions and width of the peaks, provide access to the electron-phonon and electron-electron interactions.

Observation of Landau levels of Dirac fermions in graphite

The unique electronic behaviour of monolayer and bilayer graphene1,2 is a result of the unusual quantum-relativistic characteristics of the so-called ‘Dirac fermions’ (DFs) that carry charge in these materials. Although DFs in monolayer graphene move as if they were massless, and in bilayer graphene they do so with non-zero mass, all DFs show chirality, which gives rise to an unusual Landau level (LL) energy spectrum3,4,5,6,7,8,9,10,11 and the observation of an anomalous quantum Hall effect in both types of graphene4,5,8. Here we report low-temperature scanning tunnelling spectra of graphite subjected to a magnetic field of up to 12 T, which provide the first direct observations of the LLs that produce such behaviour. Unexpectedly, we find evidence for the coexistence of both massless and massive DFs in graphite, and confirm the quantum-relativistic nature of these quasiparticles through the appearance of a zero-energy LL.

Electronic properties of graphene: a perspective from scanning tunneling microscopy and magnetotransport

This review covers recent experimental progress in probing the electronic properties of graphene and how they are influenced by various substrates, by the presence of a magnetic field and by the proximity to a superconductor. The focus is on results obtained using scanning tunneling microscopy, spectroscopy, transport and magnetotransport techniques.

Josephson current and multiple Andreev reflections in graphene SNS junctions

The Josephson effect and superconducting proximity effect were observed in superconductor-graphene-superconductor (SGS) Josephson junctions with coherence lengths comparable to the distance between the superconducting leads. By comparing the measured gate dependence of the proximity induced subgap features (multiple Andreev reflections) and of the supercurrent to theoretical predictions, we find that the diffusive junction model yields close quantitative agreement with the results. By contrast, predictions of the ballistic SGS model are inconsistent with the data. We show that all SGS devices reported so far, our own as well as those of other groups, fall in the diffusive junction category. This is attributed to substrate induced potential fluctuations due to trapped charges and to the invasiveness of the metallic leads.

Instabilities and disorder-driven first-order transition of the vortex lattice

Transport studies in a Corbino disk suggest that the Bragg glass phase undergoes a first-order transition into a disordered solid. This transition shows sharp reentrant behavior at low fields. In contrast, in the conventional strip configuration, the phase transition is obscured by the injection of the disordered vortices through the sample edges, which results in the commonly observed vortex instabilities and smearing of the peak effect in NbSe2 crystals. These features are found to be absent in the Corbino geometry in which the circulating vortices do not cross the sample edges.

Bandgap, mid-gap states, and gating effects in MoS2.

The discovery of graphene has put the spotlight on other layered materials including transition metal dichalcogenites (TMD) as building blocks for novel heterostructures assembled from stacked atomic layers. Molybdenum disulfide, MoS2, a semiconductor in the TMD family, with its remarkable thermal and chemical stability and high mobility, has emerged as a promising candidate for postsilicon applications such as switching, photonics, and flexible electronics. Because these rely on controlling the position of the Fermi energy (EF), it is crucial to understand its dependence on doping and gating. To elucidate these questions we carried out gated scanning tunneling microscopy (STM) and spectroscopy (STS) measurements and compared them with transport measurements in a field effect transistor (FET) device configuration. This made it possible to measure the bandgap and the position of EF in MoS2 and to track its evolution with gate voltage. For bulk samples, the measured bandgap (∼ 1.3 eV) is comparable to the value obtained by photoluminescence, and the position of EF (∼ 0.35 eV) below the conduction band, is consistent with N-doping reported in this material. We show that the N-doping in bulk samples can be attributed to S vacancies. In contrast, the significantly higher N-doping observed in thin MoS2 films deposited on SiO2 is dominated by charge traps at the sample-substrate interface.The discovery of graphene has put the spotlight on other layered materials including transition metal dichalcogenites (TMD) as building blocks for novel heterostructures assembled from stacked atomic layers. Molybdenum disulfide, MoS2, a semiconductor in the TMD family, with its remarkable thermal and chemical stability and high mobility, has emerged as a promising candidate for post-silicon applications such as switching, photonics, and flexible electronics. Since these rely on controlling the position of the Fermi energy (EF), it is crucial to understand its dependence on doping and gating. Here we employed scanning tunneling microscopy (STM) and spectroscopy (STS) with gating capabilities to measure the bandgap and the position of EF in MoS2, and to track its evolution with gate voltage. For bulk samples, the measured bandgap (~1.3eV) is comparable to the value obtained by photoluminescence, and the position of EF (~0.35eV) below the conduction band, is consistent with n-doping reported in this material. Using topography together with spectroscopy we traced the source of the n-doping in bulk MoS2 samples to point defects, which we attribute to S vacancies. In contrast, for thin films deposited on SiO2, we found significantly higher levels of n-doping that cannot be attributed to S vacancies. By combining gated STS with transport measurements in a field effect transistor (FET) configuration, we demonstrate that the higher levels of n-doping in thin film samples is due to charge traps at the sample-substrate interface.