Wafer scale graphene transfer kim et al nature 2010 mechanical peeling off in water support graphene nior cusio 2 ni or cu sio 2 rapid etching with fecl 3 aq graphene on polymer support graphene on arbitrary substrate transfer patterning patterned graphene on ni patterned graphene on arbtirary substrate postpatterning prepatterning. Recently there obviously was observed experimental support of the klein paradox. Pdf the socalled klein paradoxunimpeded penetration of relativistic particles through high and wide. Graphene a new form of carbon with scientific impact and. Klein tunneling in quantum mechanics, an electron can tunnel from the conduction into the valence band. Wafer scale graphene transfer kim et al nature 2010 mechanical peeling off in water supportgraphene nior cusio 2 ni or cu sio 2 rapid etching with fecl 3 aq graphene on polymer support graphene on arbitrary substrate transfer patterning patterned graphene on ni patterned graphene on arbtirary substrate postpatterning prepatterning. This book is a comprehensive guide to graphene technology, industry and market. Elementary electronic properties of graphene 112 a.
The freedom of motion associated with the klein paradox creates a problem. Teach yourself c pdf by herbert schildt download scityninin. Chiral tunnelling and the klein paradox in graphene core. The massless dirac equation in the refrigerator springerlink. An overview of the material, devices, and applications by yaw obeng and purushothaman srinivasan novoselov, and coworkers were among the first to successfully obtain the elusive freestanding graphene films,4 which was a remarkable achievement. Klein tunnelling and the klein paradox international.
The klein paradox short history scattering from potential step bosons and fermions resolution with pair production in and outstates conclusion finn ravndal, dept of physics, uio gausdal, 41 2011. Chiral tunneling and the klein paradox in graphene. The traditional term, as before, does not forbid klein phenomena. Graphene is the worlds strongest and most conductive 2d material that is set to revolutionize entire industries.
Graphene is a rapidly rising star on the horizon of materials science and condensed. The renewed interest in graphene1 and the close analogy of its band structure to the spectrum of the zero mass dirac equation suggests that a reexamination of several aspects of the one dimensional dirac equation should be carried out. Klein tunnelling is a property of relativistic wave equations, not necessarily connected with particle emission. Topics covered include berry phase, topologically protected zero modes, klein tunneling, vacuum reconstruction near supercritical charges, and deformationinduced gauge fields. The deltafunction part contains a nonvanishing positron amplitude. The phenomenon is discussed in many contexts in particle, nuclear and astro physics but direct tests of the klein paradox using elementary particles have so far proved impossible.
We show that the interplay between the metamaterial properties of graphene multilayers and the pseudospinorial properties of the charge carriers result in the occurrence of klein and anti klein tunneling for rhombohedral stacked multilayers. Massless dirac fermions in graphene allow a close realization of kleins gedanken experiment, whereas. We conclude that, depending on the boundary condition, there is either a klein paradox that can be resolved by invoking a reservoir of occupied negative energy states that can be accessed, or no klein paradox if we assume that we have no such reservoir, since the boundary conditions on the side of the barrier depend on this choice. This demonstration shows the reflection and transmission coefficients for a dirac particle with spinup incident on a square barrier of variable height the energy of the particle is fixed at 1 unit but its mass is allowed to vary from 0 to. Fall 2008 department of physics and astronomy, the university of tennessee at knoxville, 37996. Klein paradox and resonant tunneling in a graphene superlattice. In one handy volume it offers comprehensive coverage of. Temperature behavior of graphene conductance induced by. Today, the availability of high mobility graphene up to room temperature makes ballistic transport in nanodevices achievable. Many experiments in electron transport in graphene rely on the klein paradox for massless particles.
In this book, leading graphene research theorist mikhail katsnelson presents the basic concepts of graphene physics. This monograph gives a wellbalanced overview on all areas of scientific interest surrounding this fascinating nanocarbon. Here we show that the effect can be tested in a conceptually simple condensedmatter experiment by using electrostatic barriers in single and bilayer graphene. Graphene is a material of particular interest for the implementation of sensors, and the ultimate performance of devices based on such a material is often determined by its flicker noise properties. The renewed interest in graphene 1 and the close analogy of its band structure to the spectrum of the zero mass dirac equation suggests that a reexamination of several aspects of the one dimensional dirac equation should be carried out. Conductance of pnp graphene structures with airbridge. Jun 11, 2008 we have fabricated graphene devices with a top gate separated from the graphene layer by an air gapa design which does not decrease the mobility of charge carriers under the gate. Teach yourself c begins with the fundamentals, covers all the essentials, and concludes with a look at some of cs most advanced features.
