Da Jiang

Two-Dimensional Gas of Massless Dirac Fermions in Graphene

Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrödinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Diracs (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective ‘speed of light’ c* ≈ 106 m s-1. Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphenes conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass mc of massless carriers in graphene is described by E = mcc*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.

Raman Spectrum of Graphene and Graphene Layers

Graphene is the two-dimensional (2d) building block for carbon allotropes of every other dimensionality. It can be stacked into 3d graphite, rolled into 1d nanotubes, or wrapped into 0d fullerenes. Its recent discovery in free state has finally provided the possibility to study experimentally its electronic and phonon properties. Here we show that graphenes electronic structure is uniquely captured in its Raman spectrum that clearly evolves with increasing number of layers. Raman fingerprints for single-, bi- and few-layer graphene reflect changes in the electronic structure and electron-phonon interactions and allow unambiguous, high-throughput, non-destructive identification of graphene layers, which is critically lacking in this emerging research area.

Two-dimensional atomic crystals

We report free-standing atomic crystals that are strictly 2D and can be viewed as individual atomic planes pulled out of bulk crystals or as unrolled single-wall nanotubes. By using micromechanical cleavage, we have prepared and studied a variety of 2D crystals including single layers of boron nitride, graphite, several dichalcogenides, and complex oxides. These atomically thin sheets (essentially gigantic 2D molecules unprotected from the immediate environment) are stable under ambient conditions, exhibit high crystal quality, and are continuous on a macroscopic scale.

Making graphene visible

Microfabrication of graphene devices used in many experimental studies currently relies on the fact that graphene crystallites can be visualized using optical microscopy if prepared on top of Si wafers with a certain thickness of SiO2. The authors study graphene’s visibility and show that it depends strongly on both thickness of SiO2 and light wavelength. They have found that by using monochromatic illumination, graphene can be isolated for any SiO2 thickness, albeit 300nm (the current standard) and, especially, ≈100nm are most suitable for its visual detection. By using a Fresnel-law-based model, they quantitatively describe the experimental data.

Graphene-Based Liquid Crystal Device

Graphene is only one atom thick, optically transparent, chemically inert, and an excellent conductor. These properties seem to make this material an excellent candidate for applications in various photonic devices that require conducting but transparent thin films. In this letter, we demonstrate liquid crystal devices with electrodes made of graphene that show excellent performance with a high contrast ratio. We also discuss the advantages of graphene compared to conventionally used metal oxides in terms of low resistivity, high transparency and chemical stability.

Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene

There are two known distinct types of the integer quantum Hall effect. One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems1,2, and the other is its relativistic counterpart observed in graphene, where charge carriers mimic Dirac fermions characterized by Berry’s phase π, which results in shifted positions of the Hall plateaus3,4,5,6,7,8,9. Here we report a third type of the integer quantum Hall effect. Charge carriers in bilayer graphene have a parabolic energy spectrum but are chiral and show Berry’s phase 2π affecting their quantum dynamics. The Landau quantization of these fermions results in plateaus in Hall conductivity at standard integer positions, but the last (zero-level) plateau is missing. The zero-level anomaly is accompanied by metallic conductivity in the limit of low concentrations and high magnetic fields, in stark contrast to the conventional, insulating behaviour in this regime. The revealed chiral fermions have no known analogues and present an intriguing case for quantum-mechanical studies.

Strong suppression of weak localization in graphene

Low-field magnetoresistance is ubiquitous in low-dimensional metallic systems with high resistivity and well understood as arising due to quantum interference on self-intersecting diffusive trajectories. We have found that in graphene this weak-localization magnetoresistance is strongly suppressed and, in some cases, completely absent. The unexpected observation is attributed to mesoscopic corrugations of graphene sheets which can cause a dephasing effect similar to that of a random magnetic field.

Macroscopic graphene membranes and their extraordinary stiffness.

The properties of suspended graphene are currently attracting enormous interest, but the small size of available samples and the difficulties in making them severely restrict the number of experimental techniques that can be used to study the optical, mechanical, electronic, thermal, and other characteristics of this one-atom-thick material. Here, we describe a new and highly reliable approach for making graphene membranes of a macroscopic size (currently up to 100 microm in diameter) and their characterization by transmission electron microscopy. In particular, we have found that long graphene beams supported by only one side do not scroll or fold, in striking contrast to the current perception of graphene as a supple thin fabric, but demonstrate sufficient stiffness to support extremely large loads, millions of times exceeding their own weight, in agreement with the presented theory. Our work opens many avenues for studying suspended graphene and using it in various micromechanical systems and electron microscopy.

Direct Growth of Graphene Film on Germanium Substrate

Graphene has been predicted to play a role in post-silicon electronics due to the extraordinary carrier mobility. Chemical vapor deposition of graphene on transition metals has been considered as a major step towards commercial realization of graphene. However, fabrication based on transition metals involves an inevitable transfer step which can be as complicated as the deposition of graphene itself. By ambient-pressure chemical vapor deposition, we demonstrate large-scale and uniform depositon of high-quality graphene directly on a Ge substrate which is wafer scale and has been considered to replace conventional Si for the next generation of high-performance metal-oxide-semiconductor field-effect transistors (MOSFETs). The immiscible Ge-C system under equilibrium conditions dictates graphene depositon on Ge via a self-limiting and surface-mediated process rather than a precipitation process as observed from other metals with high carbon solubility. Our technique is compatible with modern microelectronics technology thus allowing integration with high-volume production of complementary metal-oxide-semiconductors (CMOS).

Two-dimensional electron and hole gases at the surface of graphite

We report two-dimensional (2D) electron and hole gases induced at the surface of graphite by the electric field effect. The 2D gases reside within a few near-surface atomic layers and exhibit mobilities up to 15 000 and 60 000 cm(2)/V s at room and liquid-helium temperatures, respectively. The mobilities imply ballistic transport on mu m scale. Pronounced Shubnikov-de Haas oscillations reveal the existence of two types of charge carries in both electron and hole gases.