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

We measured the elastic properties and intrinsic breaking strength of free-standing monolayer graphene membranes by nanoindentation in an atomic force microscope. The force-displacement behavior is interpreted within a framework of nonlinear elastic stress-strain response, and yields second- and third-order elastic stiffnesses of 340 newtons per meter (N m(-1)) and -690 Nm(-1), respectively. The breaking strength is 42 N m(-1) and represents the intrinsic strength of a defect-free sheet. These quantities correspond to a Young's modulus of E = 1.0 terapascals, third-order elastic stiffness of D = -2.0 terapascals, and intrinsic strength of sigma(int) = 130 gigapascals for bulk graphite. These experiments establish graphene as the strongest material ever measured, and show that atomically perfect nanoscale materials can be mechanically tested to deformations well beyond the linear regime.

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Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene

Single-layer metal dichalcogenides are two-dimensional semiconductors that present strong potential for electronic and sensing applications complementary to that of graphene.

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Electronics and optoelectronics of two-dimensional transition metal dichalcogenides.

Two-dimensional materials have been discovered to exhibit non-volatile resistive switching (NVRS) phenomenon. In our work, we reported the universal NVRS behavior in a dozen metal dichalcogenides, featuring low switching voltage, large on/off ratio, fast switching speed and forming free characteristics. A unique conductive-point random access memory (CPRAM) effect is used to explain the switching mechanisms, supported by experimental results from current-sweep measurements.

Universal Non-Volatile Resistive Switching Behavior in 2D Metal Dichalcogenides Featuring Unique Conductive-Point Random Access Memory Effect

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Large area THz imaging of electrically controlled graphene conductance

MoS 2 nanoribbons have attracted increased interest due to their properties which can be tailored by tuning their dimensions. Herein, we demonstrate the growth of quasi-one-dimensional (1D) MoS 2 nanoribbons and 3D triangular crystals formed by the reaction between ultra-thin films of MoO 3 grown by Pulsed Laser Deposition and

Quasi 1D MoS 2 Nanoribbons with Enhanced Edge Nonlinear Response and Photoresponsivity

MoS2 nanoribbons have attracted an increased interest due to their properties, which can be tailored by tuning their dimensions. Herein, we demonstrate the growth of MoS2 nanoribbons and 3D triangular crystals formed by the reaction between ultra-thin films of MoO3 grown by Pulsed Laser Deposition and NaF in a sulfur-rich environment. The multilayer nanoribbons can reach up to 10 μm in length, and feature single-layer edges, forming a monolayer-multilayer MoS2 junction enabled by the lateral modulation in thickness. The single-layer edges of the nanoribbons show a pronounced second harmonic generation due to the symmetry breaking, in contrast to the centrosymmetric multilayer structure, which is unsusceptible to the second-order nonlinear process. A pronounced splitting of the Raman spectra was observed in MoS2 nanoribbons arising from distinct contributions from the monolayer edges and multilayer core. Nanoscale imaging reveals a blue-shifted exciton emission of the monolayer edge compared to the triangular MoS2 monolayers due to built-in local strain and disorder. We further report on an ultrasensitive photodetector made of a single MoS2 nanoribbon with a responsivity of 8.72×102 A/W at 532 nm, among the highest reported up-to-date for single-nanoribbon photodetectors. Our findings can inspire the design of MoS2 semiconductors with tunable geometries for efficient optoelectronic devices. This article is protected by copyright. All rights reserved.

https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/adma.202302469

Molybdenum Disulfide Nanoribbons with Enhanced Edge Nonlinear Response and Photoresponsivity.

Cathodoluminescence spectroscopy in conjunction with second-order auto-correlation measurements of $g_2(\tau)$ allows to extensively study the synchronization of quantum light sources in low-dimensional structures. Co-existing excitons in two-dimensional transition metal dichalcogenide monolayers provide a great source of identical quantum emitters which can be simultaneously excited by an electron. In this article, we demonstrate large photon bunching with $g_2(0)$ up to $156\pm16$ of a tungsten disulfide monolayer, exhibiting a strong dependence on the electron-beam current density. To further improve the excitation synchronization and the electron-emitter interaction, we show exemplary that the careful selection of a simple and compact geometry -- a thin, monocrystalline gold nanodisk -- can be used to realize a record-high bunching $g_2(0)$ of up to $2152\pm236$. This approach to control the electron excitation of excitons in a \ce{WS2} monolayer allows for the synchronization of quantum emitters in an ensemble, which is important to further advance quantum information processing and computing technologies.

Timothy J. Booth

Papers

Universal Non-Volatile Resistive Switching Behavior in 2D Metal Dichalcogenides Featuring Unique Conductive-Point Random Access Memory Effect

Large area THz imaging of electrically controlled graphene conductance

Quasi 1D MoS 2 Nanoribbons with Enhanced Edge Nonlinear Response and Photoresponsivity

Molybdenum Disulfide Nanoribbons with Enhanced Edge Nonlinear Response and Photoresponsivity.

Brobdingnagian photon bunching in cathodoluminescence of excitons in WS$_2$ monolayer.