Massless dirac fermions in graphene allow a close realization of kleins gedanken experiment, whereas massive chiral fermions in bilayer. No significant macroscopp,ic defects, wrinkles from the cu foil pmma xpsraman analysis analysis i i 006 raman mapping n ts r2r clt pmma or other functional groups on graphene in pmma or r2r i ty d g 0. Evidence against klein paradox in graphene iopscience. The quantum hall effect in graphene also exhibits surprising features related to the dirac sea. Such tunneling from an electronlike to holelike state is called as interband tunneling or klein tunneling. Quantum confinement of electrons can also be used to control their motion.
We find that in the case of potential well, the bound states disappear from the spectrum for large enough potential depth. How does one confine charge carriers inside a device. Both these results can be identified as fine examples of the klein paradox. For dirac electrons the klein paradox implies that the confinement is difficult to achieve with an electrostatic potential although it can be of great importance for graphene based devices. We have fabricated graphene devices with a top gate separated from the graphene layer by an air gapa design which does not decrease the mobility of charge carriers under the gate. Number of manuscripts with graphene in the title posted on the preprint server. Chiral tunneling and the klein paradox in graphene arxiv. The book is devoted to understanding graphene fundamentally yet comprehensively through a wide range of issues in the areas of materials science, chemistry, physics, electronics and biology. For dirac electrons the klein paradox implies that the confinement is difficult to achieve with an electrostatic potential although it can be of great importance for graphenebased devices. Chiral tunnelling and the klein paradox in graphene condensed. In interpreting these numbers, one must, however, consider that several publi. Superklein tunneling refers to the omnidirectional total transmission of.
The vacuum charge and lifetime of the well are estimated. Introduction to the physical properties of graphene. Pdf klein paradox and resonant tunneling in a graphene. Solutions of the one dimensional dirac equation with piecewise constant potentials are presented using standard methods. This indicates a very peculiar type of klein paradox exhibited in dirac billiard and not observed in schrodinger billiard. The band profile of the structures is calculated taking into account the specifics of the graphene. Novoselov et al, science 306, 666 2004 a tem picture of a graphene sheet freely suspended on a micronsize metallic scaffold. In 1929, physicist oskar klein obtained a surprising result by applying the dirac equation to the. Many experiments in electron transport in graphene rely on the klein paradox for.
Apr 18, 2008 the freedom of motion associated with the klein paradox creates a problem. The term klein paradox 1,2,3,4,5,6,7 refers to a counterintuitive relativistic process in which an incoming electron starts penetrating through a potential barrier if its height, v 0, exceeds the. This gate is used to realize pnp structures where the conducting properties of chiral carriers are studied. A simple approach is to cut the graphene layer into the right shape, as for the quantum dot in the figure. It is shown that a potential well or barrier in the dirac equation can become supercritical and emit positrons. The socalled klein paradox unimpeded penetration of relativistic particles through high and wide potential barriers is one of the. Aug 20, 2006 the term klein paradox 1,2,3,4,5,6,7 refers to a counterintuitive relativistic process in which an incoming electron starts penetrating through a potential barrier if its height, v 0, exceeds the. Klein paradox for a pn junction in multilayer graphene core. These results were expanded to higher dimensions, and to other types of potentials, such as a linear step, a square barrier, a smooth potential, etc.
