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

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

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

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.

Beyond the extensively studied microcavity polaritons, which are coupled modes of semiconductor excitons and microcavity photons, nearly 2D semiconductors placed in a suitable environment can support spatially localized exciton–polariton modes. We demonstrate theoretically that two distinct types of such modes can exist in a photonic crystal with an embedded transition metal dichalcogenide (TMD) monolayer and derive an equation that determines their dispersion relations. The localized modes of two types occur in the zeroth- and first-order stop bands of the crystal and have substantially different properties. The latter type of localized modes, which appear inside the light cone, can be described as a result of coupling of the TMD exciton and an optical Tamm state of the TMD-intercalated photonic crystal. We suggest an experiment for detecting these modes and simulate it numerically.

Localized polariton states in a photonic crystal intercalated by a transition metal dichalcogenide monolayer

Transmission of plane electromagnetic wave through a tiny slit in a metal film covered by monolayer graphene is considered using a semi-analytical approach. We show that it gives rise to the diffraction accompanied by the excitation of standing waves of surface plasmon-polaritons in graphene, localized over the slit. These modes manifest themselves by characteristic peaks in the calculated absorption spectra in the THz range. It is shown that their spectral position depends on the refractive index of the material filling the slit and also can be tuned by the graphene doping level. Additionally, we clarify the physical nature of a low-frequency absorption band, which originates from the lowest order waveguide-type mode of the bare slit.

Surface-Plasmon-Polariton-Assisted Diffraction of THz Waves on a Graphene-Covered Slit

A polarimetric technique developed for phase retardation measurements of birefringent crystal plates for any visible wavelength is described. The basic characteristics of the present method are demonstrated by using the Poincare sphere representation. The incident linearly polarized light beam is modulated by a rotating slightly birefringent crystal plate; a linear analyser is adjusted until the amplitude of the doubled frequency component of the output electric signal issued from the photomultiplier vanishes; the same compensator plate is used for the measurements, whatever the visible wavelength.

http://iopscience.iop.org/article/10.1088/0022-3727/27/6/007/pdf

Method for phase retardation measurements in birefringent anisotropic crystal plates

We study the integer and fractional quantum Hall effect on a honeycomb lattice at half-filling (graphene) in the presence of disorder and electron-electron interactions. We show that the interactions between the delocalized chiral edge states (generated by the magnetic field) and Anderson-localized surface states (created by the presence of zig-zag edges) lead to edge reconstruction. As a consequence, the point contact tunneling on a graphene edge has a non-universal tunneling exponent, and the Hall conductivity is not perfectly quantized in units of e^2/h. We argue that the magneto-transport properties of graphene depend strongly on the strength of electron-electron interactions, the amount of disorder, and the details of the edges.

Quantum Hall Effect in Graphene

We revisit the classical problem of electromagnetic wave refraction from a lossless dielectric to a lossy conductor, where both media are considered to be non-magnetic, linear, isotropic and homogeneous We derive the Fresnel coefficients of the system and the Poynting vectors at the interface, in order to compute the reflectance and transmittance of the system We use a particular parametrisation of the referred Fresnel coefficients so as to make a connection with the ones obtained for refraction by an interface between two lossless media This analysis allows the discussion of an actual application, namely the Fresnel polarisation of infra-red radiation by elemental bismuth, based on the concept of pseudo Brewster's angle

Nuno M. R. Peres

Papers

Localized polariton states in a photonic crystal intercalated by a transition metal dichalcogenide monolayer

Surface-Plasmon-Polariton-Assisted Diffraction of THz Waves on a Graphene-Covered Slit

Method for phase retardation measurements in birefringent anisotropic crystal plates

Quantum Hall Effect in Graphene

Fresnel polarisation of infra-red radiation by elemental bismuth