Graphene is a rapidly rising star on the horizon of materials science and condensed-matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality, and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena, some of which are unobservable in high-energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick, and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.

The rise of graphene

This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

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The electronic properties of 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 Schrodinger 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 Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) 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, graphene's 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 m(c) of massless carriers in graphene is described by E = m(c)c*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.

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Two-dimensional gas of massless Dirac fermions in graphene

Two-dimensional materials are attractive for use in next-generation nanoelectronic devices because, compared to one-dimensional materials, it is relatively easy to fabricate complex structures from them. The most widely studied two-dimensional material is graphene, both because of its rich physics and its high mobility. However, pristine graphene does not have a bandgap, a property that is essential for many applications, including transistors. Engineering a graphene bandgap increases fabrication complexity and either reduces mobilities to the level of strained silicon films or requires high voltages. Although single layers of MoS(2) have a large intrinsic bandgap of 1.8 eV (ref. 16), previously reported mobilities in the 0.5-3 cm(2) V(-1) s(-1) range are too low for practical devices. Here, we use a halfnium oxide gate dielectric to demonstrate a room-temperature single-layer MoS(2) mobility of at least 200 cm(2) V(-1) s(-1), similar to that of graphene nanoribbons, and demonstrate transistors with room-temperature current on/off ratios of 1 × 10(8) and ultralow standby power dissipation. Because monolayer MoS(2) has a direct bandgap, it can be used to construct interband tunnel FETs, which offer lower power consumption than classical transistors. Monolayer MoS(2) could also complement graphene in applications that require thin transparent semiconductors, such as optoelectronics and energy harvesting.

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Single-layer MoS2 transistors

We report the measurement of the thermal conductivity of a suspended single-layer graphene. The room temperature values of the thermal conductivity in the range ∼(4.84 ± 0.44) × 103 to (5.30 ± 0.48) × 103 W/mK were extracted for a single-layer graphene from the dependence of the Raman G peak frequency on the excitation laser power and independently measured G peak temperature coefficient. The extremely high value of the thermal conductivity suggests that graphene can outperform carbon nanotubes in heat conduction. The superb thermal conduction property of graphene is beneficial for the proposed electronic applications and establishes graphene as an excellent material for thermal management.

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Superior Thermal Conductivity of Single-Layer Graphene

We report on mesoscopic Hall sensors allowing accurate magnetization studies of submicron or nanometer-sized samples over a wide temperature range. Even at 300 K, the probes can reliably resolve local changes in dc field of ≈ 1 G with spatial resolution of ≈ 1 μm, which corresponds to a flux sensitivity of less than 0.1 ϕ0 (ϕ0=h/e is a flux quantum). The resolution increases 100 times at temperatures below 80 K. The capabilities of new micromagnetometers are demonstrated by measuring nm-scale movements of individual domain walls in a ferromagnet.

Metallic and Semiconductor Hall Microprobes for Wide Temperature Range Applications

Merged, or giant, multi-quanta vortices (GVs) appear in very small superconductors near the superconducting transition due to strong confinement of magnetic flux. Here we present evidence for a new, pinning-related, mechanism for vortex merger. Using Bitter decoration to visualise vortices in small Nb disks, we show that confinement in combination with strong disorder causes individual vortices to merge into clusters/GVs well below Tc and Hc2, in contrast to well-defined shells of individual vortices found in the absence of pinning.

https://iopscience.iop.org/article/10.1088/1742-6596/97/1/012172/pdf

Formation of vortex clusters and giant vortices in mesoscopic superconducting disks with strong disorder

Plateaux in the Hall effect have been observed in heavily doped n+-GaAs wires with a mobility as low as 015 m2/V s and widths of 200 nm and 800 nm The observed plateaux are strongly dependent on sample width and electron temperature The usual vanishing of the longitudinal resistance is not seen Pronounced plateaux are only observed in the 200 nm sample An explanation is suggested in terms of conduction along edge states In this picture the quantized Hall effect is observed if the mean free path of an electron traveling in an edge state, or the backscattering mean free path, well exceeds the Hall probe separation

The observation of Hall plateaux in diffusive quasi-two-dimensional wires of submicron size

Nanometer-scale movements of domain walls in uniaxial garnet films have been studied by means of micromagnetization measurements using miniature gold and semiconductor Hall probes. At helium temperatures the domain walls are found to move by discrete jumps, which we attribute to pinning on isolated defects, and we were able to measure local hysteresis loops associated with pinning on individual pinning centers. The temperature dependence of the coercive field of a single pinning center allowed us to evaluate the characteristic energy and characteristic volume of the pinning center.

Coercivity of single pinning center measured by hall micromagnetometry

Movements of individual domain walls in a ferromagnetic garnet were studied with angstrom resolution. The measurements reveal that domain walls can be locked between adjacent crystallographic planes and propagate by distinct steps matching the lattice periodicity.

https://iopscience.iop.org/article/10.1088/1742-6596/17/1/016/pdf

S. V. Dubonos

Papers

Metallic and Semiconductor Hall Microprobes for Wide Temperature Range Applications

Formation of vortex clusters and giant vortices in mesoscopic superconducting disks with strong disorder

The observation of Hall plateaux in diffusive quasi-two-dimensional wires of submicron size

Coercivity of single pinning center measured by hall micromagnetometry

Ferromagnetic domain wall on nanometer scale