Pdf chiral tunneling and the klein paradox in graphene. Bowen s p 2008 1d dirac equation, klein paradox and graphene. These solutions show that the klein paradox is nonexistent and represents a failure to correctly match solutions across a step potential. Two dimensions needs a spinor treatment and is investi. The early papers by klein, sauter and hund which investigate scattering off a high step potential in the context of the dirac equation are discussed to derive the paradox first obtained by klein. A kleintunneling transistor with ballistic graphene iopscience. Since its discovery in 2004, graphene has been a great sensation due to its unique structure and unusual properties, and it has only taken 6 years for a noble prize to be awarded for the field of graphene research. Therefore, the chaotic klein paradox can be measured by the inversion of quantum antilocalization caused in a very special way by the timereversal symmetry breaking see fig. Dec 29, 2010 however, here we shall be dealing with electron transport at much lower energy and hence temperature. Graphene info is proud to present the graphene handbook. Massless dirac fermions in graphene allow a close realization of kleins gedanken experiment whereas.
Chiral tunnelling and the klein paradox in graphene nature. Grapheneinfo is proud to present the graphene handbook. If the well is wide enough, a seemingly constant current is emitted. Graphene, a single atomic layer of carbon hexagons, has stimulated a lot of research interest owing to its unique structure and fascinating properties. High quality cvd graphene of transferred by the clt technique 1 cl sem afm. In this paper, an analytical form of the realspace noninteracting green function of graphene material is developed. Because graphene is a solidstate testing ground for quantum electrodynamics phenomena involving massless dirac fermions we suggest that the transport characteristic through a pn graphene junction can decide between the results obtained in this paper and the common klein paradox theory, which imply negative transmission and higherthanunity. Pdf chiral tunnelling and the klein paradox in graphene. This theoretical work studies the temperature behavior of the graphene conductance changes induced by piezoelectric effect in a ferroelectric substrate with the domain structure. These phenomena are transient whereas the tunnelling first calculated by klein is timeindependent. Ii we turn to the underlying physics of the klein paradox and show that particle production and klein tunnelling arise naturally in the dirac equation.
Klein paradox in chaotic dirac billiards sciencedirect. The essential features of klein tunneling of massless fermions in graphene may be treated in one dimension without the need for dirac spinors. The explanation of this effect in terms of electronpositron production is reassessed. Localization of dirac electrons in rotated graphene bilayers. Jan 20, 2012 the essential features of klein tunneling of massless fermions in graphene may be treated in one dimension without the need for dirac spinors.
With the linear confining potential, we show that the dirac equation presents no bound state. Designer dirac fermions and topological phases in molecular. Klein paradox in the graphenebased doublebarrier structures. The rise of graphene ak geim and ks novoselov manchester. However, here we shall be dealing with electron transport at much lower energy and hence temperature. Graphene a new form of carbon with scientific impact and technological promise a graphic of the electron behaviour of graphene in a magnetic field as mapped with an electron microscope a visual representation of the unusual energymomentum relationship of the charge carriers in graphene, which gives rise to its unusual quantum behaviour. Klein paradox refers to a counterintuitive process of perfect tunnelling of.
Contents the klein paradox role of chirality klein tunneling in singlelayer graphene klein tunneling and conductivity klein tunneling in bilayer graphene. Superklein tunneling of kleingordon particles sciencedirect. Diraclike quasiparticles ingraphene graphene is a single layer of carbon atoms densely packed in a. Applications to graphene systems are also discussed. We also discuss the socalled klein paradox that can actually be seen, doing away with its paradoxical status forever. Indeed, graphene exhibits, with respect to the vast majority of ordinary semiconductors, a peculiar behavior of the flicker noise power spectral density as a function of the charge carrier density. Theoretical comparison between the flicker noise behavior of. Chiral tunnelling and the klein paradox in graphene. Sem of a relatively large graphene crystal fabrication of graphene. This element is unique in that its unique electronic structure allows for hybridization to build up sp3,sp2, and sp networks and, hence, to form more known stable allotropes than any. What we see is that the negative energy solutions of the dirac equation become accessible on the barrier side thus allowing both reflection and transmissi. Here, ab initio and tightbinding approaches are combined and show that the wave function of dirac electrons can be localized in rotated graphene bilayers. An algebraic blockdiagonalization of the dirac hamiltonian in a timeindependent external field reveals a chargeindex conservation law which forbids the physical phenomena of the klein paradox type and guarantees a singleparticle nature of the dirac equation in strong external fields. The change in graphene conductance caused by the piezoelectric effect requires systematic studies of ambient conditions impact on its manifestations.
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